Properties

Label 12936j
Number of curves 4
Conductor 12936
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("12936.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 12936j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
12936.t3 12936j1 [0, 1, 0, -604, 5312] [2] 6144 \(\Gamma_0(N)\)-optimal
12936.t2 12936j2 [0, 1, 0, -1584, -17424] [2, 2] 12288  
12936.t1 12936j3 [0, 1, 0, -23144, -1362768] [2] 24576  
12936.t4 12936j4 [0, 1, 0, 4296, -111504] [2] 24576  

Rank

sage: E.rank()
 

The elliptic curves in class 12936j have rank \(0\).

Modular form 12936.2.a.t

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.