Elliptic curve isogeny class with LMFDB label 64980.n (Cremona label 64980i)

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

Rank

The elliptic curves in class 64980.n 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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 64980.n do not have complex multiplication.

Modular form 64980.2.a.n

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 LMFDB numbering.

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

Isogeny graph

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

Elliptic curves in class 64980.n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
64980.n1	64980i2	\([0, 0, 0, -4503, -116242]\)	\(7888624/5\)	\(6400270080\)	\([2]\)	\(46080\)	\(0.82283\)
64980.n2	64980i1	\([0, 0, 0, -228, -2527]\)	\(-16384/25\)	\(-2000084400\)	\([2]\)	\(23040\)	\(0.47626\)	\(\Gamma_0(N)\)-optimal