LMFDB - Elliptic curves over $\Q$ of conductor 32192

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Results (32 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	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
32192.a1	32192e1	32192.a	32192e	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{12} \cdot 503 $	$3$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$0.544958568$	$1$		$38$	$18688$	$-0.055702$	$-3796416/503$	$0.64833$	$2.28080$	$[0, 0, 0, -52, 160]$	$y^2=x^3-52x+160$	1006.2.0.?	$[(2, 8), (6, 8), (4, 4)]$
32192.b1	32192y1	32192.b	32192y	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{30} \cdot 503 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$1$	$1$		$0$	$92160$	$1.081161$	$-270212594625/2060288$	$0.90140$	$3.73932$	$[0, 0, 0, -8620, -310064]$	$y^2=x^3-8620x-310064$	1006.2.0.?	$[]$
32192.c1	32192bd1	32192.c	32192bd	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{12} \cdot 503^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.3.0.1	3Nn	$6036$	$12$	$1$	$0.356234121$	$1$		$4$	$57600$	$0.933484$	$79951586112/127263527$	$0.93466$	$3.27400$	$[0, 0, 0, 1436, 27712]$	$y^2=x^3+1436x+27712$	3.3.0.a.1, 12.6.0.d.1, 1006.2.0.?, 3018.6.1.?, 6036.12.1.?	$[(156, 2012)]$
32192.d1	32192o1	32192.d	32192o	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{18} \cdot 503 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$1.543014209$	$1$		$8$	$19456$	$0.246208$	$658503/503$	$0.73029$	$2.49284$	$[0, 0, 0, 116, -272]$	$y^2=x^3+116x-272$	1006.2.0.?	$[(14, 64), (4, 16)]$
32192.e1	32192j1	32192.e	32192j	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{12} \cdot 503 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$0.707061021$	$1$		$10$	$2304$	$-0.107719$	$-21952/503$	$0.67979$	$2.12130$	$[0, -1, 0, -9, 73]$	$y^2=x^3-x^2-9x+73$	1006.2.0.?	$[(1, 8), (-3, 8)]$
32192.f1	32192v1	32192.f	32192v	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{16} \cdot 503 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$0.787744577$	$1$		$8$	$5120$	$0.174344$	$-3650692/503$	$0.71271$	$2.54486$	$[0, -1, 0, -129, 673]$	$y^2=x^3-x^2-129x+673$	1006.2.0.?	$[(13, 32), (-3, 32)]$
32192.g1	32192t1	32192.g	32192t	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{16} \cdot 503 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$0.806204091$	$1$		$10$	$6656$	$0.277433$	$-74438500/503$	$0.76253$	$2.81589$	$[0, -1, 0, -353, 2689]$	$y^2=x^3-x^2-353x+2689$	1006.2.0.?	$[(5, 32), (21, 64)]$
32192.h1	32192u1	32192.h	32192u	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{28} \cdot 503 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$4.569796145$	$1$		$8$	$23040$	$0.845325$	$-1349232625/515072$	$0.83497$	$3.27628$	$[0, -1, 0, -1473, -27551]$	$y^2=x^3-x^2-1473x-27551$	1006.2.0.?	$[(165, 2048), (1189, 40960)]$
32192.i1	32192bb1	32192.i	32192bb	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{12} \cdot 503 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$1.000439339$	$1$		$2$	$3072$	$-0.108857$	$8000/503$	$0.73265$	$2.11801$	$[0, -1, 0, 7, -71]$	$y^2=x^3-x^2+7x-71$	1006.2.0.?	$[(5, 8)]$
32192.j1	32192bc1	32192.j	32192bc	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{14} \cdot 503 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$0.874724508$	$1$		$2$	$6144$	$0.015350$	$686000/503$	$0.67133$	$2.22966$	$[0, -1, 0, 47, -79]$	$y^2=x^3-x^2+47x-79$	1006.2.0.?	$[(5, 16)]$
