Elliptic curve isogeny class with LMFDB label 103488.hr (Cremona label 103488ht)

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

Rank

The elliptic curves in class 103488.hr 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.ac
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 103488.2.a.hr

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 103488.hr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
103488.hr1	103488ht4	\([0, 1, 0, -1103937, -446809665]\)	\(4824238966273/66\)	\(2035504644096\)	\([2]\)	\(884736\)	\(1.9177\)
103488.hr2	103488ht2	\([0, 1, 0, -69057, -6985665]\)	\(1180932193/4356\)	\(134343306510336\)	\([2, 2]\)	\(442368\)	\(1.5711\)
103488.hr3	103488ht3	\([0, 1, 0, -37697, -13326657]\)	\(-192100033/2371842\)	\(-73149930394877952\)	\([2]\)	\(884736\)	\(1.9177\)
103488.hr4	103488ht1	\([0, 1, 0, -6337, 1343]\)	\(912673/528\)	\(16284037152768\)	\([2]\)	\(221184\)	\(1.2246\)	\(\Gamma_0(N)\)-optimal