Elliptic curve isogeny class with LMFDB label 47040.ep (Cremona label 47040fv)

• Label: 47040.ep
• Number of curves: $4$
• Conductor: $47040$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 47040.ep have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 47040.ep do not have complex multiplication.

Modular form 47040.2.a.ep

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 47040.ep

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
47040.ep1	47040fv4	\([0, 1, 0, -732321, -241456545]\)	\(5633270409316/14175\)	\(109292720947200\)	\([2]\)	\(393216\)	\(1.9320\)
47040.ep2	47040fv3	\([0, 1, 0, -128641, 12956159]\)	\(30534944836/8203125\)	\(63248102400000000\)	\([2]\)	\(393216\)	\(1.9320\)
47040.ep3	47040fv2	\([0, 1, 0, -46321, -3688945]\)	\(5702413264/275625\)	\(531284060160000\)	\([2, 2]\)	\(196608\)	\(1.5854\)
47040.ep4	47040fv1	\([0, 1, 0, 1699, -221901]\)	\(4499456/180075\)	\(-21694099123200\)	\([2]\)	\(98304\)	\(1.2389\)	\(\Gamma_0(N)\)-optimal