Elliptic curve isogeny class with LMFDB label 5040.v (Cremona label 5040bk)

• Label: 5040.v
• Number of curves: $3$
• Conductor: $5040$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 5040.v have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 5040.v do not have complex multiplication.

Modular form 5040.2.a.v

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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 5040.v

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5040.v1	5040bk3	\([0, 0, 0, -18912, -1047184]\)	\(-250523582464/13671875\)	\(-40824000000000\)	\([]\)	\(12960\)	\(1.3699\)
5040.v2	5040bk1	\([0, 0, 0, -192, 1136]\)	\(-262144/35\)	\(-104509440\)	\([]\)	\(1440\)	\(0.27130\)	\(\Gamma_0(N)\)-optimal
5040.v3	5040bk2	\([0, 0, 0, 1248, -2896]\)	\(71991296/42875\)	\(-128024064000\)	\([]\)	\(4320\)	\(0.82061\)