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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 4900j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4900.r1 | 4900j1 | \([0, -1, 0, -2858, -58183]\) | \(-160000\) | \(-16141442800\) | \([]\) | \(4032\) | \(0.79680\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4900j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4900j do not have complex multiplication.Modular form 4900.2.a.j
sage: E.q_eigenform(10)