Elliptic curve isogeny class with LMFDB label 3136.ba (Cremona label 3136h)

• Label: 3136.ba
• Number of curves: $2$
• Conductor: $3136$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 3136.ba have rank \(0\).

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.ac
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 3136.2.a.ba

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.ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3136.ba1	3136h2	\([0, -1, 0, -14177, -642655]\)	\(238328\)	\(1322306994176\)	\([2]\)	\(7168\)	\(1.1805\)
3136.ba2	3136h1	\([0, -1, 0, -457, -19767]\)	\(-64\)	\(-165288374272\)	\([2]\)	\(3584\)	\(0.83391\)	\(\Gamma_0(N)\)-optimal