Elliptic curve isogeny class with Cremona label 48552c (LMFDB label 48552.q)

• Label: 48552c
• Number of curves: $4$
• Conductor: $48552$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 48552c have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(7\)	\(1 - T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 + 3 T + 13 T^{2}\)	1.13.d
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 + 5 T + 23 T^{2}\)	1.23.f
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 48552c do not have complex multiplication.

Modular form 48552.2.a.c

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 48552c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
48552.q3	48552c1	\([0, -1, 0, -34487, 2476548]\)	\(11745974272/357\)	\(137873794128\)	\([4]\)	\(92160\)	\(1.2353\)	\(\Gamma_0(N)\)-optimal
48552.q2	48552c2	\([0, -1, 0, -35932, 2259220]\)	\(830321872/127449\)	\(787535112059136\)	\([2, 2]\)	\(184320\)	\(1.5819\)
48552.q4	48552c3	\([0, -1, 0, 62328, 12360348]\)	\(1083360092/3306177\)	\(-81718349274842112\)	\([2]\)	\(368640\)	\(1.9285\)
48552.q1	48552c4	\([0, -1, 0, -157312, -21774020]\)	\(17418812548/1753941\)	\(43351932835255296\)	\([2]\)	\(368640\)	\(1.9285\)