Elliptic curve isogeny class with Cremona label 204490cy (LMFDB label 204490.bc)

• Label: 204490cy
• Number of curves: $2$
• Conductor: $204490$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 204490cy have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 204490cy do not have complex multiplication.

Modular form 204490.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 204490cy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
204490.bc1	204490cy1	\([1, 0, 1, -12423194, -17127753524]\)	\(-1693700041/32000\)	\(-4006239824029702688000\)	\([]\)	\(13685760\)	\(2.9398\)	\(\Gamma_0(N)\)-optimal
204490.bc2	204490cy2	\([1, 0, 1, 49435031, -80074683284]\)	\(106718863559/83886080\)	\(-10502117324304423814430720\)	\([]\)	\(41057280\)	\(3.4891\)