Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 26520.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26520.h1 26520p4 \([0, -1, 0, -9929296, -12039444404]\) \(52862679907533400952738/90903515625\) \(186170400000000\) \([2]\) \(720896\) \(2.4270\)  
26520.h2 26520p2 \([0, -1, 0, -620776, -187836740]\) \(25836234020391349156/33847087730625\) \(34659417836160000\) \([2, 2]\) \(360448\) \(2.0805\)  
26520.h3 26520p3 \([0, -1, 0, -451776, -292549140]\) \(-4979252943420552578/15190164405108225\) \(-31109456701661644800\) \([2]\) \(720896\) \(2.4270\)  
26520.h4 26520p1 \([0, -1, 0, -49556, -1162044]\) \(52575237512036944/28081530070425\) \(7188871698028800\) \([4]\) \(180224\) \(1.7339\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 26520.2.a.h

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