Properties

Label 310464cg
Number of curves $4$
Conductor $310464$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 310464cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
310464.cg3 310464cg1 \([0, 0, 0, -1035419196, 12823968186736]\) \(87364831012240243408/1760913\) \(2474421082988101632\) \([2]\) \(70778880\) \(3.5128\) \(\Gamma_0(N)\)-optimal
310464.cg2 310464cg2 \([0, 0, 0, -1035454476, 12823050582160]\) \(21843440425782779332/3100814593569\) \(17428961010031308036440064\) \([2, 2]\) \(141557760\) \(3.8594\)  
310464.cg4 310464cg3 \([0, 0, 0, -942103596, 15229076163280]\) \(-8226100326647904626/4152140742401883\) \(-46676443833548108989181853696\) \([2]\) \(283115520\) \(4.2060\)  
310464.cg1 310464cg4 \([0, 0, 0, -1129369836, 10358298308176]\) \(14171198121996897746/4077720290568771\) \(45839843569837850284168445952\) \([2]\) \(283115520\) \(4.2060\)  

Rank

sage: E.rank()
 

The elliptic curves in class 310464cg have rank \(0\).

Complex multiplication

The elliptic curves in class 310464cg do not have complex multiplication.

Modular form 310464.2.a.cg

sage: E.q_eigenform(10)
 
\(q - 2q^{5} - q^{11} - 6q^{13} - 2q^{17} + 8q^{19} + O(q^{20})\)  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 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.