Properties

Label 479370.z
Number of curves $4$
Conductor $479370$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("479370.z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 479370.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
479370.z1 479370z4 [1, 0, 1, -522279, -145110848] [2] 6193152  
479370.z2 479370z2 [1, 0, 1, -42909, -724604] [2, 2] 3096576  
479370.z3 479370z1 [1, 0, 1, -26089, 1610012] [2] 1548288 \(\Gamma_0(N)\)-optimal
479370.z4 479370z3 [1, 0, 1, 167341, -5686504] [2] 6193152  

Rank

sage: E.rank()
 

The elliptic curves in class 479370.z have rank \(1\).

Modular form 479370.2.a.z

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} + q^{9} + q^{10} - 4q^{11} + q^{12} + 2q^{13} - q^{15} + q^{16} - 2q^{17} - q^{18} + q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.