Elliptic curve isogeny class with Cremona label 50820w (LMFDB label 50820.v)

• Label: 50820w
• Number of curves: $2$
• Conductor: $50820$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 50820w have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1 - T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 50820w do not have complex multiplication.

Modular form 50820.2.a.w

Isogeny matrix

The \((i,j)\)-th 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.

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

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 50820w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
50820.v1	50820w1	\([0, 1, 0, -645, -2532]\)	\(1048576/525\)	\(14881112400\)	\([2]\)	\(33600\)	\(0.64473\)	\(\Gamma_0(N)\)-optimal
50820.v2	50820w2	\([0, 1, 0, 2380, -17052]\)	\(3286064/2205\)	\(-1000010753280\)	\([2]\)	\(67200\)	\(0.99131\)