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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 2031.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2031.c1 | 2031b1 | \([0, -1, 1, -201848, 29995379]\) | \(909492695602190848000/139388296428077373\) | \(139388296428077373\) | \([]\) | \(24960\) | \(2.0133\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 2031.c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 2031.c do not have complex multiplication.Modular form 2031.2.a.c
sage: E.q_eigenform(10)