Elliptic curves over $\Q$ of conductor 1682

Results (15 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
1682.a1	1682b1	1682.a	1682b	$1$	$1$	\( 2 \cdot 29^{2} \)	\( 2^{5} \cdot 29^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.2		$8$	$2$	$0$	$0.621630440$	$1$		$4$	$300$	$-0.271129$	$13239457/32$	$0.92647$	$3.11445$	$[1, 0, 1, -47, -126]$	\(y^2+xy+y=x^3-47x-126\)	8.2.0.b.1	$[(-4, 2)]$
1682.b1	1682d2	1682.b	1682d	$2$	$3$	\( 2 \cdot 29^{2} \)	\( 2^{3} \cdot 29^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.2.0.2, 3.8.0.2	3B.1.2	$24$	$16$	$0$	$1$	$1$		$0$	$8700$	$1.542482$	$426477625/8$	$1.06548$	$6.30198$	$[1, 0, 1, -124486, -16915536]$	\(y^2+xy+y=x^3-124486x-16915536\)	3.8.0-3.a.1.1, 8.2.0.b.1, 24.16.0-24.b.1.4	$[]$
1682.b2	1682d1	1682.b	1682d	$2$	$3$	\( 2 \cdot 29^{2} \)	\( 2 \cdot 29^{8} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.2.0.2, 3.8.0.1	3B.1.1	$24$	$16$	$0$	$1$	$1$		$2$	$2900$	$0.993177$	$3625/2$	$0.87809$	$4.73010$	$[1, 0, 1, -2541, 10430]$	\(y^2+xy+y=x^3-2541x+10430\)	3.8.0-3.a.1.2, 8.2.0.b.1, 24.16.0-24.b.1.8	$[]$
1682.c1	1682c1	1682.c	1682c	$2$	$5$	\( 2 \cdot 29^{2} \)	\( - 2^{4} \cdot 29^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.6.0.1	5B	$580$	$48$	$1$	$1$	$1$		$0$	$6496$	$1.558475$	$-1030301/16$	$0.92316$	$5.94764$	$[1, 1, 0, -51318, -4555676]$	\(y^2+xy=x^3+x^2-51318x-4555676\)	5.6.0.a.1, 20.12.0.p.1, 116.2.0.?, 145.24.0.?, 580.48.1.?	$[]$
1682.c2	1682c2	1682.c	1682c	$2$	$5$	\( 2 \cdot 29^{2} \)	\( - 2^{20} \cdot 29^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.6.0.1	5B	$580$	$48$	$1$	$1$	$1$		$0$	$32480$	$2.363194$	$237176659/1048576$	$1.04028$	$6.93119$	$[1, 1, 0, 314517, 175069309]$	\(y^2+xy=x^3+x^2+314517x+175069309\)	5.6.0.a.1, 20.12.0.p.2, 116.2.0.?, 145.24.0.?, 580.48.1.?	$[]$
1682.d1	1682a2	1682.d	1682a	$2$	$5$	\( 2 \cdot 29^{2} \)	\( - 2^{2} \cdot 29^{11} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.2	5B.4.2	$580$	$48$	$1$	$6.520115268$	$1$		$0$	$16800$	$2.030811$	$-10418796526321/82044596$	$0.99481$	$6.75736$	$[1, 0, 1, -382673, -91764536]$	\(y^2+xy+y=x^3-382673x-91764536\)	5.12.0.a.2, 20.24.0-5.a.2.4, 116.2.0.?, 145.24.0.?, 580.48.1.?	$[(18889/5, 841652/5)]$
1682.d2	1682a1	1682.d	1682a	$2$	$5$	\( 2 \cdot 29^{2} \)	\( - 2^{10} \cdot 29^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.1	5B.4.1	$580$	$48$	$1$	$1.304023053$	$1$		$4$	$3360$	$1.226093$	$13651919/29696$	$1.08166$	$5.06856$	$[1, 0, 1, 4187, 173584]$	\(y^2+xy+y=x^3+4187x+173584\)	5.12.0.a.1, 20.24.0-5.a.1.4, 116.2.0.?, 145.24.0.?, 580.48.1.?	$[(563, 13174)]$
