Elliptic curve isogeny class with Cremona label 64980j (LMFDB label 64980.m)

• Label: 64980j
• Number of curves: $2$
• Conductor: $64980$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 64980j have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(23\)	\( 1 - 4 T + 23 T^{2}\)	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 64980j do not have complex multiplication.

Modular form 64980.2.a.j

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 64980j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
64980.m2	64980j1	\([0, 0, 0, -82308, 17332693]\)	\(-16384/25\)	\(-94095732672356400\)	\([2]\)	\(437760\)	\(1.9485\)	\(\Gamma_0(N)\)-optimal
64980.m1	64980j2	\([0, 0, 0, -1625583, 797303878]\)	\(7888624/5\)	\(301106344551540480\)	\([2]\)	\(875520\)	\(2.2951\)