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Properties

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

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 1734l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1734.l2 1734l1 \([1, 0, 0, -463562, -122187996]\) \(-1579268174113/10077696\) \(-70299562860135936\) \([3]\) \(38556\) \(2.0698\) \(\Gamma_0(N)\)-optimal
1734.l1 1734l2 \([1, 0, 0, -37605842, -88765953444]\) \(-843137281012581793/216\) \(-1506763607256\) \([]\) \(115668\) \(2.6192\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1734.2.a.l

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - 3 q^{5} + q^{6} - 4 q^{7} + q^{8} + q^{9} - 3 q^{10} + 3 q^{11} + q^{12} + 2 q^{13} - 4 q^{14} - 3 q^{15} + q^{16} + q^{18} + 8 q^{19} + O(q^{20})\) 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.