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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 12992.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12992.i1 | 12992y1 | \([0, -1, 0, -1, 929]\) | \(-1/1421\) | \(-372506624\) | \([]\) | \(4096\) | \(0.32353\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12992.i1 has rank \(2\).
Complex multiplication
The elliptic curves in class 12992.i do not have complex multiplication.Modular form 12992.2.a.i
sage: E.q_eigenform(10)