Elliptic curve isogeny class with Cremona label 178464by (LMFDB label 178464.cm)

• Label: 178464by
• Number of curves: $2$
• Conductor: $178464$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 178464by have rank \(0\).

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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 178464.2.a.by

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 178464by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
178464.cm2	178464by1	\([0, 1, 0, -147762, -23013600]\)	\(-1154981015488/69090879\)	\(-21343262500807104\)	\([2]\)	\(2128896\)	\(1.8887\)	\(\Gamma_0(N)\)-optimal
178464.cm1	178464by2	\([0, 1, 0, -2397152, -1429332228]\)	\(616425416371016/2024451\)	\(5003078813111808\)	\([2]\)	\(4257792\)	\(2.2352\)