Properties

Label 100800dy
Number of curves $6$
Conductor $100800$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("100800.gs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800dy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.gs6 100800dy1 [0, 0, 0, 143700, 29342000] [2] 1179648 \(\Gamma_0(N)\)-optimal
100800.gs5 100800dy2 [0, 0, 0, -1008300, 303518000] [2, 2] 2359296  
100800.gs4 100800dy3 [0, 0, 0, -5328300, -4474402000] [2] 4718592  
100800.gs2 100800dy4 [0, 0, 0, -15120300, 22628702000] [2, 2] 4718592  
100800.gs3 100800dy5 [0, 0, 0, -14112300, 25775678000] [2] 9437184  
100800.gs1 100800dy6 [0, 0, 0, -241920300, 1448293502000] [2] 9437184  

Rank

sage: E.rank()
 

The elliptic curves in class 100800dy have rank \(0\).

Modular form 100800.2.a.gs

sage: E.q_eigenform(10)
 
\( q - q^{7} + 4q^{11} - 2q^{13} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.