Elliptic curve isogeny class with Cremona label 47190cy (LMFDB label 47190.cs)

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

Rank

The elliptic curves in class 47190cy 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 \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 47190.2.a.cy

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 47190cy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
47190.cs4	47190cy1	\([1, 0, 0, 483695, -4837975]\)	\(7064514799444439/4094064000000\)	\(-7252884113904000000\)	\([2]\)	\(1036800\)	\(2.3085\)	\(\Gamma_0(N)\)-optimal
47190.cs3	47190cy2	\([1, 0, 0, -1936305, -39201975]\)	\(453198971846635561/261896250564000\)	\(463965183545410404000\)	\([2]\)	\(2073600\)	\(2.6550\)
47190.cs2	47190cy3	\([1, 0, 0, -6458680, 6814452800]\)	\(-16818951115904497561/1592332281446400\)	\(-2820913768851465830400\)	\([2]\)	\(3110400\)	\(2.8578\)
47190.cs1	47190cy4	\([1, 0, 0, -105581880, 417561168960]\)	\(73474353581350183614361/576510977802240\)	\(1021324364346314096640\)	\([2]\)	\(6220800\)	\(3.2043\)