Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 31478.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
31478.a1 | 31478b1 | \([1, 0, 1, -5, 12]\) | \(-10218313/62956\) | \(-62956\) | \([]\) | \(5536\) | \(-0.39551\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 31478.a1 has rank \(3\).
Complex multiplication
The elliptic curves in class 31478.a do not have complex multiplication.Modular form 31478.2.a.a
sage: E.q_eigenform(10)