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SageMath
E = EllipticCurve("fn1")
E.isogeny_class()
Elliptic curves in class 340032.fn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
340032.fn1 | 340032fn1 | \([0, 1, 0, -7425, -2440449]\) | \(-172715635009/9694992384\) | \(-2541484083511296\) | \([]\) | \(1351680\) | \(1.6358\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 340032.fn1 has rank \(1\).
Complex multiplication
The elliptic curves in class 340032.fn do not have complex multiplication.Modular form 340032.2.a.fn
sage: E.q_eigenform(10)