Properties

Label 232730h
Number of curves $2$
Conductor $232730$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 232730h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
232730.h2 232730h1 \([1, 0, 1, 546202, -48188744]\) \(7023836099951/4456448000\) \(-11434026323935232000\) \([]\) \(4173120\) \(2.3459\) \(\Gamma_0(N)\)-optimal
232730.h1 232730h2 \([1, 0, 1, -9091558, -10892245832]\) \(-32391289681150609/1228250000000\) \(-3151353461854250000000\) \([]\) \(12519360\) \(2.8952\)  

Rank

sage: E.rank()
 

The elliptic curves in class 232730h have rank \(1\).

Complex multiplication

The elliptic curves in class 232730h do not have complex multiplication.

Modular form 232730.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + 2 q^{7} - q^{8} - 2 q^{9} - q^{10} + q^{12} + q^{13} - 2 q^{14} + q^{15} + q^{16} + q^{17} + 2 q^{18} + q^{19} + O(q^{20})\) Copy content 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.