Properties

Label 92400.ia
Number of curves $6$
Conductor $92400$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ia1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400.ia

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
92400.ia1 92400hd6 [0, 1, 0, -1219680008, 16394802983988] [2] 11796480  
92400.ia2 92400hd4 [0, 1, 0, -76230008, 256149683988] [2, 2] 5898240  
92400.ia3 92400hd5 [0, 1, 0, -75852008, 258816095988] [2] 11796480  
92400.ia4 92400hd3 [0, 1, 0, -10178008, -6594196012] [2] 5898240  
92400.ia5 92400hd2 [0, 1, 0, -4788008, 3959423988] [2, 2] 2949120  
92400.ia6 92400hd1 [0, 1, 0, 13992, 185051988] [2] 1474560 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 92400.ia have rank \(1\).

Complex multiplication

The elliptic curves in class 92400.ia do not have complex multiplication.

Modular form 92400.2.a.ia

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{7} + q^{9} + q^{11} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.