Properties

Label 445280.o
Number of curves $4$
Conductor $445280$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 445280.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
445280.o1 445280o4 \([0, 0, 0, -371228, -87058048]\) \(779704121664/575\) \(4172380467200\) \([2]\) \(1802240\) \(1.7321\)  
445280.o2 445280o2 \([0, 0, 0, -53603, 2851002]\) \(18778674312/6996025\) \(6345669143052800\) \([2]\) \(1802240\) \(1.7321\) \(\Gamma_0(N)\)-optimal*
445280.o3 445280o1 \([0, 0, 0, -23353, -1341648]\) \(12422690496/330625\) \(37486230760000\) \([2, 2]\) \(901120\) \(1.3855\) \(\Gamma_0(N)\)-optimal*
445280.o4 445280o3 \([0, 0, 0, 4477, -4341722]\) \(10941048/8984375\) \(-8149180600000000\) \([2]\) \(1802240\) \(1.7321\)  
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 445280.o1.

Rank

sage: E.rank()
 

The elliptic curves in class 445280.o have rank \(0\).

Complex multiplication

The elliptic curves in class 445280.o do not have complex multiplication.

Modular form 445280.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{5} - 3 q^{9} + 2 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.