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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 157170.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
157170.j1 | 157170cy1 | \([1, 1, 0, -3895622, 2973232956]\) | \(-1354547383894636849/8173828125000\) | \(-39453507158203125000\) | \([]\) | \(8985600\) | \(2.5997\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 157170.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 157170.j do not have complex multiplication.Modular form 157170.2.a.j
sage: E.q_eigenform(10)