Elliptic curve isogeny class with LMFDB label 279312.br (Cremona label 279312br)

• Label: 279312.br
• Number of curves: $2$
• Conductor: $279312$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 279312.br have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(11\)	\(1 + T\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(13\)	\( 1 + 7 T + 13 T^{2}\)	1.13.h
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 279312.br do not have complex multiplication.

Modular form 279312.2.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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 279312.br

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
279312.br1	279312br2	\([0, -1, 0, -40686624, -99869071104]\)	\(12284337086925553/1165987944\)	\(707002621351207796736\)	\([]\)	\(32845824\)	\(3.0376\)
279312.br2	279312br1	\([0, -1, 0, -1075104, 227411712]\)	\(226646274673/94431744\)	\(57259160260036263936\)	\([]\)	\(10948608\)	\(2.4883\)	\(\Gamma_0(N)\)-optimal