Properties

Label 53040cs
Number of curves $4$
Conductor $53040$
CM no
Rank $0$
Graph

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

Elliptic curves in class 53040cs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53040.db3 53040cs1 \([0, 1, 0, -9400, -353452]\) \(22428153804601/35802000\) \(146644992000\) \([2]\) \(129024\) \(1.0403\) \(\Gamma_0(N)\)-optimal
53040.db2 53040cs2 \([0, 1, 0, -12280, -121900]\) \(50002789171321/27473062500\) \(112529664000000\) \([2, 2]\) \(258048\) \(1.3868\)  
53040.db4 53040cs3 \([0, 1, 0, 47720, -913900]\) \(2933972022568679/1789082460750\) \(-7328081759232000\) \([2]\) \(516096\) \(1.7334\)  
53040.db1 53040cs4 \([0, 1, 0, -118360, 15535508]\) \(44769506062996441/323730468750\) \(1326000000000000\) \([2]\) \(516096\) \(1.7334\)  

Rank

sage: E.rank()
 

The elliptic curves in class 53040cs have rank \(0\).

Complex multiplication

The elliptic curves in class 53040cs do not have complex multiplication.

Modular form 53040.2.a.cs

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + 4 q^{7} + q^{9} + 4 q^{11} - q^{13} + q^{15} - q^{17} + 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.