Elliptic curve isogeny class with LMFDB label 89298.ci (Cremona label 89298cs)

• Label: 89298.ci
• Number of curves: $4$
• Conductor: $89298$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 89298.ci have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(11\)	\(1\)
\(41\)	\(1 - T\)

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
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 89298.ci do not have complex multiplication.

Modular form 89298.2.a.ci

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 89298.ci

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
89298.ci1	89298cs4	\([1, -1, 1, -478094, -127112389]\)	\(9357915116017/538002\)	\(694812350257938\)	\([2]\)	\(983040\)	\(1.9114\)
89298.ci2	89298cs2	\([1, -1, 1, -31604, -1737997]\)	\(2703045457/544644\)	\(703390280508036\)	\([2, 2]\)	\(491520\)	\(1.5648\)
89298.ci3	89298cs1	\([1, -1, 1, -9824, 352883]\)	\(81182737/5904\)	\(7624826888976\)	\([2]\)	\(245760\)	\(1.2182\)	\(\Gamma_0(N)\)-optimal
89298.ci4	89298cs3	\([1, -1, 1, 66406, -10441285]\)	\(25076571983/50863698\)	\(-65688836751889362\)	\([2]\)	\(983040\)	\(1.9114\)