Elliptic curve isogeny class with Cremona label 103488em (LMFDB label 103488.ix)

• Label: 103488em
• Number of curves: $2$
• Conductor: $103488$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 103488em 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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 103488.2.a.em

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 103488em

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
103488.ix2	103488em1	\([0, 1, 0, 2679, -74313]\)	\(4410944/7623\)	\(-3673449787392\)	\([2]\)	\(245760\)	\(1.0959\)	\(\Gamma_0(N)\)-optimal
103488.ix1	103488em2	\([0, 1, 0, -18881, -785793]\)	\(193100552/43659\)	\(168310790258688\)	\([2]\)	\(491520\)	\(1.4425\)