Properties

Label 19600h
Number of curves $4$
Conductor $19600$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

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

Elliptic curves in class 19600h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19600.cj4 19600h1 [0, 0, 0, 1225, 85750] [2] 24576 \(\Gamma_0(N)\)-optimal
19600.cj3 19600h2 [0, 0, 0, -23275, 1286250] [2, 2] 49152  
19600.cj2 19600h3 [0, 0, 0, -72275, -5916750] [2] 98304  
19600.cj1 19600h4 [0, 0, 0, -366275, 85321250] [2] 98304  

Rank

sage: E.rank()
 

The elliptic curves in class 19600h have rank \(0\).

Complex multiplication

The elliptic curves in class 19600h do not have complex multiplication.

Modular form 19600.2.a.h

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.