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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 53361.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53361.e1 | 53361bz1 | \([0, 0, 1, 12705, -2000826]\) | \(3584000/29403\) | \(-1860678601932843\) | \([]\) | \(345600\) | \(1.6114\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 53361.e1 has rank \(0\).
Complex multiplication
The elliptic curves in class 53361.e do not have complex multiplication.Modular form 53361.2.a.e
sage: E.q_eigenform(10)