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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1078.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1078.a1 | 1078b1 | \([1, -1, 0, -30634, -2056076]\) | \(551516475321/5632\) | \(32467359232\) | \([]\) | \(6048\) | \(1.1752\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1078.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 1078.a do not have complex multiplication.Modular form 1078.2.a.a
sage: E.q_eigenform(10)