Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 435344k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435344.k1 | 435344k1 | \([0, 1, 0, -39798825577, 3055987513005987]\) | \(5642017163771722268092767232/570626054098424597\) | \(705101561230531259038969088\) | \([]\) | \(798336000\) | \(4.5826\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 435344k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 435344k do not have complex multiplication.Modular form 435344.2.a.k
sage: E.q_eigenform(10)