Elliptic curve isogeny class with LMFDB label 29760.cd (Cremona label 29760cn)

• Label: 29760.cd
• Number of curves: $2$
• Conductor: $29760$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 29760.cd have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(31\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 29760.cd do not have complex multiplication.

Modular form 29760.2.a.cd

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 29760.cd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
29760.cd1	29760cn2	\([0, 1, 0, -128801, 6191199]\)	\(901456690969801/457629750000\)	\(119964893184000000\)	\([2]\)	\(368640\)	\(1.9696\)
29760.cd2	29760cn1	\([0, 1, 0, 29919, 762975]\)	\(11298232190519/7472736000\)	\(-1958932905984000\)	\([2]\)	\(184320\)	\(1.6231\)	\(\Gamma_0(N)\)-optimal