Elliptic curve isogeny class with Cremona label 279864bx (LMFDB label 279864.bx)

• Label: 279864bx
• Number of curves: $4$
• Conductor: $279864$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 279864bx have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(13\)	\(1\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 279864bx do not have complex multiplication.

Modular form 279864.2.a.bx

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 279864bx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
279864.bx3	279864bx1	\([0, 0, 0, -315354, 68161925]\)	\(61604313088/621\)	\(34962238009296\)	\([2]\)	\(1769472\)	\(1.7577\)	\(\Gamma_0(N)\)-optimal
279864.bx2	279864bx2	\([0, 0, 0, -322959, 64701650]\)	\(4135597648/385641\)	\(347384796860365056\)	\([2, 2]\)	\(3538944\)	\(2.1043\)
279864.bx4	279864bx3	\([0, 0, 0, 376701, 306644078]\)	\(1640689628/12223143\)	\(-44042350767166282752\)	\([2]\)	\(7077888\)	\(2.4509\)
279864.bx1	279864bx4	\([0, 0, 0, -1144299, -398698378]\)	\(45989074372/7555707\)	\(27224675190982683648\)	\([2]\)	\(7077888\)	\(2.4509\)