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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 254512c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
254512.c1 | 254512c1 | \([0, -1, 0, 40, -784]\) | \(1685159/63628\) | \(-260620288\) | \([]\) | \(139392\) | \(0.29477\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 254512c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 254512c do not have complex multiplication.Modular form 254512.2.a.c
sage: E.q_eigenform(10)