Properties

Label 14994.i
Number of curves 6
Conductor 14994
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("14994.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14994.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14994.i1 14994bh5 [1, -1, 0, -12235113, -16469463389] [2] 393216  
14994.i2 14994bh3 [1, -1, 0, -764703, -257185895] [2, 2] 196608  
14994.i3 14994bh6 [1, -1, 0, -725013, -285103841] [2] 393216  
14994.i4 14994bh2 [1, -1, 0, -50283, -3566795] [2, 2] 98304  
14994.i5 14994bh1 [1, -1, 0, -15003, 659749] [2] 49152 \(\Gamma_0(N)\)-optimal
14994.i6 14994bh4 [1, -1, 0, 99657, -20869871] [2] 196608  

Rank

sage: E.rank()
 

The elliptic curves in class 14994.i have rank \(0\).

Modular form 14994.2.a.i

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - 2q^{5} - q^{8} + 2q^{10} + 4q^{11} + 2q^{13} + q^{16} + q^{17} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.