↑

Properties

Label 1734g
Number of curves $2$
Conductor $1734$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 1734g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1734.h1 1734g1 \([1, 0, 1, -729, 4744]\) \(1771561/612\) \(14772192228\) \([2]\) \(2304\) \(0.65308\) \(\Gamma_0(N)\)-optimal
1734.h2 1734g2 \([1, 0, 1, 2161, 33644]\) \(46268279/46818\) \(-1130072705442\) \([2]\) \(4608\) \(0.99965\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1734g have rank \(0\).

Complex multiplication

The elliptic curves in class 1734g do not have complex multiplication.

Modular form 1734.2.a.g

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.