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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 444675a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 444675.a1 | 444675a1 | \([0, -1, 1, -103806908, -405661017532]\) | \(313944395776/1240029\) | \(488631644729457692203125\) | \([]\) | \(156119040\) | \(3.4027\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 444675a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 444675a do not have complex multiplication.Modular form 444675.2.a.a
sage: E.q_eigenform(10)