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Properties

Label 320790k
Number of curves $2$
Conductor $320790$
CM no
Rank $0$
Graph

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

Elliptic curves in class 320790k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
320790.k1 320790k1 \([1, 1, 0, -628147, 191479771]\) \(-13596259609/9990\) \(-20139779065485510\) \([]\) \(4714848\) \(2.0626\) \(\Gamma_0(N)\)-optimal
320790.k2 320790k2 \([1, 1, 0, 624668, 820643464]\) \(13371532631/151959000\) \(-306348417118329591000\) \([]\) \(14144544\) \(2.6119\)  

Rank

sage: E.rank()
 

The elliptic curves in class 320790k have rank \(0\).

Complex multiplication

The elliptic curves in class 320790k do not have complex multiplication.

Modular form 320790.2.a.k

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