Properties

Label 2352.s
Number of curves $4$
Conductor $2352$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 2352.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2352.s1 2352t4 \([0, 1, 0, -89588, -10350936]\) \(2640279346000/3087\) \(92974710528\) \([2]\) \(6912\) \(1.3878\)  
2352.s2 2352t3 \([0, 1, 0, -5553, -165894]\) \(-10061824000/352947\) \(-664381785648\) \([2]\) \(3456\) \(1.0412\)  
2352.s3 2352t2 \([0, 1, 0, -1388, -6840]\) \(9826000/5103\) \(153692888832\) \([2]\) \(2304\) \(0.83846\)  
2352.s4 2352t1 \([0, 1, 0, 327, -666]\) \(2048000/1323\) \(-2490394032\) \([2]\) \(1152\) \(0.49188\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2352.s have rank \(0\).

Complex multiplication

The elliptic curves in class 2352.s do not have complex multiplication.

Modular form 2352.2.a.s

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.