Properties

Label 92400.ct
Number of curves $4$
Conductor $92400$
CM no
Rank $0$
Graph

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

Elliptic curves in class 92400.ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.ct1 92400t4 \([0, -1, 0, -16005808, 17481678112]\) \(14171198121996897746/4077720290568771\) \(130487049298200672000000\) \([2]\) \(11796480\) \(3.1419\)  
92400.ct2 92400t2 \([0, -1, 0, -14674808, 21639722112]\) \(21843440425782779332/3100814593569\) \(49613033497104000000\) \([2, 2]\) \(5898240\) \(2.7953\)  
92400.ct3 92400t1 \([0, -1, 0, -14674308, 21641270112]\) \(87364831012240243408/1760913\) \(7043652000000\) \([2]\) \(2949120\) \(2.4487\) \(\Gamma_0(N)\)-optimal
92400.ct4 92400t3 \([0, -1, 0, -13351808, 25698686112]\) \(-8226100326647904626/4152140742401883\) \(-132868503756860256000000\) \([2]\) \(11796480\) \(3.1419\)  

Rank

sage: E.rank()
 

The elliptic curves in class 92400.ct have rank \(0\).

Complex multiplication

The elliptic curves in class 92400.ct do not have complex multiplication.

Modular form 92400.2.a.ct

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} - q^{11} + 6q^{13} + 2q^{17} + 8q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.