Elliptic curve isogeny class with Cremona label 190575co (LMFDB label 190575.cr)

• Label: 190575co
• Number of curves: $3$
• Conductor: $190575$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 190575co have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 190575co do not have complex multiplication.

Modular form 190575.2.a.co

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 190575co

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
190575.cr1	190575co1	\([0, 0, 1, -2432100, 1459899031]\)	\(-78843215872/539\)	\(-10876581801421875\)	\([]\)	\(2592000\)	\(2.2580\)	\(\Gamma_0(N)\)-optimal
190575.cr2	190575co2	\([0, 0, 1, -1343100, 2770102156]\)	\(-13278380032/156590819\)	\(-3159875421530884546875\)	\([]\)	\(7776000\)	\(2.8073\)
190575.cr3	190575co3	\([0, 0, 1, 11997150, -71701843469]\)	\(9463555063808/115539436859\)	\(-2331491904057757333921875\)	\([]\)	\(23328000\)	\(3.3566\)