Elliptic curve isogeny class with Cremona label 177450ir (LMFDB label 177450.bn)

• Label: 177450ir
• Number of curves: $4$
• Conductor: $177450$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 177450ir have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 177450ir do not have complex multiplication.

Modular form 177450.2.a.ir

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 177450ir

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
177450.bn3	177450ir1	\([1, 1, 0, -3204750, -992880000]\)	\(48264326765929/22299191460\)	\(1681780281747674062500\)	\([2]\)	\(13934592\)	\(2.7675\)	\(\Gamma_0(N)\)-optimal
177450.bn4	177450ir2	\([1, 1, 0, 11287000, -7470692250]\)	\(2108526614950391/1540302022350\)	\(-116167869753080955468750\)	\([2]\)	\(27869184\)	\(3.1141\)
177450.bn1	177450ir3	\([1, 1, 0, -217475625, -1234513042875]\)	\(15082569606665230489/7751016000\)	\(584573027936625000000\)	\([2]\)	\(41803776\)	\(3.3168\)
177450.bn2	177450ir4	\([1, 1, 0, -216292625, -1248606121875]\)	\(-14837772556740428569/342100087875000\)	\(-25800809110247513671875000\)	\([2]\)	\(83607552\)	\(3.6634\)