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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 4704.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4704.i1 | 4704d1 | \([0, -1, 0, -32013, 2231685]\) | \(-3136000/27\) | \(-31239502737408\) | \([]\) | \(12096\) | \(1.4144\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4704.i1 has rank \(0\).
Complex multiplication
The elliptic curves in class 4704.i do not have complex multiplication.Modular form 4704.2.a.i
sage: E.q_eigenform(10)