Elliptic curve isogeny class with Cremona label 19110bh (LMFDB label 19110.bg)

• Label: 19110bh
• Number of curves: $4$
• Conductor: $19110$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 19110bh have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 8 T + 23 T^{2}\)	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 19110bh do not have complex multiplication.

Modular form 19110.2.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 Cremona 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 Cremona labels.

Elliptic curves in class 19110bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
19110.bg3	19110bh1	\([1, 0, 1, -663, -6422]\)	\(273359449/9360\)	\(1101194640\)	\([2]\)	\(12288\)	\(0.50684\)	\(\Gamma_0(N)\)-optimal
19110.bg2	19110bh2	\([1, 0, 1, -1643, 16706]\)	\(4165509529/1368900\)	\(161049716100\)	\([2, 2]\)	\(24576\)	\(0.85341\)
19110.bg1	19110bh3	\([1, 0, 1, -23693, 1401446]\)	\(12501706118329/2570490\)	\(302415578010\)	\([2]\)	\(49152\)	\(1.2000\)
19110.bg4	19110bh4	\([1, 0, 1, 4727, 116078]\)	\(99317171591/106616250\)	\(-12543295196250\)	\([2]\)	\(49152\)	\(1.2000\)