Elliptic curve isogeny class with Cremona label 29120cf (LMFDB label 29120.bj)

• Label: 29120cf
• Number of curves: $4$
• Conductor: $29120$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 29120cf have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 29120cf do not have complex multiplication.

Modular form 29120.2.a.cf

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 29120cf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
29120.bj3	29120cf1	\([0, 0, 0, -128012, -16127984]\)	\(884984855328729/83492864000\)	\(21887153340416000\)	\([2]\)	\(184320\)	\(1.8735\)	\(\Gamma_0(N)\)-optimal
29120.bj2	29120cf2	\([0, 0, 0, -455692, 100395024]\)	\(39920686684059609/6492304000000\)	\(1701918539776000000\)	\([2, 2]\)	\(368640\)	\(2.2201\)
29120.bj4	29120cf3	\([0, 0, 0, 824308, 562731024]\)	\(236293804275620391/658593925444000\)	\(-172646445991591936000\)	\([2]\)	\(737280\)	\(2.5667\)
29120.bj1	29120cf4	\([0, 0, 0, -6978572, 7095531536]\)	\(143378317900125424089/4976562500000\)	\(1304576000000000000\)	\([4]\)	\(737280\)	\(2.5667\)