Properties

Label 254320.e
Number of curves 4
Conductor 254320
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("254320.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 254320.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
254320.e1 254320e4 [0, 1, 0, -2051996, 1130707480] [2] 4478976  
254320.e2 254320e3 [0, 1, 0, -128701, 17504334] [2] 2239488  
254320.e3 254320e2 [0, 1, 0, -28996, 1064280] [2] 1492992  
254320.e4 254320e1 [0, 1, 0, -13101, -569726] [2] 746496 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 254320.e have rank \(0\).

Modular form 254320.2.a.e

sage: E.q_eigenform(10)
 
\( q - 2q^{3} - q^{5} - 4q^{7} + q^{9} - q^{11} - 4q^{13} + 2q^{15} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.