Elliptic curve isogeny class with LMFDB label 3136.c (Cremona label 3136bb)

• Label: 3136.c
• Number of curves: $2$
• Conductor: $3136$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 3136.c have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 2 T + 17 T^{2}\)	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.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 3136.c do not have complex multiplication.

Modular form 3136.2.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 labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 3136.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3136.c1	3136bb2	\([0, 1, 0, -7905, -269921]\)	\(3543122/49\)	\(755603996672\)	\([2]\)	\(6144\)	\(1.0849\)
3136.c2	3136bb1	\([0, 1, 0, -65, -11201]\)	\(-4/7\)	\(-53971714048\)	\([2]\)	\(3072\)	\(0.73829\)	\(\Gamma_0(N)\)-optimal