Properties

Label 53130q
Number of curves $1$
Conductor $53130$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 53130q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53130.q1 53130q1 \([1, 1, 0, -12201317, 16399907469]\) \(-200883330249962433079106521/9528985042500000000\) \(-9528985042500000000\) \([]\) \(2726400\) \(2.7155\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 53130q1 has rank \(1\).

Complex multiplication

The elliptic curves in class 53130q do not have complex multiplication.

Modular form 53130.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + q^{7} - q^{8} + q^{9} - q^{10} + q^{11} - q^{12} - 3 q^{13} - q^{14} - q^{15} + q^{16} - 3 q^{17} - q^{18} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display