Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 85176.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 85176.j1 | 85176w1 | \([0, 0, 0, -168647715444, -26657996713441756]\) | \(-588894491652244161881463808/13658611812026920011\) | \(-12303655704957601165504589150976\) | \([]\) | \(596090880\) | \(5.0783\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 85176.j1 has rank \(0\).
Complex multiplication
The elliptic curves in class 85176.j do not have complex multiplication.Modular form 85176.2.a.j
sage: E.q_eigenform(10)