Elliptic curve isogeny class with Cremona label 48960en (LMFDB label 48960.j)

• Label: 48960en
• Number of curves: $4$
• Conductor: $48960$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 48960en have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(17\)	\(1 + T\)

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.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 48960en do not have complex multiplication.

Modular form 48960.2.a.en

Isogeny matrix

The \(i,j\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 48960en

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
48960.j3	48960en1	\([0, 0, 0, -3063, 65248]\)	\(68117264704/255\)	\(11897280\)	\([2]\)	\(40960\)	\(0.57293\)	\(\Gamma_0(N)\)-optimal
48960.j2	48960en2	\([0, 0, 0, -3108, 63232]\)	\(1111934656/65025\)	\(194163609600\)	\([2, 2]\)	\(81920\)	\(0.91950\)
48960.j4	48960en3	\([0, 0, 0, 2292, 259792]\)	\(55742968/1252815\)	\(-29927084359680\)	\([2]\)	\(163840\)	\(1.2661\)
48960.j1	48960en4	\([0, 0, 0, -9228, -262352]\)	\(3638052872/860625\)	\(20558499840000\)	\([2]\)	\(163840\)	\(1.2661\)