Elliptic curve isogeny class with LMFDB label 89232.bk (Cremona label 89232cd)

• Label: 89232.bk
• Number of curves: $4$
• Conductor: $89232$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 89232.bk have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(11\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 89232.bk do not have complex multiplication.

Modular form 89232.2.a.bk

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 89232.bk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
89232.bk1	89232cd4	\([0, 1, 0, -951864, 357128916]\)	\(4824238966273/66\)	\(1304860237824\)	\([2]\)	\(737280\)	\(1.8807\)
89232.bk2	89232cd2	\([0, 1, 0, -59544, 5554836]\)	\(1180932193/4356\)	\(86120775696384\)	\([2, 2]\)	\(368640\)	\(1.5341\)
89232.bk3	89232cd3	\([0, 1, 0, -32504, 10649172]\)	\(-192100033/2371842\)	\(-46892762366681088\)	\([2]\)	\(737280\)	\(1.8807\)
89232.bk4	89232cd1	\([0, 1, 0, -5464, -4588]\)	\(912673/528\)	\(10438881902592\)	\([2]\)	\(184320\)	\(1.1875\)	\(\Gamma_0(N)\)-optimal