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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 53312cn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53312.b1 | 53312cn1 | \([0, 0, 0, -4792396, 14555399824]\) | \(-164384733177/1140850688\) | \(-84479071266962489212928\) | \([]\) | \(8386560\) | \(3.0825\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 53312cn1 has rank \(0\).
Complex multiplication
The elliptic curves in class 53312cn do not have complex multiplication.Modular form 53312.2.a.cn
sage: E.q_eigenform(10)