Elliptic curve isogeny class with LMFDB label 19110.cf (Cremona label 19110cc)

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

Rank

The elliptic curves in class 19110.cf 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 \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 19110.2.a.cf

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 19110.cf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
19110.cf1	19110cc3	\([1, 1, 1, -1255828645, -17129909270293]\)	\(1861772567578966373029167169/9401133413380800000\)	\(1106033944950837739200000\)	\([2]\)	\(8847360\)	\(3.8117\)
19110.cf2	19110cc2	\([1, 1, 1, -79828645, -258072470293]\)	\(478202393398338853167169/32244226560000000000\)	\(3793501010557440000000000\)	\([2, 2]\)	\(4423680\)	\(3.4651\)
19110.cf3	19110cc1	\([1, 1, 1, -15603365, 18841246955]\)	\(3571003510905229697089/762141946675200000\)	\(89665237884390604800000\)	\([4]\)	\(2211840\)	\(3.1185\)	\(\Gamma_0(N)\)-optimal
19110.cf4	19110cc4	\([1, 1, 1, 68566875, -1107429068565]\)	\(303025056761573589385151/4678857421875000000000\)	\(-550462896826171875000000000\)	\([2]\)	\(8847360\)	\(3.8117\)