Properties

Label 259920.r
Number of curves $1$
Conductor $259920$
CM no
Rank $2$

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

Elliptic curves in class 259920.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259920.r1 259920r1 \([0, 0, 0, -1083, 130682]\) \(-1444/75\) \(-7296307891200\) \([]\) \(460800\) \(1.1481\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 259920.r1 has rank \(2\).

Complex multiplication

The elliptic curves in class 259920.r do not have complex multiplication.

Modular form 259920.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{5} - 3 q^{7} - 2 q^{11} + q^{13} + 4 q^{17} + O(q^{20})\) Copy content Toggle raw display