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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1850.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1850.c1 | 1850c1 | \([1, 1, 0, -75, -1625]\) | \(-121945/2738\) | \(-1069531250\) | \([]\) | \(960\) | \(0.41332\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1850.c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 1850.c do not have complex multiplication.Modular form 1850.2.a.c
sage: E.q_eigenform(10)