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SageMath
E = EllipticCurve("fr1")
E.isogeny_class()
Elliptic curves in class 121968.fr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
121968.fr1 | 121968gg1 | \([0, 0, 0, 429, 18898]\) | \(24167/441\) | \(-159335092224\) | \([]\) | \(147456\) | \(0.82997\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 121968.fr1 has rank \(1\).
Complex multiplication
The elliptic curves in class 121968.fr do not have complex multiplication.Modular form 121968.2.a.fr
sage: E.q_eigenform(10)