Properties

Label 479370cu
Number of curves $2$
Conductor $479370$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cu1")
 
E.isogeny_class()
 

Elliptic curves in class 479370cu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
479370.cu2 479370cu1 \([1, 0, 0, -82856, 10065216]\) \(-105756712489/12476160\) \(-7421110924527360\) \([2]\) \(4494336\) \(1.7811\) \(\Gamma_0(N)\)-optimal*
479370.cu1 479370cu2 \([1, 0, 0, -1361176, 611131280]\) \(468898230633769/5540400\) \(3295559127668400\) \([2]\) \(8988672\) \(2.1276\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 479370cu1.

Rank

sage: E.rank()
 

The elliptic curves in class 479370cu have rank \(0\).

Complex multiplication

The elliptic curves in class 479370cu do not have complex multiplication.

Modular form 479370.2.a.cu

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