Properties

Label 26520.q
Number of curves $4$
Conductor $26520$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 26520.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26520.q1 26520b4 \([0, -1, 0, -254600, -49361748]\) \(891190736491222802/3729375\) \(7637760000\) \([2]\) \(122880\) \(1.5279\)  
26520.q2 26520b2 \([0, -1, 0, -15920, -766500]\) \(435792975088324/890127225\) \(911490278400\) \([2, 2]\) \(61440\) \(1.1813\)  
26520.q3 26520b3 \([0, -1, 0, -10520, -1300020]\) \(-62875617222962/322034842935\) \(-659527358330880\) \([2]\) \(122880\) \(1.5279\)  
26520.q4 26520b1 \([0, -1, 0, -1340, -2508]\) \(1040212820176/587242305\) \(150334030080\) \([2]\) \(30720\) \(0.83471\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 26520.q have rank \(0\).

Complex multiplication

The elliptic curves in class 26520.q do not have complex multiplication.

Modular form 26520.2.a.q

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