Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 100020.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100020.a1 | 100020a1 | \([0, -1, 0, -20, -120]\) | \(-3631696/25005\) | \(-6401280\) | \([]\) | \(26400\) | \(-0.010722\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 100020.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 100020.a do not have complex multiplication.Modular form 100020.2.a.a
sage: E.q_eigenform(10)