Properties

Label 259182.r
Number of curves $1$
Conductor $259182$
CM no
Rank $2$

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

Elliptic curves in class 259182.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259182.r1 259182r1 \([1, -1, 0, -905163, 452716919]\) \(-19438895619/9714446\) \(-40987441727510428458\) \([]\) \(11404800\) \(2.4684\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 259182.r1 has rank \(2\).

Complex multiplication

The elliptic curves in class 259182.r do not have complex multiplication.

Modular form 259182.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 2 q^{5} - q^{7} - q^{8} + 2 q^{10} - 7 q^{13} + q^{14} + q^{16} - q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display