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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 27200f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27200.z1 | 27200f1 | \([0, -1, 0, -193, 1217]\) | \(-121945/17\) | \(-111411200\) | \([]\) | \(6144\) | \(0.27553\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 27200f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 27200f do not have complex multiplication.Modular form 27200.2.a.f
sage: E.q_eigenform(10)