Elliptic curve isogeny class with Cremona label 64320ba (LMFDB label 64320.bw)

• Label: 64320ba
• Number of curves: $2$
• Conductor: $64320$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 64320ba have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(67\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 64320ba do not have complex multiplication.

Modular form 64320.2.a.ba

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 64320ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
64320.bw1	64320ba1	\([0, 1, 0, -19041, -938241]\)	\(2912566550041/254390625\)	\(66686976000000\)	\([2]\)	\(184320\)	\(1.3931\)	\(\Gamma_0(N)\)-optimal
64320.bw2	64320ba2	\([0, 1, 0, 20959, -4322241]\)	\(3883959939959/33133870125\)	\(-8685845250048000\)	\([2]\)	\(368640\)	\(1.7397\)