Elliptic curve isogeny class with Cremona label 66654bl (LMFDB label 66654.br)

• Label: 66654bl
• Number of curves: $4$
• Conductor: $66654$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 66654bl have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(7\)	\(1 - T\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 66654bl do not have complex multiplication.

Modular form 66654.2.a.bl

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 66654bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
66654.br4	66654bl1	\([1, -1, 1, 22112365, 281857562291]\)	\(11079872671250375/324440155855872\)	\(-35012985649679051627461632\)	\([2]\)	\(20275200\)	\(3.5815\)	\(\Gamma_0(N)\)-optimal
66654.br2	66654bl2	\([1, -1, 1, -533210675, 4515418290035]\)	\(155355156733986861625/8291568305839392\)	\(894810820626826390449886752\)	\([2]\)	\(40550400\)	\(3.9281\)
66654.br3	66654bl3	\([1, -1, 1, -199631210, -7743964870231]\)	\(-8152944444844179625/235342826399858688\)	\(-25397765519363422006938697728\)	\([2]\)	\(60825600\)	\(4.1308\)
66654.br1	66654bl4	\([1, -1, 1, -7220011370, -234985246193239]\)	\(385693937170561837203625/2159357734550274048\)	\(233033920147415182905306021888\)	\([2]\)	\(121651200\)	\(4.4774\)