Elliptic curve isogeny class with LMFDB label 5610.bh (Cremona label 5610bi)

• Label: 5610.bh
• Number of curves: $4$
• Conductor: $5610$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 5610.bh have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(11\)	\(1 - T\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 5610.bh do not have complex multiplication.

Modular form 5610.2.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 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 5610.bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5610.bh1	5610bi3	\([1, 0, 0, -19971, -1059399]\)	\(880895732965860529/26454814115400\)	\(26454814115400\)	\([2]\)	\(18432\)	\(1.3521\)
5610.bh2	5610bi2	\([1, 0, 0, -2971, 38801]\)	\(2900285849172529/1019696040000\)	\(1019696040000\)	\([2, 2]\)	\(9216\)	\(1.0055\)
5610.bh3	5610bi1	\([1, 0, 0, -2651, 52305]\)	\(2060455000819249/517017600\)	\(517017600\)	\([2]\)	\(4608\)	\(0.65894\)	\(\Gamma_0(N)\)-optimal
5610.bh4	5610bi4	\([1, 0, 0, 8909, 274025]\)	\(78200142092480591/77517928125000\)	\(-77517928125000\)	\([2]\)	\(18432\)	\(1.3521\)