Properties

Label 130130r
Number of curves $1$
Conductor $130130$
CM no
Rank $1$

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

Elliptic curves in class 130130r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
130130.r1 130130r1 \([1, 1, 0, -577307, -256515059]\) \(-26085462395161/19685702960\) \(-16058232668952634160\) \([]\) \(3594240\) \(2.3843\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 130130r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 130130r do not have complex multiplication.

Modular form 130130.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{7} - q^{8} - 2 q^{9} - q^{10} + q^{11} - q^{12} + q^{14} - q^{15} + q^{16} + 3 q^{17} + 2 q^{18} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display