Elliptic curve isogeny class with Cremona label 48510da (LMFDB label 48510.cp)

• Label: 48510da
• Number of curves: $4$
• Conductor: $48510$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 48510da have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 48510da do not have complex multiplication.

Modular form 48510.2.a.da

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 48510da

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
48510.cp3	48510da1	\([1, -1, 1, -380813, -90174283]\)	\(71210194441849/165580800\)	\(14201222928076800\)	\([2]\)	\(589824\)	\(1.9799\)	\(\Gamma_0(N)\)-optimal
48510.cp2	48510da2	\([1, -1, 1, -521933, -17187019]\)	\(183337554283129/104587560000\)	\(8970069326054760000\)	\([2, 2]\)	\(1179648\)	\(2.3265\)
48510.cp4	48510da3	\([1, -1, 1, 2071147, -138543163]\)	\(11456208593737991/6725709375000\)	\(-576838004067084375000\)	\([2]\)	\(2359296\)	\(2.6731\)
48510.cp1	48510da4	\([1, -1, 1, -5372933, 4773660581]\)	\(200005594092187129/1027287538200\)	\(88106467303053322200\)	\([2]\)	\(2359296\)	\(2.6731\)