Elliptic curve isogeny class with LMFDB label 1638.c (Cremona label 1638e)

• Label: 1638.c
• Number of curves: $4$
• Conductor: $1638$
• CM: no
• Rank: $0$

Elliptic curves in class 1638.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1638.c1	1638e3	$[1, -1, 0, -532203, -149255515]$	$22868021811807457713/8953460393696$	$6527072627004384$	$[2]$	$23040$	$1.9993$
1638.c2	1638e4	$[1, -1, 0, -281643, 56492261]$	$3389174547561866673/74853681183008$	$54568333582412832$	$[2]$	$23040$	$1.9993$
1638.c3	1638e2	$[1, -1, 0, -38283, -1573435]$	$8511781274893233/3440817243136$	$2508355770246144$	$[2, 2]$	$11520$	$1.6527$
1638.c4	1638e1	$[1, -1, 0, 7797, -181819]$	$71903073502287/60782804992$	$-44310664839168$	$[2]$	$5760$	$1.3062$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 1638.c have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$3$	$1$
$7$	$1 + T$
$13$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 + 2 T + 5 T^{2}$	1.5.c
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$17$	$1 - 6 T + 17 T^{2}$	1.17.ag
$19$	$1 + 19 T^{2}$	1.19.a
$23$	$1 + 8 T + 23 T^{2}$	1.23.i
$29$	$1 - 10 T + 29 T^{2}$	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1638.c do not have complex multiplication.

Modular form 1638.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.