Elliptic curves over $\Q$ of conductor 1870

Results (13 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
1870.a1	1870c1	1870.a	1870c	$1$	$1$	\( 2 \cdot 5 \cdot 11 \cdot 17 \)	\( - 2^{23} \cdot 5 \cdot 11^{2} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$680$	$2$	$0$	$1$	$1$		$0$	$8832$	$1.232912$	$-5527291469021688969/86276833280$	$0.99152$	$5.72843$	$[1, -1, 0, -36835, -2711915]$	\(y^2+xy=x^3-x^2-36835x-2711915\)	680.2.0.?	$[]$
1870.b1	1870e1	1870.b	1870e	$1$	$1$	\( 2 \cdot 5 \cdot 11 \cdot 17 \)	\( - 2^{5} \cdot 5 \cdot 11^{4} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$680$	$2$	$0$	$0.205052200$	$1$		$6$	$640$	$0.263581$	$-2796665386969/39823520$	$0.88184$	$3.80740$	$[1, 1, 0, -293, 1837]$	\(y^2+xy=x^3+x^2-293x+1837\)	680.2.0.?	$[(9, 1)]$
1870.c1	1870a2	1870.c	1870a	$2$	$2$	\( 2 \cdot 5 \cdot 11 \cdot 17 \)	\( 2^{5} \cdot 5^{10} \cdot 11^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$7480$	$12$	$0$	$1$	$1$		$0$	$2400$	$0.956092$	$1153957554747369/642812500000$	$1.07122$	$4.60358$	$[1, -1, 0, -2185, -7059]$	\(y^2+xy=x^3-x^2-2185x-7059\)	2.3.0.a.1, 136.6.0.?, 220.6.0.?, 7480.12.0.?	$[]$
1870.c2	1870a1	1870.c	1870a	$2$	$2$	\( 2 \cdot 5 \cdot 11 \cdot 17 \)	\( - 2^{10} \cdot 5^{5} \cdot 11 \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$7480$	$12$	$0$	$1$	$1$		$1$	$1200$	$0.609518$	$16917195186711/10172800000$	$0.97150$	$4.04308$	$[1, -1, 0, 535, -1075]$	\(y^2+xy=x^3-x^2+535x-1075\)	2.3.0.a.1, 110.6.0.?, 136.6.0.?, 7480.12.0.?	$[]$
1870.d1	1870f2	1870.d	1870f	$2$	$2$	\( 2 \cdot 5 \cdot 11 \cdot 17 \)	\( 2^{3} \cdot 5^{2} \cdot 11^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$7480$	$12$	$0$	$1$	$1$		$0$	$672$	$0.237824$	$42002659053081/411400$	$0.95878$	$4.16379$	$[1, -1, 0, -724, -7320]$	\(y^2+xy=x^3-x^2-724x-7320\)	2.3.0.a.1, 136.6.0.?, 220.6.0.?, 7480.12.0.?	$[]$
1870.d2	1870f1	1870.d	1870f	$2$	$2$	\( 2 \cdot 5 \cdot 11 \cdot 17 \)	\( - 2^{6} \cdot 5 \cdot 11 \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$7480$	$12$	$0$	$1$	$1$		$1$	$336$	$-0.108750$	$-9541617561/1017280$	$0.84580$	$3.07260$	$[1, -1, 0, -44, -112]$	\(y^2+xy=x^3-x^2-44x-112\)	2.3.0.a.1, 110.6.0.?, 136.6.0.?, 7480.12.0.?	$[]$
1870.e1	1870b1	1870.e	1870b	$2$	$3$	\( 2 \cdot 5 \cdot 11 \cdot 17 \)	\( - 2 \cdot 5^{3} \cdot 11^{2} \cdot 17^{3} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.1	3B.1.1	$2040$	$16$	$0$	$1$	$1$		$2$	$3456$	$0.963210$	$-820470116876114809/148618250$	$0.95913$	$5.47522$	$[1, 0, 1, -19504, 1046752]$	\(y^2+xy+y=x^3-19504x+1046752\)	3.8.0-3.a.1.2, 680.2.0.?, 2040.16.0.?	$[]$
