Properties

Label 4650a
Number of curves $6$
Conductor $4650$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("4650.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4650a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4650.h6 4650a1 [1, 1, 0, 1500, -126000] [2] 12288 \(\Gamma_0(N)\)-optimal
4650.h5 4650a2 [1, 1, 0, -30500, -1950000] [2, 2] 24576  
4650.h2 4650a3 [1, 1, 0, -480500, -128400000] [2, 2] 49152  
4650.h4 4650a4 [1, 1, 0, -92500, 8404000] [2] 49152  
4650.h1 4650a5 [1, 1, 0, -7688000, -8208007500] [2] 98304  
4650.h3 4650a6 [1, 1, 0, -473000, -132592500] [2] 98304  

Rank

sage: E.rank()
 

The elliptic curves in class 4650a have rank \(1\).

Modular form 4650.2.a.h

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 4q^{11} - q^{12} - 6q^{13} + q^{16} - 2q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.