Elliptic curve isogeny class with Cremona label 134064r (LMFDB label 134064.bq)

• Label: 134064r
• Number of curves: $2$
• Conductor: $134064$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 134064r have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 134064r do not have complex multiplication.

Modular form 134064.2.a.r

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 134064r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
134064.bq1	134064r1	\([0, 0, 0, -2497971, 1212265586]\)	\(4906933498657/1032471552\)	\(362705223917116588032\)	\([2]\)	\(4423680\)	\(2.6597\)	\(\Gamma_0(N)\)-optimal
134064.bq2	134064r2	\([0, 0, 0, 5404749, 7330551410]\)	\(49702082429663/94844496096\)	\(-33318684788136196571136\)	\([2]\)	\(8847360\)	\(3.0063\)