Properties

Label 46800.fh
Number of curves 44
Conductor 4680046800
CM no
Rank 00
Graph

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Copy content sage:E = EllipticCurve("fh1") E.isogeny_class()
 

Elliptic curves in class 46800.fh

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.fh1 46800v4 [0,0,0,126360075,546717437750][0, 0, 0, -126360075, -546717437750] 19129597231400697604/2632519129597231400697604/26325 307054800000000307054800000000 [2][2] 23592962359296 2.94612.9461  
46800.fh2 46800v2 [0,0,0,7897575,8542300250][0, 0, 0, -7897575, -8542300250] 18681746265374416/69300562518681746265374416/693005625 20208044025000000002020804402500000000 [2,2][2, 2] 11796481179648 2.59962.5996  
46800.fh3 46800v3 [0,0,0,7533075,9366434750][0, 0, 0, -7533075, -9366434750] 4053153720264484/903687890625-4053153720264484/903687890625 10540615556250000000000-10540615556250000000000 [2][2] 23592962359296 2.94612.9461  
46800.fh4 46800v1 [0,0,0,516450,120436625][0, 0, 0, -516450, -120436625] 83587439220736/1399018432583587439220736/13990184325 25497110932312500002549711093231250000 [2][2] 589824589824 2.25302.2530 Γ0(N)\Gamma_0(N)-optimal

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 46800.fh have rank 00.

L-function data

 
Bad L-factors:
Prime L-Factor
2211
3311
5511
13131+T1 + T
 
Good L-factors:
Prime L-Factor Isogeny Class over Fp\mathbb{F}_p
77 14T+7T2 1 - 4 T + 7 T^{2} 1.7.ae
1111 1+11T2 1 + 11 T^{2} 1.11.a
1717 12T+17T2 1 - 2 T + 17 T^{2} 1.17.ac
1919 1+19T2 1 + 19 T^{2} 1.19.a
2323 1+23T2 1 + 23 T^{2} 1.23.a
2929 12T+29T2 1 - 2 T + 29 T^{2} 1.29.ac
\cdots\cdots\cdots
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 46800.fh do not have complex multiplication.

Modular form 46800.2.a.fh

Copy content sage:E.q_eigenform(10)
 
q+4q7q13+2q17+O(q20)q + 4 q^{7} - 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 LMFDB 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 LMFDB labels.