Elliptic curve isogeny class with LMFDB label 185.c (Cremona label 185c)

• Label: 185.c
• Number of curves: $2$
• Conductor: $185$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 185.c have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$5$	$1 + T$
$37$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$2$	$1 - T + 2 T^{2}$	1.2.ab
$3$	$1 + 2 T + 3 T^{2}$	1.3.c
$7$	$1 + 2 T + 7 T^{2}$	1.7.c
$11$	$1 + 11 T^{2}$	1.11.a
$13$	$1 + 2 T + 13 T^{2}$	1.13.c
$17$	$1 - 2 T + 17 T^{2}$	1.17.ac
$19$	$1 - 2 T + 19 T^{2}$	1.19.ac
$23$	$1 + 8 T + 23 T^{2}$	1.23.i
$29$	$1 - 2 T + 29 T^{2}$	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 185.c do not have complex multiplication.

Modular form 185.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 185.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
185.c1	185c1	$[1, 0, 1, -4, -3]$	$4826809/185$	$185$	$[2]$	$6$	$-0.79707$	$\Gamma_0(N)$-optimal
185.c2	185c2	$[1, 0, 1, 1, -9]$	$357911/34225$	$-34225$	$[2]$	$12$	$-0.45050$