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SageMath
E = EllipticCurve("fc1")
E.isogeny_class()
Elliptic curves in class 130050fc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
130050.bj1 | 130050fc1 | \([1, -1, 0, -3155067, -5108673659]\) | \(-43713001/116640\) | \(-9268008775506202500000\) | \([]\) | \(7050240\) | \(2.9026\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 130050fc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 130050fc do not have complex multiplication.Modular form 130050.2.a.fc
sage: E.q_eigenform(10)