Elliptic curve isogeny class with Cremona label 11616bb (LMFDB label 11616.ba)

• Label: 11616bb
• Number of curves: $4$
• Conductor: $11616$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 11616bb have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 11616bb do not have complex multiplication.

Modular form 11616.2.a.bb

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 11616bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
11616.ba3	11616bb1	\([0, 1, 0, -2371882, -1406718040]\)	\(13015685560572352/864536409\)	\(98021055056924736\)	\([2, 2]\)	\(230400\)	\(2.3162\)	\(\Gamma_0(N)\)-optimal
11616.ba1	11616bb2	\([0, 1, 0, -37949512, -89995016740]\)	\(6663712298552914184/29403\)	\(26669674538496\)	\([2]\)	\(460800\)	\(2.6627\)
11616.ba2	11616bb3	\([0, 1, 0, -2518897, -1222625857]\)	\(243578556889408/52089208083\)	\(377975642360740098048\)	\([2]\)	\(460800\)	\(2.6627\)
11616.ba4	11616bb4	\([0, 1, 0, -2225472, -1587797928]\)	\(-1343891598641864/421900912521\)	\(-382680679673147023872\)	\([2]\)	\(460800\)	\(2.6627\)