Properties

Label 2352o
Number of curves $6$
Conductor $2352$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("2352.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2352o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2352.l5 2352o1 [0, -1, 0, -3152, 151488] [2] 4608 \(\Gamma_0(N)\)-optimal
2352.l4 2352o2 [0, -1, 0, -65872, 6523840] [2, 2] 9216  
2352.l3 2352o3 [0, -1, 0, -81552, 3199680] [2, 2] 18432  
2352.l1 2352o4 [0, -1, 0, -1053712, 416675008] [4] 18432  
2352.l2 2352o5 [0, -1, 0, -716592, -231003072] [2] 36864  
2352.l6 2352o6 [0, -1, 0, 302608, 24405312] [2] 36864  

Rank

sage: E.rank()
 

The elliptic curves in class 2352o have rank \(1\).

Modular form 2352.2.a.l

sage: E.q_eigenform(10)
 
\( q - q^{3} + 2q^{5} + q^{9} + 4q^{11} - 6q^{13} - 2q^{15} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.