Elliptic curve isogeny class with Cremona label 50864bd (LMFDB label 50864.bl)

• Label: 50864bd
• Number of curves: $2$
• Conductor: $50864$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 50864bd have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(11\)	\(1 + T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 50864bd do not have complex multiplication.

Modular form 50864.2.a.bd

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 50864bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
50864.bl2	50864bd1	\([0, 1, 0, 771, 9719]\)	\(8192/11\)	\(-67971394304\)	\([]\)	\(36864\)	\(0.76431\)	\(\Gamma_0(N)\)-optimal
50864.bl1	50864bd2	\([0, 1, 0, -22349, 1285943]\)	\(-199794688/1331\)	\(-8224538710784\)	\([]\)	\(110592\)	\(1.3136\)