Properties

Label 1950.c
Number of curves 22
Conductor 19501950
CM no
Rank 11
Graph

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

Elliptic curves in class 1950.c

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.c1 1950e2 [1,1,0,160,200][1, 1, 0, -160, -200] 3659383421/20563923659383421/2056392 257049000257049000 [2][2] 768768 0.303860.30386  
1950.c2 1950e1 [1,1,0,40,0][1, 1, 0, 40, 0] 54439939/3244854439939/32448 4056000-4056000 [2][2] 384384 0.042709-0.042709 Γ0(N)\Gamma_0(N)-optimal

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 1950.c have rank 11.

L-function data

 
Bad L-factors:
Prime L-Factor
221+T1 + T
331+T1 + T
5511
13131T1 - T
 
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 12T+11T2 1 - 2 T + 11 T^{2} 1.11.ac
1717 1+2T+17T2 1 + 2 T + 17 T^{2} 1.17.c
1919 1+4T+19T2 1 + 4 T + 19 T^{2} 1.19.e
2323 1+23T2 1 + 23 T^{2} 1.23.a
2929 14T+29T2 1 - 4 T + 29 T^{2} 1.29.ae
\cdots\cdots\cdots
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 1950.c do not have complex multiplication.

Modular form 1950.2.a.c

Copy content sage:E.q_eigenform(10)
 
qq2q3+q4+q62q7q8+q9+2q11q12+q13+2q14+q162q17q184q19+O(q20)q - q^{2} - q^{3} + q^{4} + q^{6} - 2 q^{7} - q^{8} + q^{9} + 2 q^{11} - q^{12} + q^{13} + 2 q^{14} + q^{16} - 2 q^{17} - q^{18} - 4 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.