Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1670.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1670.a1 | 1670a1 | \([1, 1, 0, -38, -1132]\) | \(-6321363049/534400000\) | \(-534400000\) | \([]\) | \(1000\) | \(0.35435\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1670.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 1670.a do not have complex multiplication.Modular form 1670.2.a.a
sage: E.q_eigenform(10)