Elliptic curve isogeny class with Cremona label 298116bi (LMFDB label 298116.bi)

• Label: 298116bi
• Number of curves: $4$
• Conductor: $298116$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 298116bi have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 298116bi do not have complex multiplication.

Modular form 298116.2.a.bi

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 298116bi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
298116.bi4	298116bi1	\([0, 0, 0, 496860, -45967831]\)	\(2048000/1323\)	\(-8763058462531634352\)	\([2]\)	\(5308416\)	\(2.3237\)	\(\Gamma_0(N)\)-optimal
298116.bi3	298116bi2	\([0, 0, 0, -2111655, -378292642]\)	\(9826000/5103\)	\(540805893687666577152\)	\([2]\)	\(10616832\)	\(2.6702\)
298116.bi2	298116bi3	\([0, 0, 0, -8446620, -9730862323]\)	\(-10061824000/352947\)	\(-2337789263170939342128\)	\([2]\)	\(15925248\)	\(2.8730\)
298116.bi1	298116bi4	\([0, 0, 0, -136263855, -612235744666]\)	\(2640279346000/3087\)	\(327154182601181015808\)	\([2]\)	\(31850496\)	\(3.2195\)