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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 117208e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
117208.f1 | 117208e1 | \([0, -1, 0, -53769, -7207283]\) | \(-570820369408/418447211\) | \(-12602853357296384\) | \([]\) | \(675840\) | \(1.7889\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 117208e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 117208e do not have complex multiplication.Modular form 117208.2.a.e
sage: E.q_eigenform(10)