Properties

Label 123840ey
Number of curves $4$
Conductor $123840$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ey1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 123840ey

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
123840.i3 123840ey1 [0, 0, 0, -39468, -3014192] [2] 294912 \(\Gamma_0(N)\)-optimal
123840.i2 123840ey2 [0, 0, 0, -50988, -1111088] [2, 2] 589824  
123840.i4 123840ey3 [0, 0, 0, 196692, -8739632] [2] 1179648  
123840.i1 123840ey4 [0, 0, 0, -482988, 128316112] [2] 1179648  

Rank

sage: E.rank()
 

The elliptic curves in class 123840ey have rank \(1\).

Complex multiplication

The elliptic curves in class 123840ey do not have complex multiplication.

Modular form 123840.2.a.ey

sage: E.q_eigenform(10)
 
\( q - q^{5} - 4q^{7} + 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.