Elliptic curve isogeny class with LMFDB label 177870.cx (Cremona label 177870gl)

• Label: 177870.cx
• Number of curves: $2$
• Conductor: $177870$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 177870.cx have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 177870.cx do not have complex multiplication.

Modular form 177870.2.a.cx

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 177870.cx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
177870.cx1	177870gl1	\([1, 0, 1, -89059, -3917014]\)	\(1092727/540\)	\(38603993240084580\)	\([2]\)	\(1881600\)	\(1.8758\)	\(\Gamma_0(N)\)-optimal
177870.cx2	177870gl2	\([1, 0, 1, 325971, -29980898]\)	\(53582633/36450\)	\(-2605769543705709150\)	\([2]\)	\(3763200\)	\(2.2223\)