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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 12696.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12696.e1 | 12696f1 | \([0, -1, 0, -9169, -334955]\) | \(-1190106112/243\) | \(-17408348928\) | \([]\) | \(21120\) | \(0.96245\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12696.e1 has rank \(0\).
Complex multiplication
The elliptic curves in class 12696.e do not have complex multiplication.Modular form 12696.2.a.e
sage: E.q_eigenform(10)