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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 117117.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
117117.i1 | 117117bz1 | \([0, 0, 1, 66417, 42185146]\) | \(9208180736/223810587\) | \(-787532106651997707\) | \([]\) | \(3193344\) | \(2.1142\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 117117.i1 has rank \(0\).
Complex multiplication
The elliptic curves in class 117117.i do not have complex multiplication.Modular form 117117.2.a.i
sage: E.q_eigenform(10)