Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 191466.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 191466.k1 | 191466c1 | \([1, -1, 1, -116599775, -485624236089]\) | \(-240485733454722137254419625/598436911327003803648\) | \(-436260508357385772859392\) | \([]\) | \(45782784\) | \(3.4137\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 191466.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 191466.k do not have complex multiplication.Modular form 191466.2.a.k
sage: E.q_eigenform(10)