Elliptic curve isogeny class with Cremona label 3600g (LMFDB label 3600.bp)

• Label: 3600g
• Number of curves: $2$
• Conductor: $3600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 3600g have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 3600.2.a.g

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.

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

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 3600g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3600.bp2	3600g1	\([0, 0, 0, -135, 1350]\)	\(-432\)	\(-629856000\)	\([2]\)	\(1536\)	\(0.37680\)	\(\Gamma_0(N)\)-optimal
3600.bp1	3600g2	\([0, 0, 0, -2835, 58050]\)	\(1000188\)	\(2519424000\)	\([2]\)	\(3072\)	\(0.72338\)