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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 714c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
714.c1 | 714c1 | \([1, 1, 0, -14597, -686643]\) | \(-344002044213921241/1011143540736\) | \(-1011143540736\) | \([]\) | \(2040\) | \(1.1738\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 714c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 714c do not have complex multiplication.Modular form 714.2.a.c
sage: E.q_eigenform(10)