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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 83490j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
83490.n1 | 83490j1 | \([1, 1, 0, -12707, 555141]\) | \(-128100283921/2459160\) | \(-4356551948760\) | \([]\) | \(201600\) | \(1.2193\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 83490j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 83490j do not have complex multiplication.Modular form 83490.2.a.j
sage: E.q_eigenform(10)