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Properties

Label 164730di
Number of curves $2$
Conductor $164730$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("di1")
 
E.isogeny_class()
 

Elliptic curves in class 164730di

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
164730.l1 164730di1 \([1, 1, 0, -2630798, 1641305952]\) \(409863944170874967353/742829700\) \(3649522316100\) \([2]\) \(2723840\) \(2.0960\) \(\Gamma_0(N)\)-optimal
164730.l2 164730di2 \([1, 1, 0, -2629948, 1642420642]\) \(-409466796536364790553/551795963202090\) \(-2710973567211868170\) \([2]\) \(5447680\) \(2.4425\)  

Rank

sage: E.rank()
 

The elliptic curves in class 164730di have rank \(1\).

Complex multiplication

The elliptic curves in class 164730di do not have complex multiplication.

Modular form 164730.2.a.di

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.