Properties

Label 107800i
Number of curves 44
Conductor 107800107800
CM no
Rank 00
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("i1") E.isogeny_class()
 

Elliptic curves in class 107800i

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
107800.be4 107800i1 [0,0,0,57575,13119750][0, 0, 0, -57575, -13119750] 44851536/132055-44851536/132055 62144554780000000-62144554780000000 [2][2] 589824589824 1.90931.9093 Γ0(N)\Gamma_0(N)-optimal
107800.be3 107800i2 [0,0,0,1258075,542540250][0, 0, 0, -1258075, -542540250] 116986321764/148225116986321764/148225 279016368400000000279016368400000000 [2,2][2, 2] 11796481179648 2.25582.2558  
107800.be2 107800i3 [0,0,0,1601075,223207250][0, 0, 0, -1601075, -223207250] 120564797922/64054375120564797922/64054375 241149861260000000000241149861260000000000 [2][2] 23592962359296 2.60242.6024  
107800.be1 107800i4 [0,0,0,20123075,34744785250][0, 0, 0, -20123075, -34744785250] 239369344910082/385239369344910082/385 14494356800000001449435680000000 [2][2] 23592962359296 2.60242.6024  

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 107800i have rank 00.

L-function data

 
Bad L-factors:
Prime L-Factor
2211
5511
7711
11111T1 - T
 
Good L-factors:
Prime L-Factor Isogeny Class over Fp\mathbb{F}_p
33 1+2T+3T2 1 + 2 T + 3 T^{2} 1.3.c
1313 1+7T+13T2 1 + 7 T + 13 T^{2} 1.13.h
1717 1+7T+17T2 1 + 7 T + 17 T^{2} 1.17.h
1919 13T+19T2 1 - 3 T + 19 T^{2} 1.19.ad
2323 1+23T2 1 + 23 T^{2} 1.23.a
2929 14T+29T2 1 - 4 T + 29 T^{2} 1.29.ae
\cdots\cdots\cdots
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 107800i do not have complex multiplication.

Modular form 107800.2.a.i

Copy content sage:E.q_eigenform(10)
 
q3q9q112q13+2q17+O(q20)q - 3 q^{9} - q^{11} - 2 q^{13} + 2 q^{17} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

Copy content sage:E.isogeny_class().matrix()
 

The i,ji,j entry is the smallest degree of a cyclic isogeny between the ii-th and jj-th curve in the isogeny class, in the Cremona numbering.

(1244212242144241)\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

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

The vertices are labelled with Cremona labels.