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SageMath
E = EllipticCurve("et1")
E.isogeny_class()
Elliptic curves in class 40950.et
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40950.et1 | 40950ek1 | \([1, -1, 1, -22608905, 41620153097]\) | \(-112205650221491190337/745029571313664\) | \(-8486352460744704000000\) | \([]\) | \(4112640\) | \(3.0433\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 40950.et1 has rank \(1\).
Complex multiplication
The elliptic curves in class 40950.et do not have complex multiplication.Modular form 40950.2.a.et
sage: E.q_eigenform(10)