Elliptic curve isogeny class with Cremona label 206310b (LMFDB label 206310.cm)

• Label: 206310b
• Number of curves: $4$
• Conductor: $206310$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 206310b have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 + T\)
\(5\)	\(1 + T\)
\(13\)	\(1 + T\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 206310b do not have complex multiplication.

Modular form 206310.2.a.b

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 206310b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
206310.cm3	206310b1	\([1, 0, 0, -3185, -444375]\)	\(-24137569/561600\)	\(-83136955262400\)	\([2]\)	\(570240\)	\(1.3517\)	\(\Gamma_0(N)\)-optimal
206310.cm2	206310b2	\([1, 0, 0, -108985, -13796335]\)	\(967068262369/4928040\)	\(729526782427560\)	\([2]\)	\(1140480\)	\(1.6983\)
206310.cm4	206310b3	\([1, 0, 0, 28555, 11737437]\)	\(17394111071/411937500\)	\(-60981534024937500\)	\([2]\)	\(1710720\)	\(1.9010\)
206310.cm1	206310b4	\([1, 0, 0, -632695, 183794687]\)	\(189208196468929/10860320250\)	\(1607717163033452250\)	\([2]\)	\(3421440\)	\(2.2476\)