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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 117740.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
117740.a1 | 117740c1 | \([0, 0, 0, 26912, 5170468]\) | \(14155776/84035\) | \(-12796410311740160\) | \([]\) | \(1375920\) | \(1.7726\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 117740.a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 117740.a do not have complex multiplication.Modular form 117740.2.a.a
sage: E.q_eigenform(10)