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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 123627.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
123627.a1 | 123627m1 | \([0, -1, 1, -673080, 2979633152]\) | \(-200704/22707\) | \(-3815295211687913161803\) | \([]\) | \(14817600\) | \(2.8206\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 123627.a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 123627.a do not have complex multiplication.Modular form 123627.2.a.a
sage: E.q_eigenform(10)