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Properties

Label 482734k
Number of curves $2$
Conductor $482734$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 482734k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
482734.k2 482734k1 \([1, -1, 0, -16275610, 23268128564]\) \(801581275315909089/70810888830976\) \(42119968057402951991296\) \([]\) \(86436000\) \(3.0814\) \(\Gamma_0(N)\)-optimal
482734.k1 482734k2 \([1, -1, 0, -8083113970, -279713243622916]\) \(98191033604529537629349729/10906239337336\) \(6487285502255038812856\) \([]\) \(605052000\) \(4.0544\)  

Rank

sage: E.rank()
 

The elliptic curves in class 482734k have rank \(1\).

Complex multiplication

The elliptic curves in class 482734k do not have complex multiplication.

Modular form 482734.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + 3 q^{3} + q^{4} - q^{5} - 3 q^{6} + q^{7} - q^{8} + 6 q^{9} + q^{10} + 2 q^{11} + 3 q^{12} - q^{14} - 3 q^{15} + q^{16} + 3 q^{17} - 6 q^{18} + 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.