Elliptic curves over $\Q$ of conductor 1922

Results (12 matches)

 

Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
1922.a1	1922b2	1922.a	1922b	$2$	$3$	\( 2 \cdot 31^{2} \)	\( 2^{6} \cdot 31^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.2.0.1, 3.4.0.1	2Cn, 3B	$744$	$96$	$2$	$0.301445788$	$1$		$18$	$360$	$-0.063208$	$467145913/64$	$0.96361$	$3.54843$	$[1, 1, 0, -159, 709]$	\(y^2+xy=x^3+x^2-159x+709\)	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 24.16.0.a.2, 62.6.0.a.1, $\ldots$	$[(6, 1), (22, 81)]$
1922.a2	1922b1	1922.a	1922b	$2$	$3$	\( 2 \cdot 31^{2} \)	\( 2^{2} \cdot 31^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.2.0.1, 3.4.0.1	2Cn, 3B	$744$	$96$	$2$	$0.301445788$	$1$		$16$	$120$	$-0.612514$	$10633/4$	$0.82178$	$2.13456$	$[1, 1, 0, -4, -4]$	\(y^2+xy=x^3+x^2-4x-4\)	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 24.16.0.a.1, 62.6.0.a.1, $\ldots$	$[(-2, 2), (-1, 1)]$
1922.b1	1922a2	1922.b	1922a	$2$	$3$	\( 2 \cdot 31^{2} \)	\( 2^{6} \cdot 31^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.4.0.1, 3.8.0.2	2Cn, 3B.1.2	$744$	$96$	$2$	$1.526140046$	$1$		$2$	$11160$	$1.653786$	$467145913/64$	$0.96361$	$6.27341$	$[1, 0, 1, -153300, -23112558]$	\(y^2+xy+y=x^3-153300x-23112558\)	2.2.0.a.1, 3.8.0-3.a.1.1, 6.16.0-6.a.1.1, 8.4.0-2.a.1.1, 24.32.0-24.a.2.4, $\ldots$	$[(1041, 30231)]$
1922.b2	1922a1	1922.b	1922a	$2$	$3$	\( 2 \cdot 31^{2} \)	\( 2^{2} \cdot 31^{8} \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.4.0.1, 3.8.0.1	2Cn, 3B.1.1	$744$	$96$	$2$	$4.578420139$	$1$		$4$	$3720$	$1.104479$	$10633/4$	$0.82178$	$4.85955$	$[1, 0, 1, -4345, 64840]$	\(y^2+xy+y=x^3-4345x+64840\)	2.2.0.a.1, 3.8.0-3.a.1.2, 6.16.0-6.a.1.2, 8.4.0-2.a.1.1, 24.32.0-24.a.1.7, $\ldots$	$[(119, 1052)]$
1922.c1	1922e2	1922.c	1922e	$2$	$7$	\( 2 \cdot 31^{2} \)	\( 2^{2} \cdot 31^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 7$	2.2.0.1, 7.8.0.1	2Cn, 7B	$1736$	$576$	$16$	$0.815886613$	$1$		$0$	$5880$	$1.052927$	$51181724570498001/4$	$1.10803$	$5.99675$	$[1, -1, 1, -76332, 8136267]$	\(y^2+xy+y=x^3-x^2-76332x+8136267\)	2.2.0.a.1, 7.8.0.a.1, 14.48.0.b.1, 56.96.2.a.1, 62.6.0.a.1, $\ldots$	$[(639/2, -641/2)]$
1922.c2	1922e1	1922.c	1922e	$2$	$7$	\( 2 \cdot 31^{2} \)	\( 2^{14} \cdot 31^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 7$	2.2.0.1, 7.8.0.1	2Cn, 7B	$1736$	$576$	$16$	$0.116555230$	$1$		$10$	$840$	$0.079973$	$42396561/16384$	$1.03599$	$3.23108$	$[1, -1, 1, -72, -117]$	\(y^2+xy+y=x^3-x^2-72x-117\)	2.2.0.a.1, 7.8.0.a.1, 14.48.0.b.2, 56.96.2.a.2, 62.6.0.a.1, $\ldots$	$[(-3, 9)]$
