Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 100008.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100008.a1 | 100008b1 | \([0, 0, 0, -459, -5994]\) | \(-530604/463\) | \(-9331946496\) | \([]\) | \(65088\) | \(0.61035\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 100008.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 100008.a do not have complex multiplication.Modular form 100008.2.a.a
sage: E.q_eigenform(10)