Elliptic curve isogeny class with LMFDB label 4176.k (Cremona label 4176b)

• Label: 4176.k
• Number of curves: $2$
• Conductor: $4176$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 4176.k have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(29\)	\(1 + T\)

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.ae
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 4176.k do not have complex multiplication.

Modular form 4176.2.a.k

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 4176.k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4176.k1	4176b2	\([0, 0, 0, -891, 5130]\)	\(1940598/841\)	\(33901369344\)	\([2]\)	\(2688\)	\(0.71675\)
4176.k2	4176b1	\([0, 0, 0, 189, 594]\)	\(37044/29\)	\(-584506368\)	\([2]\)	\(1344\)	\(0.37018\)	\(\Gamma_0(N)\)-optimal