Properties

Label 53130h
Number of curves $2$
Conductor $53130$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 53130h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53130.h1 53130h1 \([1, 1, 0, -468250148, 3584540196252]\) \(11354224670262535781399662607689/1019390529976200592619062500\) \(1019390529976200592619062500\) \([2]\) \(33868800\) \(3.9221\) \(\Gamma_0(N)\)-optimal
53130.h2 53130h2 \([1, 1, 0, 528236882, 16794171563338]\) \(16300835816496943562017955390231/131273254164601244421386718750\) \(-131273254164601244421386718750\) \([2]\) \(67737600\) \(4.2687\)  

Rank

sage: E.rank()
 

The elliptic curves in class 53130h have rank \(0\).

Complex multiplication

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

Modular form 53130.2.a.h

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

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.