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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 422370.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
422370.j1 | 422370j1 | \([1, -1, 0, -161541630, 1027388855700]\) | \(-1771504931165862139195321/707368735840665600000\) | \(-186157522842452125286400000\) | \([]\) | \(136857600\) | \(3.7495\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 422370.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 422370.j do not have complex multiplication.Modular form 422370.2.a.j
sage: E.q_eigenform(10)