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 \((i,j)\)-th 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 labeled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

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	\([1, 0, 1, 1, -9]\)	\(357911/34225\)	\(-34225\)	\([2]\)	\(12\)	\(-0.45050\)