Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("2352.s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2352.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2352.s1 2352t4 [0, 1, 0, -89588, -10350936] [2] 6912  
2352.s2 2352t3 [0, 1, 0, -5553, -165894] [2] 3456  
2352.s3 2352t2 [0, 1, 0, -1388, -6840] [2] 2304  
2352.s4 2352t1 [0, 1, 0, 327, -666] [2] 1152 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 2352.2.a.s

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

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 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.