Properties

Label 12495h
Number of curves 4
Conductor 12495
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("12495.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 12495h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
12495.c4 12495h1 [1, 1, 1, 685, -11320] [4] 12288 \(\Gamma_0(N)\)-optimal
12495.c3 12495h2 [1, 1, 1, -5440, -128920] [2, 2] 24576  
12495.c1 12495h3 [1, 1, 1, -82615, -9173830] [2] 49152  
12495.c2 12495h4 [1, 1, 1, -26265, 1512090] [2] 49152  

Rank

sage: E.rank()
 

The elliptic curves in class 12495h have rank \(0\).

Modular form 12495.2.a.c

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} - q^{4} + q^{5} + q^{6} + 3q^{8} + q^{9} - q^{10} + q^{12} + 6q^{13} - q^{15} - q^{16} + q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.