Properties

Label 370881i
Number of curves $6$
Conductor $370881$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("370881.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 370881i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
370881.i5 370881i1 [1, -1, 1, -290778431, 2043453982182] [2] 123863040 \(\Gamma_0(N)\)-optimal
370881.i4 370881i2 [1, -1, 1, -4743204836, 125735421454206] [2, 2] 247726080  
370881.i1 370881i3 [1, -1, 1, -75891161471, 8047035862185912] [2] 495452160  
370881.i3 370881i4 [1, -1, 1, -4834070681, 120667469815176] [2, 2] 495452160  
370881.i6 370881i5 [1, -1, 1, 4628958034, 535503937411860] [2] 990904320  
370881.i2 370881i6 [1, -1, 1, -15750952916, -618518993069568] [2] 990904320  

Rank

sage: E.rank()
 

The elliptic curves in class 370881i have rank \(1\).

Modular form 370881.2.a.i

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{4} - 2q^{5} + 3q^{8} + 2q^{10} + 4q^{11} + 2q^{13} - q^{16} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.