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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 414736c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
414736.c1 | 414736c1 | \([0, 0, 0, 633120425, 155311577884981]\) | \(100718081964000000/37453512751940327\) | \(-10436810428354359504417152995952\) | \([]\) | \(1240842240\) | \(4.6310\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 414736c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 414736c do not have complex multiplication.Modular form 414736.2.a.c
sage: E.q_eigenform(10)