Elliptic curve isogeny class with Cremona label 197136c (LMFDB label 197136.h)

• Label: 197136c
• Number of curves: $2$
• Conductor: $197136$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 197136c have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(37\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(13\)	\( 1 + 3 T + 13 T^{2}\)	1.13.d
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 197136c do not have complex multiplication.

Modular form 197136.2.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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 197136c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
197136.h1	197136c1	\([0, 0, 0, -9269499, 10933855274]\)	\(-8398297/64\)	\(-671245276783157968896\)	\([]\)	\(12275712\)	\(2.8262\)	\(\Gamma_0(N)\)-optimal
197136.h2	197136c2	\([0, 0, 0, 27200661, 58162712474]\)	\(212207543/262144\)	\(-2749420653703815040598016\)	\([]\)	\(36827136\)	\(3.3755\)