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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 61347.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61347.r1 | 61347b1 | \([0, -1, 1, -33318237, -74018632777]\) | \(-2830523957248/264627\) | \(-382416905392781560587\) | \([]\) | \(3669120\) | \(2.9872\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 61347.r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 61347.r do not have complex multiplication.Modular form 61347.2.a.r
sage: E.q_eigenform(10)