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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 40310f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40310.l1 | 40310f1 | \([1, 0, 1, -3548, 81178]\) | \(-4937402992298041/10319360000\) | \(-10319360000\) | \([]\) | \(41472\) | \(0.80695\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 40310f1 has rank \(2\).
Complex multiplication
The elliptic curves in class 40310f do not have complex multiplication.Modular form 40310.2.a.f
sage: E.q_eigenform(10)