Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 43681.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43681.k1 | 43681d1 | \([1, -1, 0, -10841078, -12459109107]\) | \(9747\) | \(14456733525949878687491\) | \([]\) | \(2708640\) | \(2.9877\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 43681.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 43681.k do not have complex multiplication.Modular form 43681.2.a.k
sage: E.q_eigenform(10)