Properties

Label 344760cc
Number of curves $4$
Conductor $344760$
CM no
Rank $0$
Graph

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

Elliptic curves in class 344760cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
344760.cc3 344760cc1 \([0, 1, 0, -5295671, 4688836530]\) \(212670222886967296/616241925\) \(47591713116277200\) \([4]\) \(8257536\) \(2.4302\) \(\Gamma_0(N)\)-optimal
344760.cc2 344760cc2 \([0, 1, 0, -5364116, 4561337184]\) \(13813960087661776/714574355625\) \(882973166310387360000\) \([2, 2]\) \(16515072\) \(2.7768\)  
344760.cc4 344760cc3 \([0, 1, 0, 3427264, 18057863760]\) \(900753985478876/29018422265625\) \(-143427974919699600000000\) \([2]\) \(33030144\) \(3.1233\)  
344760.cc1 344760cc4 \([0, 1, 0, -15250616, -17094052416]\) \(79364416584061444/20404090514925\) \(100850327279876735308800\) \([2]\) \(33030144\) \(3.1233\)  

Rank

sage: E.rank()
 

The elliptic curves in class 344760cc have rank \(0\).

Complex multiplication

The elliptic curves in class 344760cc do not have complex multiplication.

Modular form 344760.2.a.cc

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + 4q^{7} + q^{9} - q^{15} + q^{17} + O(q^{20})\)  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.