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Properties

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

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

Elliptic curves in class 40425cs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40425.dd2 40425cs1 \([0, 1, 1, -10951908, -16340583031]\) \(-79028701534867456/16987307596875\) \(-31227183616636669921875\) \([]\) \(6912000\) \(3.0374\) \(\Gamma_0(N)\)-optimal
40425.dd1 40425cs2 \([0, 1, 1, -32818158, 1368065726969]\) \(-2126464142970105856/438611057788643355\) \(-806283630277751594881171875\) \([]\) \(34560000\) \(3.8422\)  

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)
 
\(q + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{6} + q^{9} + q^{11} + 2 q^{12} - 6 q^{13} - 4 q^{16} - 7 q^{17} + 2 q^{18} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.