Elliptic curve isogeny class with Cremona label 254898bx (LMFDB label 254898.bx)

• Label: 254898bx
• Number of curves: $2$
• Conductor: $254898$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 254898bx have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(7\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 254898bx do not have complex multiplication.

Modular form 254898.2.a.bx

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 254898bx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
254898.bx1	254898bx1	\([1, -1, 0, -335022, 70590932]\)	\(9869198625/614656\)	\(258996954851244288\)	\([2]\)	\(3145728\)	\(2.0927\)	\(\Gamma_0(N)\)-optimal
254898.bx2	254898bx2	\([1, -1, 0, 264738, 295261028]\)	\(4869777375/92236816\)	\(-38865730537364845968\)	\([2]\)	\(6291456\)	\(2.4393\)