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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 76050cn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76050.bc1 | 76050cn1 | \([1, -1, 0, 75258, -76785084]\) | \(34295/1872\) | \(-2573081375231250000\) | \([]\) | \(1290240\) | \(2.2123\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 76050cn1 has rank \(1\).
Complex multiplication
The elliptic curves in class 76050cn do not have complex multiplication.Modular form 76050.2.a.cn
sage: E.q_eigenform(10)