Elliptic curve isogeny class with LMFDB label 208080.em (Cremona label 208080i)

• Label: 208080.em
• Number of curves: $2$
• Conductor: $208080$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 208080.em have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 208080.em do not have complex multiplication.

Modular form 208080.2.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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 208080.em

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
208080.em1	208080i2	\([0, 0, 0, -34347072, -77478176464]\)	\(17968412610002944/158203125\)	\(39454652232000000000\)	\([]\)	\(11943936\)	\(2.9267\)
208080.em2	208080i1	\([0, 0, 0, -638112, 11980784]\)	\(115220905984/66430125\)	\(16567166290825728000\)	\([]\)	\(3981312\)	\(2.3774\)	\(\Gamma_0(N)\)-optimal