Properties

Label 129360.ct
Number of curves $4$
Conductor $129360$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ct1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 129360.ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
129360.ct1 129360bj4 \([0, -1, 0, -1459040, 678717600]\) \(1425631925916578/270703125\) \(65224605600000000\) \([4]\) \(1572864\) \(2.2275\)  
129360.ct2 129360bj3 \([0, -1, 0, -639760, -190512608]\) \(120186986927618/4332064275\) \(1043789885213644800\) \([2]\) \(1572864\) \(2.2275\)  
129360.ct3 129360bj2 \([0, -1, 0, -100760, 8270592]\) \(939083699236/300155625\) \(36160521344640000\) \([2, 2]\) \(786432\) \(1.8809\)  
129360.ct4 129360bj1 \([0, -1, 0, 17820, 871200]\) \(20777545136/23059575\) \(-694511600428800\) \([2]\) \(393216\) \(1.5344\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 129360.ct have rank \(1\).

Complex multiplication

The elliptic curves in class 129360.ct do not have complex multiplication.

Modular form 129360.2.a.ct

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} - q^{11} + 2 q^{13} - q^{15} + 2 q^{17} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.