passagemath-eclib

============================================================================================== passagemath: Elliptic curves over the rationals with eclib/mwrank

About SageMath

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SageMath fully supports all major Linux distributions, recent versions of macOS, and Windows (Windows Subsystem for Linux).

See https://doc.sagemath.org/html/en/installation/index.html for general installation instructions.

About this pip-installable distribution

This pip-installable distribution passagemath-eclib provides the Cython interface to John Cremona's programs for enumerating and computing with elliptic curves defined over the rational numbers.

What is included

• Sage interface to Cremona’s eclib library (also known as mwrank) <https://doc.sagemath.org/html/en/reference/libs/sage/libs/eclib/interface.html>_

• Cython interface to Cremona’s eclib library (also known as mwrank) <https://doc.sagemath.org/html/en/reference/libs/sage/libs/eclib/mwrank.html>_

• Cremona matrices <https://doc.sagemath.org/html/en/reference/libs/sage/libs/eclib/mat.html>_

• Modular symbols using eclib newforms <https://doc.sagemath.org/html/en/reference/libs/sage/libs/eclib/newforms.html>_

• Cremona modular symbols <https://doc.sagemath.org/html/en/reference/libs/sage/libs/eclib/homspace.html>_

• Cremona modular symbols (constructor) <https://doc.sagemath.org/html/en/reference/libs/sage/libs/eclib/constructor.html>_

• Interface to the mwrank program <https://doc.sagemath.org/html/en/reference/interfaces/sage/interfaces/mwrank.html#module-sage.interfaces.mwrank>_

Examples

A quick way to try it out interactively::

$ pipx run --pip-args="--prefer-binary" --spec "passagemath-eclib[test]" ipython

In [1]: from sage.all__sagemath_eclib import *

In [2]: M = CremonaModularSymbols(43, cuspidal=True); M
Out[2]: Cremona Cuspidal Modular Symbols space of dimension 6 for Gamma_0(43) of weight 2 with sign 0

Finding the installation location of the mwrank program::

$ pipx run --pip-args="--prefer-binary" --spec "passagemath-eclib" python
>>> from sage.features.eclib import Mwrank
>>> Mwrank().absolute_filename()
'/Users/mkoeppe/.local/pipx/.cache/6c494549ef80bf7/lib/python3.11/site-packages/sage_wheels/bin/mwrank'

Use with sage.schemes.elliptic_curves <https://doc.sagemath.org/html/en/reference/arithmetic_curves/index.html#elliptic-curves>_::

$ pipx run --pip-args="--prefer-binary" --spec "passagemath-eclib[test]" ipython

In [1]: from sage.all__sagemath_eclib import *

In [2]: x = polygen(ZZ, 'x')

In [3]: K = NumberField(x**2 + 23, 'a'); a = K.gen()

In [4]: E = EllipticCurve(K, [0,0,0,101,0])

In [5]: E.gens()

Development

::

$ git clone --origin passagemath https://github.com/passagemath/passagemath.git
$ cd passagemath
passagemath $ ./bootstrap
passagemath $ python3 -m venv eclib-venv
passagemath $ source eclib-venv/bin/activate
(eclib-venv) passagemath $ pip install -v -e pkgs/sagemath-eclib