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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 85176.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 85176.k1 | 85176cf1 | \([0, 0, 0, -487134219, 4630758698774]\) | \(-20994006260678308/3063651608241\) | \(-1865579153429997879207699456\) | \([]\) | \(47923200\) | \(3.9631\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 85176.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 85176.k do not have complex multiplication.Modular form 85176.2.a.k
sage: E.q_eigenform(10)