Elliptic curve isogeny class with LMFDB label 33600.be (Cremona label 33600b)

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

Rank

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

See L-function page for more information

Complex multiplication

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

Modular form 33600.2.a.be

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 33600.be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
33600.be1	33600b4	\([0, -1, 0, -373633, -87780863]\)	\(5633270409316/14175\)	\(14515200000000\)	\([2]\)	\(196608\)	\(1.7638\)
33600.be2	33600b3	\([0, -1, 0, -65633, 4759137]\)	\(30534944836/8203125\)	\(8400000000000000\)	\([2]\)	\(196608\)	\(1.7638\)
33600.be3	33600b2	\([0, -1, 0, -23633, -1330863]\)	\(5702413264/275625\)	\(70560000000000\)	\([2, 2]\)	\(98304\)	\(1.4172\)
33600.be4	33600b1	\([0, -1, 0, 867, -81363]\)	\(4499456/180075\)	\(-2881200000000\)	\([2]\)	\(49152\)	\(1.0706\)	\(\Gamma_0(N)\)-optimal