Elliptic curve isogeny class with Cremona label 8736ba (LMFDB label 8736.r)

• Label: 8736ba
• Number of curves: $2$
• Conductor: $8736$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 8736ba have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(7\)	\(1 - T\)
\(13\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 8736ba do not have complex multiplication.

Modular form 8736.2.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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 8736ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8736.r2	8736ba1	\([0, 1, 0, 6, -180]\)	\(314432/223587\)	\(-14309568\)	\([2]\)	\(1536\)	\(0.052074\)	\(\Gamma_0(N)\)-optimal
8736.r1	8736ba2	\([0, 1, 0, -449, -3729]\)	\(2449456192/66339\)	\(271724544\)	\([2]\)	\(3072\)	\(0.39865\)