Elliptic curve isogeny class with LMFDB label 2760.g (Cremona label 2760g)

• Label: 2760.g
• Number of curves: $2$
• Conductor: $2760$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 2760.g have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(23\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 2760.g do not have complex multiplication.

Modular form 2760.2.a.g

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 2760.g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2760.g1	2760g2	\([0, -1, 0, -960, -9108]\)	\(47825527682/8926875\)	\(18282240000\)	\([2]\)	\(2304\)	\(0.68713\)
2760.g2	2760g1	\([0, -1, 0, 120, -900]\)	\(185073116/419175\)	\(-429235200\)	\([2]\)	\(1152\)	\(0.34056\)	\(\Gamma_0(N)\)-optimal