Elliptic curve isogeny class with Cremona label 177450bk (LMFDB label 177450.ia)

• Label: 177450bk
• Number of curves: $2$
• Conductor: $177450$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 177450bk have rank \(0\).

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 \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 177450.2.a.bk

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 177450bk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
177450.ia1	177450bk1	\([1, 0, 0, -179813, 28965117]\)	\(18729968230693/270112500\)	\(9272455664062500\)	\([2]\)	\(2580480\)	\(1.8678\)	\(\Gamma_0(N)\)-optimal
177450.ia2	177450bk2	\([1, 0, 0, -20563, 78491867]\)	\(-28011371653/77519531250\)	\(-2661100158691406250\)	\([2]\)	\(5160960\)	\(2.2144\)