Elliptic curve isogeny class with Cremona label 98838bl (LMFDB label 98838.bh)

• Label: 98838bl
• Number of curves: $3$
• Conductor: $98838$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 98838bl have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(17\)	\(1\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 98838bl do not have complex multiplication.

Modular form 98838.2.a.bl

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 98838bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
98838.bh2	98838bl1	\([1, -1, 1, -40370, -3112887]\)	\(-413493625/152\)	\(-2674635745752\)	\([]\)	\(302400\)	\(1.3525\)	\(\Gamma_0(N)\)-optimal
98838.bh3	98838bl2	\([1, -1, 1, 24655, -11873055]\)	\(94196375/3511808\)	\(-61794784269854208\)	\([]\)	\(907200\)	\(1.9018\)
98838.bh1	98838bl3	\([1, -1, 1, -222440, 324868011]\)	\(-69173457625/2550136832\)	\(-44872941627802386432\)	\([]\)	\(2721600\)	\(2.4511\)