Elliptic curve isogeny class with Cremona label 2960n (LMFDB label 2960.m)

• Label: 2960n
• Number of curves: $4$
• Conductor: $2960$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 2960n have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(37\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 3 T + 3 T^{2}\)	1.3.ad
\(7\)	\( 1 - 5 T + 7 T^{2}\)	1.7.af
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2960n do not have complex multiplication.

Modular form 2960.2.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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 2960n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2960.m3	2960n1	\([0, -1, 0, -1200, 9152]\)	\(46694890801/18944000\)	\(77594624000\)	\([2]\)	\(2304\)	\(0.78735\)	\(\Gamma_0(N)\)-optimal
2960.m4	2960n2	\([0, -1, 0, 3920, 62400]\)	\(1625964918479/1369000000\)	\(-5607424000000\)	\([2]\)	\(4608\)	\(1.1339\)
2960.m1	2960n3	\([0, -1, 0, -84400, 9465792]\)	\(16232905099479601/4052240\)	\(16597975040\)	\([2]\)	\(6912\)	\(1.3367\)
2960.m2	2960n4	\([0, -1, 0, -84080, 9540800]\)	\(-16048965315233521/256572640900\)	\(-1050921537126400\)	\([2]\)	\(13824\)	\(1.6832\)