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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 208725j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
208725.a1 | 208725j1 | \([0, -1, 1, -303508, -73046832]\) | \(-111701610496/18862875\) | \(-522136464029296875\) | \([]\) | \(6451200\) | \(2.1265\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 208725j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 208725j do not have complex multiplication.Modular form 208725.2.a.j
sage: E.q_eigenform(10)