Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 61347.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 61347.k1 | 61347h1 | \([0, -1, 1, -8059714329, 278504219221139]\) | \(-462482914449031168/3326427\) | \(-416452009972739119479243\) | \([]\) | \(57480192\) | \(4.1290\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 61347.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 61347.k do not have complex multiplication.Modular form 61347.2.a.k
sage: E.q_eigenform(10)