Properties

Label 95370cf
Number of curves 2
Conductor 95370
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("95370.cd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 95370cf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
95370.cd2 95370cf1 [1, 1, 1, -254326, 21635699] [2] 1548288 \(\Gamma_0(N)\)-optimal
95370.cd1 95370cf2 [1, 1, 1, -3398646, 2408803443] [2] 3096576  

Rank

sage: E.rank()
 

The elliptic curves in class 95370cf have rank \(1\).

Modular form 95370.2.a.cd

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + 2q^{7} + q^{8} + q^{9} - q^{10} + q^{11} - q^{12} - 4q^{13} + 2q^{14} + q^{15} + q^{16} + q^{18} - 6q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.