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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 4704.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4704.x1 | 4704m1 | \([0, 1, 0, -32013, -2231685]\) | \(-3136000/27\) | \(-31239502737408\) | \([]\) | \(12096\) | \(1.4144\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4704.x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4704.x do not have complex multiplication.Modular form 4704.2.a.x
sage: E.q_eigenform(10)