Elliptic curve isogeny class with LMFDB label 8976.ba (Cremona label 8976x)

• Label: 8976.ba
• Number of curves: $4$
• Conductor: $8976$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 8976.ba have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(11\)	\(1 + T\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 8976.ba do not have complex multiplication.

Modular form 8976.2.a.ba

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 8976.ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8976.ba1	8976x3	\([0, 1, 0, -7743032, -8295458988]\)	\(12534210458299016895673/315581882565708\)	\(1292623390989139968\)	\([2]\)	\(368640\)	\(2.5834\)
8976.ba2	8976x2	\([0, 1, 0, -502392, -119328300]\)	\(3423676911662954233/483711578981136\)	\(1981282627506733056\)	\([2, 2]\)	\(184320\)	\(2.2368\)
8976.ba3	8976x1	\([0, 1, 0, -132472, 16654292]\)	\(62768149033310713/6915442583808\)	\(28325652823277568\)	\([2]\)	\(92160\)	\(1.8903\)	\(\Gamma_0(N)\)-optimal
8976.ba4	8976x4	\([0, 1, 0, 819528, -640164780]\)	\(14861225463775641287/51859390496937804\)	\(-212416063475457245184\)	\([2]\)	\(368640\)	\(2.5834\)