1682.e1	1682e1	1682.e	1682e	$1$	$1$	\( 2 \cdot 29^{2} \)	\( - 2^{11} \cdot 29^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.1		$8$	$2$	$0$	$1$	$1$		$0$	$1650$	$0.446189$	$2838375/2048$	$1.15496$	$3.81380$	$[1, -1, 0, 263, 749]$	\(y^2+xy=x^3-x^2+263x+749\)	8.2.0.a.1	$[]$
1682.f1	1682h1	1682.f	1682h	$1$	$1$	\( 2 \cdot 29^{2} \)	\( - 2^{11} \cdot 29^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.1		$8$	$2$	$0$	$1$	$1$		$0$	$47850$	$2.129837$	$2838375/2048$	$1.15496$	$6.53385$	$[1, -1, 1, 221025, 19814919]$	\(y^2+xy+y=x^3-x^2+221025x+19814919\)	8.2.0.a.1	$[]$
1682.g1	1682i1	1682.g	1682i	$2$	$5$	\( 2 \cdot 29^{2} \)	\( - 2^{4} \cdot 29^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.6.0.1	5B	$580$	$48$	$1$	$0.606259805$	$1$		$4$	$224$	$-0.125173$	$-1030301/16$	$0.92316$	$3.22759$	$[1, 0, 0, -61, -191]$	\(y^2+xy=x^3-61x-191\)	5.6.0.a.1, 20.12.0.p.1, 116.2.0.?, 145.24.0.?, 580.48.1.?	$[(12, 23)]$
1682.g2	1682i2	1682.g	1682i	$2$	$5$	\( 2 \cdot 29^{2} \)	\( - 2^{20} \cdot 29^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.6.0.1	5B	$580$	$48$	$1$	$0.121251961$	$1$		$6$	$1120$	$0.679546$	$237176659/1048576$	$1.04028$	$4.21114$	$[1, 0, 0, 374, 7204]$	\(y^2+xy=x^3+374x+7204\)	5.6.0.a.1, 20.12.0.p.2, 116.2.0.?, 145.24.0.?, 580.48.1.?	$[(12, 110)]$
1682.h1	1682j1	1682.h	1682j	$1$	$1$	\( 2 \cdot 29^{2} \)	\( 2^{5} \cdot 29^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.2		$8$	$2$	$0$	$0.869339815$	$1$		$0$	$8700$	$1.412519$	$13239457/32$	$0.92647$	$5.83449$	$[1, 1, 1, -39124, -2988683]$	\(y^2+xy+y=x^3+x^2-39124x-2988683\)	8.2.0.b.1	$[(-1055/3, 3251/3)]$
1682.i1	1682f2	1682.i	1682f	$2$	$3$	\( 2 \cdot 29^{2} \)	\( 2^{3} \cdot 29^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.2.0.2, 3.4.0.1	3B	$696$	$16$	$0$	$1$	$1$		$0$	$300$	$-0.141165$	$426477625/8$	$1.06548$	$3.58193$	$[1, 1, 1, -148, -755]$	\(y^2+xy+y=x^3+x^2-148x-755\)	3.4.0.a.1, 8.2.0.b.1, 24.8.0.b.1, 87.8.0.?, 696.16.0.?	$[]$
1682.i2	1682f1	1682.i	1682f	$2$	$3$	\( 2 \cdot 29^{2} \)	\( 2 \cdot 29^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.2.0.2, 3.4.0.1	3B	$696$	$16$	$0$	$1$	$1$		$0$	$100$	$-0.690471$	$3625/2$	$0.87809$	$2.01006$	$[1, 1, 1, -3, -1]$	\(y^2+xy+y=x^3+x^2-3x-1\)	3.4.0.a.1, 8.2.0.b.1, 24.8.0.b.1, 87.8.0.?, 696.16.0.?	$[]$
1682.j1	1682g1	1682.j	1682g	$1$	$1$	\( 2 \cdot 29^{2} \)	\( - 2^{2} \cdot 29^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$116$	$2$	$0$	$1$	$1$		$0$	$3360$	$0.781420$	$-185193/116$	$0.85122$	$4.45175$	$[1, -1, 1, -999, 17779]$	\(y^2+xy+y=x^3-x^2-999x+17779\)	116.2.0.?	$[]$