Elliptic curve isogeny class with Cremona label 290400dx (LMFDB label 290400.dx)

• Label: 290400dx
• Number of curves: $4$
• Conductor: $290400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 290400dx have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 290400dx do not have complex multiplication.

Modular form 290400.2.a.dx

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 290400dx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
290400.dx3	290400dx1	\([0, 1, 0, -91758, -10333512]\)	\(48228544/2025\)	\(3587411025000000\)	\([2, 2]\)	\(2211840\)	\(1.7494\)	\(\Gamma_0(N)\)-optimal
290400.dx2	290400dx2	\([0, 1, 0, -243008, 32318988]\)	\(111980168/32805\)	\(464928468840000000\)	\([2]\)	\(4423680\)	\(2.0960\)
290400.dx4	290400dx3	\([0, 1, 0, 44367, -38239137]\)	\(85184/5625\)	\(-637761960000000000\)	\([2]\)	\(4423680\)	\(2.0960\)
290400.dx1	290400dx4	\([0, 1, 0, -1453008, -674623512]\)	\(23937672968/45\)	\(637761960000000\)	\([2]\)	\(4423680\)	\(2.0960\)