Elliptic curve isogeny class with Cremona label 226512bc (LMFDB label 226512.cg)

• Label: 226512bc
• Number of curves: $4$
• Conductor: $226512$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 226512bc have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 226512bc do not have complex multiplication.

Modular form 226512.2.a.bc

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 226512bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
226512.cg4	226512bc1	\([0, 0, 0, 6263565, -4338413134]\)	\(5137417856375/4510142208\)	\(-23857988392005368020992\)	\([2]\)	\(13271040\)	\(2.9813\)	\(\Gamma_0(N)\)-optimal
226512.cg3	226512bc2	\([0, 0, 0, -31372275, -38534337358]\)	\(645532578015625/252306960048\)	\(1334666679327763261489152\)	\([2]\)	\(26542080\)	\(3.3279\)
226512.cg2	226512bc3	\([0, 0, 0, -65087715, 269893096418]\)	\(-5764706497797625/2612665516032\)	\(-13820615998120689578016768\)	\([2]\)	\(39813120\)	\(3.5307\)
226512.cg1	226512bc4	\([0, 0, 0, -1135618275, 14728264733666]\)	\(30618029936661765625/3678951124992\)	\(19461109913369327129591808\)	\([2]\)	\(79626240\)	\(3.8772\)