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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 493040.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
493040.f1 | 493040f1 | \([0, -1, 0, -261, -1939]\) | \(-481890304/154075\) | \(-631091200\) | \([]\) | \(323840\) | \(0.40148\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 493040.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 493040.f do not have complex multiplication.Modular form 493040.2.a.f
sage: E.q_eigenform(10)