Properties

Label 62475bs
Number of curves 4
Conductor 62475
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("62475.cm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 62475bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
62475.cm4 62475bs1 [1, 0, 1, 17124, -1449227] [2] 294912 \(\Gamma_0(N)\)-optimal
62475.cm3 62475bs2 [1, 0, 1, -136001, -15842977] [2, 2] 589824  
62475.cm2 62475bs3 [1, 0, 1, -656626, 190324523] [2] 1179648  
62475.cm1 62475bs4 [1, 0, 1, -2065376, -1142597977] [2] 1179648  

Rank

sage: E.rank()
 

The elliptic curves in class 62475bs have rank \(1\).

Modular form 62475.2.a.cm

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

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 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.