Elliptic curve isogeny class with LMFDB label 33600.ca (Cremona label 33600eo)

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

Rank

The elliptic curves in class 33600.ca 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 \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 33600.2.a.ca

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 33600.ca

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
33600.ca1	33600eo4	\([0, -1, 0, -10206000033, 396858041351937]\)	\(229625675762164624948320008/9568125\)	\(4898880000000000\)	\([2]\)	\(20643840\)	\(3.9113\)
33600.ca2	33600eo2	\([0, -1, 0, -637875033, 6201065726937]\)	\(448487713888272974160064/91549016015625\)	\(5859137025000000000000\)	\([2, 2]\)	\(10321920\)	\(3.5647\)
33600.ca3	33600eo3	\([0, -1, 0, -635688033, 6245695835937]\)	\(-55486311952875723077768/801237030029296875\)	\(-410233359375000000000000000\)	\([2]\)	\(20643840\)	\(3.9113\)
33600.ca4	33600eo1	\([0, -1, 0, -40003908, 96203669562]\)	\(7079962908642659949376/100085966990454375\)	\(100085966990454375000000\)	\([2]\)	\(5160960\)	\(3.2181\)	\(\Gamma_0(N)\)-optimal