Properties

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

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 66248.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66248.p1 66248e4 \([0, 0, 0, -2476019, -1499606290]\) \(1443468546/7\) \(8140973597259776\) \([2]\) \(884736\) \(2.2534\)  
66248.p2 66248e3 \([0, 0, 0, -488579, 103992798]\) \(11090466/2401\) \(2792353943860103168\) \([2]\) \(884736\) \(2.2534\)  
66248.p3 66248e2 \([0, 0, 0, -157339, -22607130]\) \(740772/49\) \(28493407590409216\) \([2, 2]\) \(442368\) \(1.9068\)  
66248.p4 66248e1 \([0, 0, 0, 8281, -1507142]\) \(432/7\) \(-1017621699657472\) \([2]\) \(221184\) \(1.5602\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 66248.2.a.p

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.