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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 58870.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58870.j1 | 58870h1 | \([1, 1, 0, -197652, 753942224]\) | \(-1707052201/490000000\) | \(-245120742350890000000\) | \([]\) | \(2728320\) | \(2.5916\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 58870.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 58870.j do not have complex multiplication.Modular form 58870.2.a.j
sage: E.q_eigenform(10)