Elliptic curve isogeny class with Cremona label 36800bc (LMFDB label 36800.t)

• Label: 36800bc
• Number of curves: $2$
• Conductor: $36800$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 36800bc have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 36800bc do not have complex multiplication.

Modular form 36800.2.a.bc

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 36800bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
36800.t2	36800bc1	\([0, 1, 0, -10833, 420463]\)	\(878800/23\)	\(3680000000000\)	\([]\)	\(80640\)	\(1.1927\)	\(\Gamma_0(N)\)-optimal
36800.t1	36800bc2	\([0, 1, 0, -110833, -14079537]\)	\(941054800/12167\)	\(1946720000000000\)	\([]\)	\(241920\)	\(1.7420\)