Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1001.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1001.a1 | 1001c1 | \([0, 0, 1, -199, 1092]\) | \(-871531204608/11022011\) | \(-11022011\) | \([]\) | \(1008\) | \(0.16110\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1001.a1 has rank \(2\).
Complex multiplication
The elliptic curves in class 1001.a do not have complex multiplication.Modular form 1001.2.a.a
sage: E.q_eigenform(10)