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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 489762.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
489762.p1 | 489762p1 | \([1, -1, 0, 179622, 176349460]\) | \(5202195898618823/112114092318816\) | \(-13812568287770450016\) | \([]\) | \(10321920\) | \(2.3530\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 489762.p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 489762.p do not have complex multiplication.Modular form 489762.2.a.p
sage: E.q_eigenform(10)