Elliptic curve isogeny class with Cremona label 316050hm (LMFDB label 316050.hm)

• Label: 316050hm
• Number of curves: $4$
• Conductor: $316050$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 316050hm have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1\)
\(43\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.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 316050hm do not have complex multiplication.

Modular form 316050.2.a.hm

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 316050hm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
316050.hm4	316050hm1	\([1, 0, 0, -131713, -5465083]\)	\(137467988281/72562500\)	\(133389149414062500\)	\([2]\)	\(4147200\)	\(1.9776\)	\(\Gamma_0(N)\)-optimal
316050.hm3	316050hm2	\([1, 0, 0, -1662963, -824683833]\)	\(276670733768281/336980250\)	\(619459209878906250\)	\([2]\)	\(8294400\)	\(2.3241\)
316050.hm2	316050hm3	\([1, 0, 0, -6103588, 5803331792]\)	\(13679527032530281/381633600\)	\(701543928225000000\)	\([2]\)	\(12441600\)	\(2.5269\)
316050.hm1	316050hm4	\([1, 0, 0, -6348588, 5312106792]\)	\(15393836938735081/2275690697640\)	\(4183323982603880625000\)	\([2]\)	\(24883200\)	\(2.8734\)