Properties

Label 66248e
Number of curves $4$
Conductor $66248$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 66248e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
66248.p4 66248e1 [0, 0, 0, 8281, -1507142] [2] 221184 \(\Gamma_0(N)\)-optimal
66248.p3 66248e2 [0, 0, 0, -157339, -22607130] [2, 2] 442368  
66248.p2 66248e3 [0, 0, 0, -488579, 103992798] [2] 884736  
66248.p1 66248e4 [0, 0, 0, -2476019, -1499606290] [2] 884736  

Rank

sage: E.rank()
 

The elliptic curves in class 66248e have rank \(0\).

Complex multiplication

The elliptic curves in class 66248e do not have complex multiplication.

Modular form 66248.2.a.e

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

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.