Properties

Label 144150cc
Number of curves 44
Conductor 144150144150
CM no
Rank 11
Graph

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Copy content sage:E = EllipticCurve("cc1") E.isogeny_class()
 

Elliptic curves in class 144150cc

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
144150.dh3 144150cc1 [1,1,1,2607213,1439514531][1, 1, 1, -2607213, 1439514531] 141339344329/17141760141339344329/17141760 237708985919040000000237708985919040000000 [4][4] 66355206635520 2.64032.6403 Γ0(N)\Gamma_0(N)-optimal
144150.dh2 144150cc2 [1,1,1,10295213,11214933469][1, 1, 1, -10295213, -11214933469] 8702409880009/11209104008702409880009/1120910400 1554393915736222500000015543939157362225000000 [2,2][2, 2] 1327104013271040 2.98692.9869  
144150.dh4 144150cc3 [1,1,1,15651787,58594155469][1, 1, 1, 15651787, -58594155469] 30579142915511/12467533500030579142915511/124675335000 1728903417850127109375000-1728903417850127109375000 [2][2] 2654208026542080 3.33343.3334  
144150.dh1 144150cc4 [1,1,1,159250213,773566623469][1, 1, 1, -159250213, -773566623469] 32208729120020809/65898684032208729120020809/658986840 91383319723524693750009138331972352469375000 [2][2] 2654208026542080 3.33343.3334  

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 144150cc have rank 11.

L-function data

 
Bad L-factors:
Prime L-Factor
221+T1 + T
331T1 - T
5511
313111
 
Good L-factors:
Prime L-Factor Isogeny Class over Fp\mathbb{F}_p
77 1T+7T2 1 - T + 7 T^{2} 1.7.ab
1111 1+5T+11T2 1 + 5 T + 11 T^{2} 1.11.f
1313 14T+13T2 1 - 4 T + 13 T^{2} 1.13.ae
1717 1+2T+17T2 1 + 2 T + 17 T^{2} 1.17.c
1919 1+2T+19T2 1 + 2 T + 19 T^{2} 1.19.c
2323 1+4T+23T2 1 + 4 T + 23 T^{2} 1.23.e
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 144150cc do not have complex multiplication.

Modular form 144150.2.a.cc

Copy content sage:E.q_eigenform(10)
 
q+q2q3+q4q6+q8+q9+4q11q12+6q13+q16+2q17+q184q19+O(q20)q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} + 4 q^{11} - q^{12} + 6 q^{13} + 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 Cremona numbering.

(1244212242144241)\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with Cremona labels.