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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 77658.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
77658.f1 | 77658l1 | \([1, 1, 0, -7735, 258709]\) | \(-27685698258625/7838208\) | \(-14492846592\) | \([]\) | \(105840\) | \(0.93067\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 77658.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 77658.f do not have complex multiplication.Modular form 77658.2.a.f
sage: E.q_eigenform(10)