32192.k1	32192d1	32192.k	32192d	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{18} \cdot 503 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$2.908258325$	$1$		$2$	$11264$	$0.572989$	$-3463512697/503$	$0.83466$	$3.31832$	$[0, -1, 0, -2017, -34207]$	$y^2=x^3-x^2-2017x-34207$	1006.2.0.?	$[(121, 1216)]$
32192.l1	32192c1	32192.l	32192c	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{22} \cdot 503 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$1.111981705$	$1$		$2$	$9216$	$0.470044$	$-389017/8048$	$0.80210$	$2.78936$	$[0, -1, 0, -97, 2273]$	$y^2=x^3-x^2-97x+2273$	1006.2.0.?	$[(41, 256)]$
32192.m1	32192l1	32192.m	32192l	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{18} \cdot 503 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$1$	$1$		$0$	$51200$	$0.892880$	$-1024497361441/503$	$0.93909$	$3.86647$	$[0, -1, 0, -13441, -595327]$	$y^2=x^3-x^2-13441x-595327$	1006.2.0.?	$[]$
32192.n1	32192k1	32192.n	32192k	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{22} \cdot 503 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$1$	$1$		$0$	$18432$	$0.478524$	$13651919/8048$	$0.83435$	$2.78492$	$[0, -1, 0, 319, 193]$	$y^2=x^3-x^2+319x+193$	1006.2.0.?	$[]$
32192.o1	32192f2	32192.o	32192f	$2$	$2$	$ 2^{6} \cdot 503 $	$ 2^{21} \cdot 503^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$4024$	$12$	$0$	$1$	$1$		$1$	$24192$	$0.940443$	$3687953625/2024072$	$0.91410$	$3.32435$	$[0, 0, 0, -2060, 8176]$	$y^2=x^3-2060x+8176$	2.3.0.a.1, 8.6.0.b.1, 2012.6.0.?, 4024.12.0.?	$[]$
32192.o2	32192f1	32192.o	32192f	$2$	$2$	$ 2^{6} \cdot 503 $	$ - 2^{24} \cdot 503 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$4024$	$12$	$0$	$1$	$1$		$1$	$12096$	$0.593870$	$52734375/32192$	$1.25681$	$2.91512$	$[0, 0, 0, 500, 1008]$	$y^2=x^3+500x+1008$	2.3.0.a.1, 8.6.0.c.1, 1006.6.0.?, 4024.12.0.?	$[]$
32192.p1	32192p2	32192.p	32192p	$2$	$2$	$ 2^{6} \cdot 503 $	$ 2^{21} \cdot 503^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$4024$	$12$	$0$	$1$	$1$		$1$	$24192$	$0.940443$	$3687953625/2024072$	$0.91410$	$3.32435$	$[0, 0, 0, -2060, -8176]$	$y^2=x^3-2060x-8176$	2.3.0.a.1, 8.6.0.b.1, 2012.6.0.?, 4024.12.0.?	$[]$
32192.p2	32192p1	32192.p	32192p	$2$	$2$	$ 2^{6} \cdot 503 $	$ - 2^{24} \cdot 503 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$4024$	$12$	$0$	$1$	$1$		$1$	$12096$	$0.593870$	$52734375/32192$	$1.25681$	$2.91512$	$[0, 0, 0, 500, -1008]$	$y^2=x^3+500x-1008$	2.3.0.a.1, 8.6.0.c.1, 1006.6.0.?, 4024.12.0.?	$[]$
32192.q1	32192i1	32192.q	32192i	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{16} \cdot 503 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$3.123444269$	$1$		$6$	$5120$	$0.174344$	$-3650692/503$	$0.71271$	$2.54486$	$[0, 1, 0, -129, -673]$	$y^2=x^3+x^2-129x-673$	1006.2.0.?	$[(19, 64), (13, 4)]$
32192.r1	32192b1	32192.r	32192b	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{12} \cdot 503 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$1.288223808$	$1$		$2$	$2304$	$-0.107719$	$-21952/503$	$0.67979$	$2.12130$	$[0, 1, 0, -9, -73]$	$y^2=x^3+x^2-9x-73$	1006.2.0.?	$[(7, 16)]$
32192.s1	32192a1	32192.s	32192a	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{14} \cdot 503 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$0.849698734$	$1$		$2$	$6144$	$0.015350$	$686000/503$	$0.67133$	$2.22966$	$[0, 1, 0, 47, 79]$	$y^2=x^3+x^2+47x+79$	1006.2.0.?	$[(3, 16)]$
