Properties

Label 95304v
Number of curves 4
Conductor 95304
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("95304.x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 95304v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
95304.x3 95304v1 [0, 1, 0, -4452, 108768] [2] 115200 \(\Gamma_0(N)\)-optimal
95304.x2 95304v2 [0, 1, 0, -11672, -341760] [2, 2] 230400  
95304.x4 95304v3 [0, 1, 0, 31648, -2247840] [2] 460800  
95304.x1 95304v4 [0, 1, 0, -170512, -27153952] [2] 460800  

Rank

sage: E.rank()
 

The elliptic curves in class 95304v have rank \(1\).

Modular form 95304.2.a.x

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.