Elliptic curve isogeny class with Cremona label 29040bp (LMFDB label 29040.dp)

• Label: 29040bp
• Number of curves: $4$
• Conductor: $29040$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 29040bp have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 29040bp do not have complex multiplication.

Modular form 29040.2.a.bp

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 29040bp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
29040.dp4	29040bp1	\([0, 1, 0, -6695, -37380]\)	\(1171019776/658845\)	\(18674945712720\)	\([2]\)	\(61440\)	\(1.2366\)	\(\Gamma_0(N)\)-optimal
29040.dp2	29040bp2	\([0, 1, 0, -79900, -8704852]\)	\(124386546256/245025\)	\(111123643910400\)	\([2, 2]\)	\(122880\)	\(1.5832\)
29040.dp3	29040bp3	\([0, 1, 0, -53280, -14571900]\)	\(-9220796644/45106875\)	\(-81827410515840000\)	\([4]\)	\(245760\)	\(1.9298\)
29040.dp1	29040bp4	\([0, 1, 0, -1277800, -556384732]\)	\(127191074376964/495\)	\(897968839680\)	\([2]\)	\(245760\)	\(1.9298\)