1870.e2	1870b2	1870.e	1870b	$2$	$3$	\( 2 \cdot 5 \cdot 11 \cdot 17 \)	\( - 2^{3} \cdot 5^{9} \cdot 11^{6} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.2	3B.1.2	$2040$	$16$	$0$	$1$	$1$		$0$	$10368$	$1.512516$	$-530829093701949769/470570890625000$	$0.96832$	$5.54073$	$[1, 0, 1, -16869, 1340376]$	\(y^2+xy+y=x^3-16869x+1340376\)	3.8.0-3.a.1.1, 680.2.0.?, 2040.16.0.?	$[]$
1870.f1	1870d1	1870.f	1870d	$1$	$1$	\( 2 \cdot 5 \cdot 11 \cdot 17 \)	\( - 2^{3} \cdot 5 \cdot 11^{2} \cdot 17^{5} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$680$	$2$	$0$	$0.384697580$	$1$		$4$	$960$	$0.566887$	$49471280711/6872107880$	$0.94401$	$3.99555$	$[1, 0, 1, 76, -3974]$	\(y^2+xy+y=x^3+76x-3974\)	680.2.0.?	$[(136, 1521)]$
1870.g1	1870i1	1870.g	1870i	$1$	$1$	\( 2 \cdot 5 \cdot 11 \cdot 17 \)	\( - 2^{9} \cdot 5^{5} \cdot 11^{2} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$680$	$2$	$0$	$0.025521330$	$1$		$18$	$2880$	$0.506242$	$-72043225281/3291200000$	$0.95685$	$3.90006$	$[1, -1, 1, -87, 2799]$	\(y^2+xy+y=x^3-x^2-87x+2799\)	680.2.0.?	$[(-3, 56)]$
1870.h1	1870h1	1870.h	1870h	$2$	$5$	\( 2 \cdot 5 \cdot 11 \cdot 17 \)	\( - 2^{15} \cdot 5^{5} \cdot 11^{4} \cdot 17^{5} \)	$1$	$\Z/5\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$5$	5.24.0.1	5B.1.1	$680$	$48$	$1$	$0.231977688$	$1$		$26$	$48000$	$2.423168$	$-1606220241149825308027441/2128704136908800000$	$1.01195$	$7.39852$	$[1, 1, 1, -2439835, 1467522537]$	\(y^2+xy+y=x^3+x^2-2439835x+1467522537\)	5.24.0-5.a.1.2, 680.48.1.?	$[(867, 1766)]$
1870.h2	1870h2	1870.h	1870h	$2$	$5$	\( 2 \cdot 5 \cdot 11 \cdot 17 \)	\( - 2^{3} \cdot 5 \cdot 11^{20} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$5$	5.24.0.3	5B.1.2	$680$	$48$	$1$	$1.159888440$	$1$		$0$	$240000$	$3.227886$	$570983676137286216962798159/457469996554140806256680$	$1.10476$	$8.17785$	$[1, 1, 1, 17283565, -17141361543]$	\(y^2+xy+y=x^3+x^2+17283565x-17141361543\)	5.24.0-5.a.2.2, 680.48.1.?	$[(9265/3, 1113446/3)]$
1870.i1	1870g1	1870.i	1870g	$1$	$1$	\( 2 \cdot 5 \cdot 11 \cdot 17 \)	\( - 2 \cdot 5 \cdot 11^{2} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$680$	$2$	$0$	$1$	$1$		$0$	$128$	$-0.486991$	$13651919/20570$	$0.77068$	$2.24348$	$[1, 0, 0, 5, -5]$	\(y^2+xy=x^3+5x-5\)	680.2.0.?	$[]$