Elliptic curve isogeny class with Cremona label 164934bq (LMFDB label 164934.dq)

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

Rank

The elliptic curves in class 164934bq 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 \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 164934.2.a.bq

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 164934bq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
164934.dq3	164934bq1	\([1, -1, 1, -3651269, -2415404995]\)	\(62768149033310713/6915442583808\)	\(593110685411429568768\)	\([2]\)	\(8847360\)	\(2.7194\)	\(\Gamma_0(N)\)-optimal
164934.dq2	164934bq2	\([1, -1, 1, -13847189, 17246407133]\)	\(3423676911662954233/483711578981136\)	\(41486065811997166893456\)	\([2, 2]\)	\(17694720\)	\(3.0660\)
164934.dq1	164934bq3	\([1, -1, 1, -213417329, 1200058712885]\)	\(12534210458299016895673/315581882565708\)	\(27066233925538302778668\)	\([2]\)	\(35389440\)	\(3.4125\)
164934.dq4	164934bq4	\([1, -1, 1, 22588231, 92667726533]\)	\(14861225463775641287/51859390496937804\)	\(-4447778760346617827338284\)	\([2]\)	\(35389440\)	\(3.4125\)