Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 16744b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16744.k1 | 16744b1 | \([0, -1, 0, -317073, -68614891]\) | \(13770918300093568000/31622653517\) | \(8095399300352\) | \([]\) | \(81600\) | \(1.7204\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 16744b1 has rank \(0\).
Complex multiplication
The elliptic curves in class 16744b do not have complex multiplication.Modular form 16744.2.a.b
sage: E.q_eigenform(10)