1922.d1	1922d3	1922.d	1922d	$4$	$4$	\( 2 \cdot 31^{2} \)	\( 2 \cdot 31^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.61	2B	$248$	$48$	$0$	$37.78228561$	$1$		$0$	$7680$	$1.608915$	$3999236143617/62$	$1.07559$	$6.56266$	$[1, -1, 1, -317791, -68874615]$	\(y^2+xy+y=x^3-x^2-317791x-68874615\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.p.1.6, 248.48.0.?	$[(25237419818650411/1089534, 3994045625106542444756791/1089534)]$
1922.d2	1922d4	1922.d	1922d	$4$	$4$	\( 2 \cdot 31^{2} \)	\( 2 \cdot 31^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.105	2B	$248$	$48$	$0$	$9.445571402$	$1$		$0$	$7680$	$1.608915$	$3196010817/1847042$	$1.17908$	$5.61942$	$[1, -1, 1, -29491, 79057]$	\(y^2+xy+y=x^3-x^2-29491x+79057\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.k.1.3, 124.12.0.?, 248.48.0.?	$[(-275159/40, 18635919/40)]$
1922.d3	1922d2	1922.d	1922d	$4$	$4$	\( 2 \cdot 31^{2} \)	\( 2^{2} \cdot 31^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.5	2Cs	$248$	$48$	$0$	$18.89114280$	$1$		$2$	$3840$	$1.262342$	$979146657/3844$	$1.02504$	$5.46296$	$[1, -1, 1, -19881, -1070299]$	\(y^2+xy+y=x^3-x^2-19881x-1070299\)	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.3, 124.24.0.?, 248.48.0.?	$[(225517435/103, 3374899848614/103)]$
1922.d4	1922d1	1922.d	1922d	$4$	$4$	\( 2 \cdot 31^{2} \)	\( - 2^{4} \cdot 31^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.51	2B	$248$	$48$	$0$	$9.445571402$	$1$		$5$	$1920$	$0.915769$	$-35937/496$	$0.93090$	$4.53720$	$[1, -1, 1, -661, -32419]$	\(y^2+xy+y=x^3-x^2-661x-32419\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.p.1.8, 62.6.0.b.1, 124.24.0.?, $\ldots$	$[(21257, 3088538)]$
1922.e1	1922c2	1922.e	1922c	$2$	$7$	\( 2 \cdot 31^{2} \)	\( 2^{2} \cdot 31^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 7$	8.4.0.1, 7.16.0.2	2Cn, 7B.2.3	$1736$	$576$	$16$	$1$	$49$	$7$	$0$	$182280$	$2.769920$	$51181724570498001/4$	$1.10803$	$8.72173$	$[1, -1, 1, -73354752, -241800700097]$	\(y^2+xy+y=x^3-x^2-73354752x-241800700097\)	2.2.0.a.1, 7.16.0-7.a.1.1, 8.4.0-2.a.1.1, 14.96.0-14.b.1.1, 56.192.2-56.a.1.3, $\ldots$	$[]$
1922.e2	1922c1	1922.e	1922c	$2$	$7$	\( 2 \cdot 31^{2} \)	\( 2^{14} \cdot 31^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 7$	8.4.0.1, 7.16.0.1	2Cn, 7B.2.1	$1736$	$576$	$16$	$1$	$1$		$0$	$26040$	$1.796967$	$42396561/16384$	$1.03599$	$5.95606$	$[1, -1, 1, -68892, 4028767]$	\(y^2+xy+y=x^3-x^2-68892x+4028767\)	2.2.0.a.1, 7.16.0-7.a.1.2, 8.4.0-2.a.1.1, 14.96.0-14.b.2.1, 56.192.2-56.a.2.1, $\ldots$	$[]$