Properties

Label 53130k
Number of curves $1$
Conductor $53130$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 53130k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53130.k1 53130k1 \([1, 1, 0, 23182, 8829108]\) \(1377676163129481431/34399384177213440\) \(-34399384177213440\) \([]\) \(705600\) \(1.8532\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 53130k1 has rank \(0\).

Complex multiplication

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

Modular form 53130.2.a.k

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