Elliptic curve isogeny class with LMFDB label 2480.c (Cremona label 2480l)

• Label: 2480.c
• Number of curves: $2$
• Conductor: $2480$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 2480.c have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(31\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2480.c do not have complex multiplication.

Modular form 2480.2.a.c

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 2480.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2480.c1	2480l2	\([0, 1, 0, -17056, 851700]\)	\(133974081659809/192200\)	\(787251200\)	\([2]\)	\(2304\)	\(0.97809\)
2480.c2	2480l1	\([0, 1, 0, -1056, 13300]\)	\(-31824875809/1240000\)	\(-5079040000\)	\([2]\)	\(1152\)	\(0.63151\)	\(\Gamma_0(N)\)-optimal