Properties

Label 2352.v
Number of curves 6
Conductor 2352
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("2352.v1")
sage: E.isogeny_class()

Elliptic curves in class 2352.v

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
2352.v1 2352v5 [0, 1, 0, -614672, -185691948] 2 12288  
2352.v2 2352v3 [0, 1, 0, -38432, -2908620] 4 6144  
2352.v3 2352v4 [0, 1, 0, -30592, 2036852] 4 6144  
2352.v4 2352v6 [0, 1, 0, -26672, -4710252] 2 12288  
2352.v5 2352v2 [0, 1, 0, -3152, -15660] 4 3072  
2352.v6 2352v1 [0, 1, 0, 768, -1548] 2 1536 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

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

Modular form 2352.2.a.v

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.