Properties

Label 428400lv
Number of curves 4
Conductor 428400
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("428400.lv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 428400lv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
428400.lv4 428400lv1 [0, 0, 0, 50325, 7308250] [2] 3145728 \(\Gamma_0(N)\)-optimal*
428400.lv3 428400lv2 [0, 0, 0, -399675, 79758250] [2, 2] 6291456 \(\Gamma_0(N)\)-optimal*
428400.lv1 428400lv3 [0, 0, 0, -6069675, 5755428250] [2] 12582912 \(\Gamma_0(N)\)-optimal*
428400.lv2 428400lv4 [0, 0, 0, -1929675, -959111750] [2] 12582912  
*optimality has not been proved rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 428400lv1.

Rank

sage: E.rank()
 

The elliptic curves in class 428400lv have rank \(0\).

Modular form 428400.2.a.lv

sage: E.q_eigenform(10)
 
\( q + q^{7} + 6q^{13} - q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.