Properties

Label 58080.r
Number of curves 22
Conductor 5808058080
CM no
Rank 11
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("r1") E.isogeny_class()
 

Elliptic curves in class 58080.r

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58080.r1 58080k2 [0,1,0,97795265,372268086225][0, -1, 0, -97795265, 372268086225] 14254800421166387776/26905582687514254800421166387776/269055826875 19523535245905996800001952353524590599680000 [2][2] 73728007372800 3.20933.2093  
58080.r2 58080k1 [0,1,0,5910890,6219113100][0, -1, 0, -5910890, 6219113100] 201440287521417664/30700866796875-201440287521417664/30700866796875 3480861330146475000000-3480861330146475000000 [2][2] 36864003686400 2.86272.8627 Γ0(N)\Gamma_0(N)-optimal

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 58080.r have rank 11.

L-function data

 
Bad L-factors:
Prime L-Factor
2211
331+T1 + T
551T1 - T
111111
 
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
1313 12T+13T2 1 - 2 T + 13 T^{2} 1.13.ac
1717 1+17T2 1 + 17 T^{2} 1.17.a
1919 16T+19T2 1 - 6 T + 19 T^{2} 1.19.ag
2323 18T+23T2 1 - 8 T + 23 T^{2} 1.23.ai
2929 18T+29T2 1 - 8 T + 29 T^{2} 1.29.ai
\cdots\cdots\cdots
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 58080.r do not have complex multiplication.

Modular form 58080.2.a.r

Copy content sage:E.q_eigenform(10)
 
qq3+q52q7+q9+2q13q15+6q19+O(q20)q - q^{3} + q^{5} - 2 q^{7} + q^{9} + 2 q^{13} - q^{15} + 6 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.

(1221)\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.