Properties

Label 4235.c
Number of curves 33
Conductor 42354235
CM no
Rank 00
Graph

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

Elliptic curves in class 4235.c

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4235.c1 4235b3 [0,1,1,15891,801301][0, 1, 1, -15891, 801301] 250523582464/13671875-250523582464/13671875 24220560546875-24220560546875 [][] 81008100 1.32641.3264  
4235.c2 4235b1 [0,1,1,161,929][0, 1, 1, -161, -929] 262144/35-262144/35 62004635-62004635 [][] 900900 0.227800.22780 Γ0(N)\Gamma_0(N)-optimal
4235.c3 4235b2 [0,1,1,1049,2580][0, 1, 1, 1049, 2580] 71991296/4287571991296/42875 75955677875-75955677875 [][] 27002700 0.777100.77710  

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 4235.c have rank 00.

L-function data

 
Bad L-factors:
Prime L-Factor
551+T1 + T
771+T1 + T
111111
 
Good L-factors:
Prime L-Factor Isogeny Class over Fp\mathbb{F}_p
22 1+2T2 1 + 2 T^{2} 1.2.a
33 1T+3T2 1 - T + 3 T^{2} 1.3.ab
1313 1+5T+13T2 1 + 5 T + 13 T^{2} 1.13.f
1717 1+3T+17T2 1 + 3 T + 17 T^{2} 1.17.d
1919 1+2T+19T2 1 + 2 T + 19 T^{2} 1.19.c
2323 1+6T+23T2 1 + 6 T + 23 T^{2} 1.23.g
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 4235.c do not have complex multiplication.

Modular form 4235.2.a.c

Copy content sage:E.q_eigenform(10)
 
q+q32q4q5q72q92q125q13q15+4q163q172q19+O(q20)q + q^{3} - 2 q^{4} - q^{5} - q^{7} - 2 q^{9} - 2 q^{12} - 5 q^{13} - q^{15} + 4 q^{16} - 3 q^{17} - 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 LMFDB numbering.

(193913331)\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.