Elliptic curve isogeny class with Cremona label 103488r (LMFDB label 103488.dm)

• Label: 103488r
• Number of curves: $4$
• Conductor: $103488$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 103488r have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 103488r do not have complex multiplication.

Modular form 103488.2.a.r

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 103488r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
103488.dm3	103488r1	\([0, -1, 0, -2417, 44913]\)	\(810448/33\)	\(63609520128\)	\([2]\)	\(98304\)	\(0.83879\)	\(\Gamma_0(N)\)-optimal
103488.dm2	103488r2	\([0, -1, 0, -6337, -133055]\)	\(3650692/1089\)	\(8396456656896\)	\([2, 2]\)	\(196608\)	\(1.1854\)
103488.dm4	103488r3	\([0, -1, 0, 17183, -909215]\)	\(36382894/43923\)	\(-677314170322944\)	\([2]\)	\(393216\)	\(1.5319\)
103488.dm1	103488r4	\([0, -1, 0, -92577, -10809567]\)	\(5690357426/891\)	\(13739656347648\)	\([2]\)	\(393216\)	\(1.5319\)