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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 67830s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67830.p1 | 67830s1 | \([1, 0, 1, 86849626, 4484452919672]\) | \(72448196218150707243102543911/8729555368583338109588880000\) | \(-8729555368583338109588880000\) | \([]\) | \(64995840\) | \(4.0407\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 67830s1 has rank \(1\).
Complex multiplication
The elliptic curves in class 67830s do not have complex multiplication.Modular form 67830.2.a.s
sage: E.q_eigenform(10)