Properties

Label 5040.v
Number of curves $3$
Conductor $5040$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5040.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5040.v1 5040bk3 \([0, 0, 0, -18912, -1047184]\) \(-250523582464/13671875\) \(-40824000000000\) \([]\) \(12960\) \(1.3699\)  
5040.v2 5040bk1 \([0, 0, 0, -192, 1136]\) \(-262144/35\) \(-104509440\) \([]\) \(1440\) \(0.27130\) \(\Gamma_0(N)\)-optimal
5040.v3 5040bk2 \([0, 0, 0, 1248, -2896]\) \(71991296/42875\) \(-128024064000\) \([]\) \(4320\) \(0.82061\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5040.v have rank \(0\).

Complex multiplication

The elliptic curves in class 5040.v do not have complex multiplication.

Modular form 5040.2.a.v

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} - 3q^{11} + 5q^{13} - 3q^{17} - 2q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.