Elliptic curve isogeny class with LMFDB label 47190.ci (Cremona label 47190cq)

• Label: 47190.ci
• Number of curves: $4$
• Conductor: $47190$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 47190.ci have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(11\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 47190.ci do not have complex multiplication.

Modular form 47190.2.a.ci

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 47190.ci

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
47190.ci1	47190cq4	\([1, 0, 0, -10469951, -13040497095]\)	\(71647584155243142409/10140000\)	\(17963628540000\)	\([2]\)	\(1843200\)	\(2.3962\)
47190.ci2	47190cq3	\([1, 0, 0, -751231, -139542919]\)	\(26465989780414729/10571870144160\)	\(18728712844458233760\)	\([2]\)	\(1843200\)	\(2.3962\)
47190.ci3	47190cq2	\([1, 0, 0, -654431, -203760039]\)	\(17496824387403529/6580454400\)	\(11657676377318400\)	\([2, 2]\)	\(921600\)	\(2.0496\)
47190.ci4	47190cq1	\([1, 0, 0, -34911, -4150695]\)	\(-2656166199049/2658140160\)	\(-4709057439989760\)	\([2]\)	\(460800\)	\(1.7031\)	\(\Gamma_0(N)\)-optimal