Elliptic curve isogeny class with Cremona label 254800w (LMFDB label 254800.w)

• Label: 254800w
• Number of curves: $2$
• Conductor: $254800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 254800w have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 254800w do not have complex multiplication.

Modular form 254800.2.a.w

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 Cremona numbering.

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

Isogeny graph

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

Elliptic curves in class 254800w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
254800.w1	254800w1	\([0, 1, 0, -24908, -1497812]\)	\(3631696/65\)	\(30588740000000\)	\([2]\)	\(589824\)	\(1.3833\)	\(\Gamma_0(N)\)-optimal
254800.w2	254800w2	\([0, 1, 0, -408, -4290812]\)	\(-4/4225\)	\(-7953072400000000\)	\([2]\)	\(1179648\)	\(1.7299\)