Properties

Label 1058c
Number of curves 22
Conductor 10581058
CM no
Rank 22
Graph

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

Elliptic curves in class 1058c

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1058.a2 1058c1 [1,0,1,0,2][1, 0, 1, 0, 2] 23/423/4 2116-2116 [][] 8080 0.68263-0.68263 Γ0(N)\Gamma_0(N)-optimal
1058.a1 1058c2 [1,0,1,115,462][1, 0, 1, -115, 462] 313994137/64-313994137/64 33856-33856 [][] 240240 0.13332-0.13332  

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 1058c have rank 22.

L-function data

 
Bad L-factors:
Prime L-Factor
221+T1 + T
232311
 
Good L-factors:
Prime L-Factor Isogeny Class over Fp\mathbb{F}_p
33 1+3T2 1 + 3 T^{2} 1.3.a
55 1+4T+5T2 1 + 4 T + 5 T^{2} 1.5.e
77 14T+7T2 1 - 4 T + 7 T^{2} 1.7.ae
1111 1+2T+11T2 1 + 2 T + 11 T^{2} 1.11.c
1313 1+2T+13T2 1 + 2 T + 13 T^{2} 1.13.c
1717 12T+17T2 1 - 2 T + 17 T^{2} 1.17.ac
1919 12T+19T2 1 - 2 T + 19 T^{2} 1.19.ac
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 1058c do not have complex multiplication.

Modular form 1058.2.a.c

Copy content sage:E.q_eigenform(10)
 
qq22q3+q43q5+2q62q7q8+q9+3q106q112q12q13+2q14+6q15+q166q17q182q19+O(q20)q - q^{2} - 2 q^{3} + q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} - q^{8} + q^{9} + 3 q^{10} - 6 q^{11} - 2 q^{12} - q^{13} + 2 q^{14} + 6 q^{15} + q^{16} - 6 q^{17} - q^{18} - 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 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.