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SageMath
E = EllipticCurve("et1")
E.isogeny_class()
Elliptic curves in class 226512.et
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
226512.et1 | 226512cl1 | \([0, 0, 0, -20635824, -36088776592]\) | \(-1518309117952/369603\) | \(-236572601242841690112\) | \([]\) | \(11827200\) | \(2.8979\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 226512.et1 has rank \(1\).
Complex multiplication
The elliptic curves in class 226512.et do not have complex multiplication.Modular form 226512.2.a.et
sage: E.q_eigenform(10)