32192.t1	32192q1	32192.t	32192q	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{12} \cdot 503 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$1.123298206$	$1$		$6$	$3072$	$-0.108857$	$8000/503$	$0.73265$	$2.11801$	$[0, 1, 0, 7, 71]$	$y^2=x^3+x^2+7x+71$	1006.2.0.?	$[(-1, 8), (5, 16)]$
32192.u1	32192g1	32192.u	32192g	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{16} \cdot 503 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$1$	$1$		$0$	$6656$	$0.277433$	$-74438500/503$	$0.76253$	$2.81589$	$[0, 1, 0, -353, -2689]$	$y^2=x^3+x^2-353x-2689$	1006.2.0.?	$[]$
32192.v1	32192h1	32192.v	32192h	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{28} \cdot 503 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$1$	$1$		$0$	$23040$	$0.845325$	$-1349232625/515072$	$0.83497$	$3.27628$	$[0, 1, 0, -1473, 27551]$	$y^2=x^3+x^2-1473x+27551$	1006.2.0.?	$[]$
32192.w1	32192z1	32192.w	32192z	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{22} \cdot 503 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$3.103979421$	$1$		$0$	$9216$	$0.470044$	$-389017/8048$	$0.80210$	$2.78936$	$[0, 1, 0, -97, -2273]$	$y^2=x^3+x^2-97x-2273$	1006.2.0.?	$[(271/3, 4096/3)]$
32192.x1	32192ba1	32192.x	32192ba	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{18} \cdot 503 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$1.176960074$	$1$		$2$	$11264$	$0.572989$	$-3463512697/503$	$0.83466$	$3.31832$	$[0, 1, 0, -2017, 34207]$	$y^2=x^3+x^2-2017x+34207$	1006.2.0.?	$[(39, 128)]$
32192.y1	32192r1	32192.y	32192r	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{22} \cdot 503 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$1$	$1$		$0$	$18432$	$0.478524$	$13651919/8048$	$0.83435$	$2.78492$	$[0, 1, 0, 319, -193]$	$y^2=x^3+x^2+319x-193$	1006.2.0.?	$[]$
32192.z1	32192s1	32192.z	32192s	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{18} \cdot 503 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$1$	$1$		$0$	$51200$	$0.892880$	$-1024497361441/503$	$0.93909$	$3.86647$	$[0, 1, 0, -13441, 595327]$	$y^2=x^3+x^2-13441x+595327$	1006.2.0.?	$[]$
32192.ba1	32192n1	32192.ba	32192n	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{12} \cdot 503 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$1$	$1$		$0$	$18688$	$-0.055702$	$-3796416/503$	$0.64833$	$2.28080$	$[0, 0, 0, -52, -160]$	$y^2=x^3-52x-160$	1006.2.0.?	$[]$
32192.bb1	32192m1	32192.bb	32192m	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{30} \cdot 503 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$1$	$1$		$0$	$92160$	$1.081161$	$-270212594625/2060288$	$0.90140$	$3.73932$	$[0, 0, 0, -8620, 310064]$	$y^2=x^3-8620x+310064$	1006.2.0.?	$[]$
32192.bc1	32192x1	32192.bc	32192x	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{18} \cdot 503 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1006$	$2$	$0$	$1$	$1$		$0$	$19456$	$0.246208$	$658503/503$	$0.73029$	$2.49284$	$[0, 0, 0, 116, 272]$	$y^2=x^3+116x+272$	1006.2.0.?	$[]$
32192.bd1	32192w1	32192.bd	32192w	$1$	$1$	$ 2^{6} \cdot 503 $	$ - 2^{12} \cdot 503^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.3.0.1	3Nn	$6036$	$12$	$1$	$1$	$4$	$2$	$0$	$57600$	$0.933484$	$79951586112/127263527$	$0.93466$	$3.27400$	$[0, 0, 0, 1436, -27712]$	$y^2=x^3+1436x-27712$	3.3.0.a.1, 12.6.0.d.1, 1006.2.0.?, 3018.6.1.?, 6036.12.1.?	$[]$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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