Elliptic curve isogeny class with Cremona label 33600gs (LMFDB label 33600.hj)

• Label: 33600gs
• Number of curves: $4$
• Conductor: $33600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 33600gs have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 33600gs do not have complex multiplication.

Modular form 33600.2.a.gs

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 33600gs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
33600.hj3	33600gs1	\([0, 1, 0, -132508, 17266238]\)	\(257307998572864/19456203375\)	\(19456203375000000\)	\([2]\)	\(221184\)	\(1.8707\)	\(\Gamma_0(N)\)-optimal
33600.hj2	33600gs2	\([0, 1, 0, -432633, -89278137]\)	\(139927692143296/27348890625\)	\(1750329000000000000\)	\([2, 2]\)	\(442368\)	\(2.2173\)
33600.hj4	33600gs3	\([0, 1, 0, 890367, -527191137]\)	\(152461584507448/322998046875\)	\(-165375000000000000000\)	\([2]\)	\(884736\)	\(2.5639\)
33600.hj1	33600gs4	\([0, 1, 0, -6557633, -6465403137]\)	\(60910917333827912/3255076125\)	\(1666598976000000000\)	\([2]\)	\(884736\)	\(2.5639\)