Properties

Label 92400cc
Number of curves $4$
Conductor $92400$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.fo3 92400cc1 \([0, 1, 0, -1783, -25312]\) \(2508888064/396165\) \(99041250000\) \([2]\) \(73728\) \(0.83266\) \(\Gamma_0(N)\)-optimal
92400.fo2 92400cc2 \([0, 1, 0, -7908, 244188]\) \(13674725584/1334025\) \(5336100000000\) \([2, 2]\) \(147456\) \(1.1792\)  
92400.fo4 92400cc3 \([0, 1, 0, 9592, 1189188]\) \(6099383804/41507235\) \(-664115760000000\) \([4]\) \(294912\) \(1.5258\)  
92400.fo1 92400cc4 \([0, 1, 0, -123408, 16645188]\) \(12990838708516/144375\) \(2310000000000\) \([2]\) \(294912\) \(1.5258\)  

Rank

sage: E.rank()
 

The elliptic curves in class 92400cc have rank \(1\).

Complex multiplication

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

Modular form 92400.2.a.cc

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