Elliptic curve isogeny class with Cremona label 342720md (LMFDB label 342720.md)

• Label: 342720md
• Number of curves: $6$
• Conductor: $342720$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 342720md have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1 - T\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 342720md do not have complex multiplication.

Modular form 342720.2.a.md

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 342720md

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
342720.md5	342720md1	\([0, 0, 0, 1762548, 874812944]\)	\(3168685387909439/3563732336640\)	\(-681039855199337840640\)	\([2]\)	\(14155776\)	\(2.6840\)	\(\Gamma_0(N)\)-optimal
342720.md4	342720md2	\([0, 0, 0, -10033932, 8240535056]\)	\(584614687782041281/184812061593600\)	\(35318134971232262553600\)	\([2, 2]\)	\(28311552\)	\(3.0305\)
342720.md2	342720md3	\([0, 0, 0, -145509132, 675482990096]\)	\(1782900110862842086081/328139630024640\)	\(62708459841247657328640\)	\([2]\)	\(56623104\)	\(3.3771\)
342720.md3	342720md4	\([0, 0, 0, -63302412, -187595704816]\)	\(146796951366228945601/5397929064360000\)	\(1031560308436091535360000\)	\([2, 2]\)	\(56623104\)	\(3.3771\)
342720.md6	342720md5	\([0, 0, 0, 24825588, -669021343216]\)	\(8854313460877886399/1016927675429790600\)	\(-194337905151395062716825600\)	\([2]\)	\(113246208\)	\(3.7237\)
342720.md1	342720md6	\([0, 0, 0, -1003726092, -12239689418224]\)	\(585196747116290735872321/836876053125000\)	\(159929504295321600000000\)	\([2]\)	\(113246208\)	\(3.7237\)