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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 10766e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10766.f1 | 10766e1 | \([1, 1, 1, -147, 625]\) | \(-351447414193/172256\) | \(-172256\) | \([]\) | \(2320\) | \(-0.041537\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 10766e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 10766e do not have complex multiplication.Modular form 10766.2.a.e
sage: E.q_eigenform(10)