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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 12870.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12870.j1 | 12870d1 | \([1, -1, 0, 0, 416]\) | \(-27/2768480\) | \(-74748960\) | \([]\) | \(4800\) | \(0.18969\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12870.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 12870.j do not have complex multiplication.Modular form 12870.2.a.j
sage: E.q_eigenform(10)