Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 35322.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35322.k1 | 35322e1 | \([1, 1, 0, -35339, 2558343]\) | \(-8205738913/59682\) | \(-35500245443922\) | \([]\) | \(181440\) | \(1.4319\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 35322.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 35322.k do not have complex multiplication.Modular form 35322.2.a.k
sage: E.q_eigenform(10)