Properties

Label 59200.u
Number of curves 33
Conductor 5920059200
CM no
Rank 22
Graph

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Copy content sage:E = EllipticCurve("u1") E.isogeny_class()
 

Elliptic curves in class 59200.u

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
59200.u1 59200be1 [0,1,0,85633,9616863][0, 1, 0, -85633, 9616863] 16954786009/370-16954786009/370 1515520000000-1515520000000 [][] 165888165888 1.45321.4532 Γ0(N)\Gamma_0(N)-optimal
59200.u2 59200be2 [0,1,0,29633,21992863][0, 1, 0, -29633, 21992863] 702595369/50653000-702595369/50653000 207474688000000000-207474688000000000 [][] 497664497664 2.00252.0025  
59200.u3 59200be3 [0,1,0,266367,589839137][0, 1, 0, 266367, -589839137] 510273943271/37000000000510273943271/37000000000 151552000000000000000-151552000000000000000 [][] 14929921492992 2.55182.5518  

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 59200.u have rank 22.

L-function data

 
Bad L-factors:
Prime L-Factor
2211
5511
37371T1 - 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
77 1T+7T2 1 - T + 7 T^{2} 1.7.ab
1111 1+3T+11T2 1 + 3 T + 11 T^{2} 1.11.d
1313 1+4T+13T2 1 + 4 T + 13 T^{2} 1.13.e
1717 1+3T+17T2 1 + 3 T + 17 T^{2} 1.17.d
1919 1+2T+19T2 1 + 2 T + 19 T^{2} 1.19.c
2323 1+6T+23T2 1 + 6 T + 23 T^{2} 1.23.g
2929 1+3T+29T2 1 + 3 T + 29 T^{2} 1.29.d
\cdots\cdots\cdots
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 59200.u do not have complex multiplication.

Modular form 59200.2.a.u

Copy content sage:E.q_eigenform(10)
 
q2q3+q7+q93q114q133q172q19+O(q20)q - 2 q^{3} + q^{7} + q^{9} - 3 q^{11} - 4 q^{13} - 3 q^{17} - 2 q^{19} + 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.

(139313931)\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.