Properties

Label 32912bb
Number of curves 4
Conductor 32912
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("32912.y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 32912bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
32912.y4 32912bb1 [0, -1, 0, -5848, 108528] [2] 51840 \(\Gamma_0(N)\)-optimal
32912.y3 32912bb2 [0, -1, 0, -83288, 9277424] [2] 103680  
32912.y2 32912bb3 [0, -1, 0, -199448, -34212880] [2] 155520  
32912.y1 32912bb4 [0, -1, 0, -218808, -27150352] [2] 311040  

Rank

sage: E.rank()
 

The elliptic curves in class 32912bb have rank \(0\).

Modular form 32912.2.a.y

sage: E.q_eigenform(10)
 
\( q + 2q^{3} - 4q^{7} + q^{9} - 2q^{13} + q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.