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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 5712.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5712.i1 | 5712o1 | \([0, -1, 0, 315, 1389]\) | \(841232384/722211\) | \(-2958176256\) | \([]\) | \(1920\) | \(0.50490\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5712.i1 has rank \(1\).
Complex multiplication
The elliptic curves in class 5712.i do not have complex multiplication.Modular form 5712.2.a.i
sage: E.q_eigenform(10)