Properties

Label 26520.z
Number of curves $4$
Conductor $26520$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 26520.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26520.z1 26520bb4 \([0, 1, 0, -2040056, -1122211200]\) \(916959671620739147236/2731145625\) \(2796693120000\) \([2]\) \(393216\) \(2.0417\)  
26520.z2 26520bb2 \([0, 1, 0, -127556, -17551200]\) \(896581610757188944/1545359765625\) \(395612100000000\) \([2, 2]\) \(196608\) \(1.6951\)  
26520.z3 26520bb3 \([0, 1, 0, -87776, -28657776]\) \(-73039208963041156/303497314453125\) \(-310781250000000000\) \([2]\) \(393216\) \(2.0417\)  
26520.z4 26520bb1 \([0, 1, 0, -10511, -88086]\) \(8027441608013824/4452347908125\) \(71237566530000\) \([4]\) \(98304\) \(1.3485\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 26520.z have rank \(1\).

Complex multiplication

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

Modular form 26520.2.a.z

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