Elliptic curve isogeny class with Cremona label 164934dr (LMFDB label 164934.bj)

• Label: 164934dr
• Number of curves: $4$
• Conductor: $164934$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 164934dr have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 + T\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 164934dr do not have complex multiplication.

Modular form 164934.2.a.dr

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 164934dr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
164934.bj3	164934dr1	\([1, -1, 0, -170676, 27181440]\)	\(6411014266033/296208\)	\(25404611169168\)	\([2]\)	\(884736\)	\(1.6474\)	\(\Gamma_0(N)\)-optimal
164934.bj2	164934dr2	\([1, -1, 0, -179496, 24223212]\)	\(7457162887153/1370924676\)	\(117578891643701796\)	\([2, 2]\)	\(1769472\)	\(1.9939\)
164934.bj4	164934dr3	\([1, -1, 0, 354114, 140443470]\)	\(57258048889007/132611470002\)	\(-11373571382179402242\)	\([2]\)	\(3538944\)	\(2.3405\)
164934.bj1	164934dr4	\([1, -1, 0, -854226, -281429478]\)	\(803760366578833/65593817586\)	\(5625727295932803906\)	\([2]\)	\(3538944\)	\(2.3405\)