Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 26520.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26520.x1 26520f4 \([0, 1, 0, -62496, -6034320]\) \(26362547147244676/244298925\) \(250162099200\) \([2]\) \(73728\) \(1.3508\)  
26520.x2 26520f2 \([0, 1, 0, -3996, -90720]\) \(27572037674704/2472575625\) \(632979360000\) \([2, 2]\) \(36864\) \(1.0042\)  
26520.x3 26520f1 \([0, 1, 0, -871, 8030]\) \(4572531595264/776953125\) \(12431250000\) \([2]\) \(18432\) \(0.65763\) \(\Gamma_0(N)\)-optimal
26520.x4 26520f3 \([0, 1, 0, 4504, -417120]\) \(9865576607324/79640206425\) \(-81551571379200\) \([4]\) \(73728\) \(1.3508\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 26520.2.a.x

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.