Properties

Label 286110.r
Number of curves $1$
Conductor $286110$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 286110.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
286110.r1 286110r1 \([1, -1, 0, -209604240, 2566765481800]\) \(-11780292753143153/26103515625000\) \(-2256663595077682119140625000\) \([]\) \(142571520\) \(3.9373\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 286110.r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 286110.r do not have complex multiplication.

Modular form 286110.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} + q^{11} - 6 q^{13} + q^{14} + q^{16} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display