Elliptic curve isogeny class with Cremona label 33600ev (LMFDB label 33600.de)

• Label: 33600ev
• Number of curves: $4$
• Conductor: $33600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 33600ev have rank \(1\).

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
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 33600.2.a.ev

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 33600ev

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
33600.de3	33600ev1	\([0, -1, 0, -3633, 85137]\)	\(20720464/105\)	\(26880000000\)	\([2]\)	\(24576\)	\(0.84777\)	\(\Gamma_0(N)\)-optimal
33600.de2	33600ev2	\([0, -1, 0, -5633, -16863]\)	\(19307236/11025\)	\(11289600000000\)	\([2, 2]\)	\(49152\)	\(1.1943\)
33600.de4	33600ev3	\([0, -1, 0, 22367, -156863]\)	\(604223422/354375\)	\(-725760000000000\)	\([2]\)	\(98304\)	\(1.5409\)
33600.de1	33600ev4	\([0, -1, 0, -65633, -6436863]\)	\(15267472418/36015\)	\(73758720000000\)	\([2]\)	\(98304\)	\(1.5409\)