Elliptic curve isogeny class with LMFDB label 637.c (Cremona label 637a)

• Label: 637.c
• Number of curves: $2$
• Conductor: $637$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 637.c have rank $1$.

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$2$	$1 - T + 2 T^{2}$	1.2.ab
$3$	$1 + 3 T^{2}$	1.3.a
$5$	$1 + 5 T^{2}$	1.5.a
$11$	$1 + 3 T + 11 T^{2}$	1.11.d
$17$	$1 - 7 T + 17 T^{2}$	1.17.ah
$19$	$1 + 7 T + 19 T^{2}$	1.19.h
$23$	$1 + 6 T + 23 T^{2}$	1.23.g
$29$	$1 + 5 T + 29 T^{2}$	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 637.c do not have complex multiplication.

Modular form 637.2.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.

$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 637.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
637.c1	637a1	$[1, -1, 0, -107, 454]$	$-56723625/13$	$-31213$	$[]$	$60$	$-0.14604$	$\Gamma_0(N)$-optimal
637.c2	637a2	$[1, -1, 0, 628, -17823]$	$11397810375/62748517$	$-150659189317$	$[]$	$420$	$0.82691$