Elliptic curve isogeny class with Cremona label 27200br (LMFDB label 27200.bp)

• Label: 27200br
• Number of curves: $4$
• Conductor: $27200$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 27200br have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 27200br do not have complex multiplication.

Modular form 27200.2.a.br

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 27200br

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
27200.bp3	27200br1	\([0, 0, 0, -1100, -6000]\)	\(35937/17\)	\(69632000000\)	\([2]\)	\(16384\)	\(0.77466\)	\(\Gamma_0(N)\)-optimal
27200.bp2	27200br2	\([0, 0, 0, -9100, 330000]\)	\(20346417/289\)	\(1183744000000\)	\([2, 2]\)	\(32768\)	\(1.1212\)
27200.bp4	27200br3	\([0, 0, 0, -1100, 890000]\)	\(-35937/83521\)	\(-342102016000000\)	\([2]\)	\(65536\)	\(1.4678\)
27200.bp1	27200br4	\([0, 0, 0, -145100, 21274000]\)	\(82483294977/17\)	\(69632000000\)	\([2]\)	\(65536\)	\(1.4678\)