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SageMath
E = EllipticCurve("fn1")
E.isogeny_class()
Elliptic curves in class 291312.fn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
291312.fn1 | 291312fn1 | \([0, 0, 0, 261069, 21942002]\) | \(2280364702703/1560674304\) | \(-1346782916776034304\) | \([]\) | \(4700160\) | \(2.1673\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 291312.fn1 has rank \(0\).
Complex multiplication
The elliptic curves in class 291312.fn do not have complex multiplication.Modular form 291312.2.a.fn
sage: E.q_eigenform(10)