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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 51870.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51870.c1 | 51870c1 | \([1, 1, 0, -13188, -1978032]\) | \(-253695042842616649/1534055250000000\) | \(-1534055250000000\) | \([]\) | \(290304\) | \(1.5976\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 51870.c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 51870.c do not have complex multiplication.Modular form 51870.2.a.c
sage: E.q_eigenform(10)