Elliptic curve isogeny class with Cremona label 40898bh (LMFDB label 40898.bu)

• Label: 40898bh
• Number of curves: $2$
• Conductor: $40898$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 40898bh have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(11\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 40898bh do not have complex multiplication.

Modular form 40898.2.a.bh

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 40898bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
40898.bu2	40898bh1	\([1, 0, 0, -1288713, -275717287]\)	\(1890625/832\)	\(104162235424772269888\)	\([]\)	\(1241856\)	\(2.5369\)	\(\Gamma_0(N)\)-optimal
40898.bu1	40898bh2	\([1, 0, 0, -50775293, 139246746365]\)	\(115636266625/8788\)	\(1100213611674157100692\)	\([]\)	\(3725568\)	\(3.0862\)