Elliptic curve isogeny class with Cremona label 3600bh (LMFDB label 3600.be)

• Label: 3600bh
• Number of curves: $4$
• Conductor: $3600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 3600bh have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 3600bh do not have complex multiplication.

Modular form 3600.2.a.bh

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 3600bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3600.be3	3600bh1	\([0, 0, 0, -300, 1375]\)	\(16384/5\)	\(911250000\)	\([2]\)	\(1152\)	\(0.42408\)	\(\Gamma_0(N)\)-optimal
3600.be4	3600bh2	\([0, 0, 0, 825, 9250]\)	\(21296/25\)	\(-72900000000\)	\([2]\)	\(2304\)	\(0.77065\)
3600.be1	3600bh3	\([0, 0, 0, -9300, -345125]\)	\(488095744/125\)	\(22781250000\)	\([2]\)	\(3456\)	\(0.97338\)
3600.be2	3600bh4	\([0, 0, 0, -8175, -431750]\)	\(-20720464/15625\)	\(-45562500000000\)	\([2]\)	\(6912\)	\(1.3200\)