Properties

Label 8100c
Number of curves 22
Conductor 81008100
CM no
Rank 00
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("c1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 8100c have rank 00.

L-function data

 
Bad L-factors:
Prime L-Factor
2211
3311
5511
 
Good L-factors:
Prime L-Factor Isogeny Class over Fp\mathbb{F}_p
77 1+2T+7T2 1 + 2 T + 7 T^{2} 1.7.c
1111 1+T+11T2 1 + T + 11 T^{2} 1.11.b
1313 1+13T2 1 + 13 T^{2} 1.13.a
1717 1+2T+17T2 1 + 2 T + 17 T^{2} 1.17.c
1919 1+3T+19T2 1 + 3 T + 19 T^{2} 1.19.d
2323 14T+23T2 1 - 4 T + 23 T^{2} 1.23.ae
2929 13T+29T2 1 - 3 T + 29 T^{2} 1.29.ad
\cdots\cdots\cdots
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 8100c do not have complex multiplication.

Modular form 8100.2.a.c

Copy content sage:E.q_eigenform(10)
 
q2q7+3q11+4q136q177q19+O(q20)q - 2 q^{7} + 3 q^{11} + 4 q^{13} - 6 q^{17} - 7 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 Cremona numbering.

(1331)\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 8100c

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8100.e2 8100c1 [0,0,0,169200,26788500][0, 0, 0, -169200, 26788500] 183711891456/125183711891456/125 364500000000364500000000 [][] 3110431104 1.53371.5337 Γ0(N)\Gamma_0(N)-optimal
8100.e1 8100c2 [0,0,0,205200,14566500][0, 0, 0, -205200, 14566500] 4045602816/19531254045602816/1953125 461320312500000000461320312500000000 [][] 9331293312 2.08302.0830