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Properties

Label 40425cs
Number of curves $2$
Conductor $40425$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 40425cs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
40425.dd2 40425cs1 [0, 1, 1, -10951908, -16340583031] [] 6912000 \(\Gamma_0(N)\)-optimal
40425.dd1 40425cs2 [0, 1, 1, -32818158, 1368065726969] [] 34560000  

Rank

sage: E.rank()
 

The elliptic curves in class 40425cs have rank \(0\).

Complex multiplication

The elliptic curves in class 40425cs do not have complex multiplication.

Modular form 40425.2.a.cs

sage: E.q_eigenform(10)
 
\( q + 2q^{2} + q^{3} + 2q^{4} + 2q^{6} + q^{9} + q^{11} + 2q^{12} - 6q^{13} - 4q^{16} - 7q^{17} + 2q^{18} + 5q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.