Elliptic curve isogeny class with Cremona label 19110ch (LMFDB label 19110.bz)

• Label: 19110ch
• Number of curves: $2$
• Conductor: $19110$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 19110ch 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
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 19110ch do not have complex multiplication.

Modular form 19110.2.a.ch

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 19110ch

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
19110.bz2	19110ch1	\([1, 1, 1, -435, 10737]\)	\(-26543596087/134784000\)	\(-46230912000\)	\([2]\)	\(23040\)	\(0.73075\)	\(\Gamma_0(N)\)-optimal
19110.bz1	19110ch2	\([1, 1, 1, -10515, 409905]\)	\(374852148636727/760500000\)	\(260851500000\)	\([2]\)	\(46080\)	\(1.0773\)