Elliptic curve isogeny class with LMFDB label 178464.bq (Cremona label 178464e)

• Label: 178464.bq
• Number of curves: $4$
• Conductor: $178464$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 178464.bq have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(11\)	\(1 - T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 178464.bq do not have complex multiplication.

Modular form 178464.2.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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 178464.bq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
178464.bq1	178464e2	\([0, 1, 0, -53003864, 148510701756]\)	\(6663712298552914184/29403\)	\(72664404493824\)	\([2]\)	\(8847360\)	\(2.7463\)
178464.bq2	178464e4	\([0, 1, 0, -3518129, 2015554815]\)	\(243578556889408/52089208083\)	\(1029835400715866714112\)	\([2]\)	\(8847360\)	\(2.7463\)
178464.bq3	178464e1	\([0, 1, 0, -3312794, 2319573816]\)	\(13015685560572352/864536409\)	\(267068935666488384\)	\([2, 2]\)	\(4423680\)	\(2.3997\)	\(\Gamma_0(N)\)-optimal
178464.bq4	178464e3	\([0, 1, 0, -3108304, 2618619992]\)	\(-1343891598641864/421900912521\)	\(-1042654782292262650368\)	\([2]\)	\(8847360\)	\(2.7463\)