Properties

Label 265200.h
Number of curves 4
Conductor 265200
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("265200.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 265200.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
265200.h1 265200h4 [0, -1, 0, -353608, -80816288] [2] 1572864  
265200.h2 265200h3 [0, -1, 0, -28608, -450288] [2] 1572864  
265200.h3 265200h2 [0, -1, 0, -22108, -1256288] [2, 2] 786432  
265200.h4 265200h1 [0, -1, 0, -983, -31038] [2] 393216 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 265200.h have rank \(1\).

Modular form 265200.2.a.h

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.