Elliptic curve isogeny class with LMFDB label 5202.c (Cremona label 5202b)

• Label: 5202.c
• Number of curves: $6$
• Conductor: $5202$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 5202.c have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$3$	$1$
$17$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 + 2 T + 5 T^{2}$	1.5.c
$7$	$1 + 7 T^{2}$	1.7.a
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$13$	$1 + 2 T + 13 T^{2}$	1.13.c
$19$	$1 - 4 T + 19 T^{2}$	1.19.ae
$23$	$1 + 23 T^{2}$	1.23.a
$29$	$1 + 10 T + 29 T^{2}$	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 5202.c do not have complex multiplication.

Modular form 5202.2.a.c

Isogeny matrix

The $i,j$ entry is the smallest degree of a cyclic isogeny between the $i$-th and $j$-th curve in the isogeny class, in the LMFDB numbering.

$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 5202.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5202.c1	5202b5	$[1, -1, 0, -72162198, 235964108794]$	$2361739090258884097/5202$	$91535889140802$	$[2]$	$294912$	$2.8130$
5202.c2	5202b3	$[1, -1, 0, -4510188, 3687697660]$	$576615941610337/27060804$	$476169695310452004$	$[2, 2]$	$147456$	$2.4664$
5202.c3	5202b6	$[1, -1, 0, -4276098, 4087382926]$	$-491411892194497/125563633938$	$-2209453840112458990338$	$[2]$	$294912$	$2.8130$
5202.c4	5202b2	$[1, -1, 0, -296568, 51343600]$	$163936758817/30338064$	$533837305469157264$	$[2, 2]$	$73728$	$2.1198$
5202.c5	5202b1	$[1, -1, 0, -88488, -9374144]$	$4354703137/352512$	$6202902605306112$	$[2]$	$36864$	$1.7733$	$\Gamma_0(N)$-optimal
5202.c6	5202b4	$[1, -1, 0, 587772, 298428196]$	$1276229915423/2927177028$	$-51507449429163835428$	$[2]$	$147456$	$2.4664$