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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 116242.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116242.x1 | 116242q1 | \([1, 0, 0, -409697644, -3187118709488]\) | \(23568486981643074043/40748749519744\) | \(13149120169899323265448576\) | \([]\) | \(38814720\) | \(3.7139\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 116242.x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 116242.x do not have complex multiplication.Modular form 116242.2.a.x
sage: E.q_eigenform(10)