Elliptic curve search results

Results (26 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
3192.i3	3192a1	3192.i	3192a	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{4} \cdot 3^{4} \cdot 7 \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$512$	$-0.191954$	$733001728/10773$	$0.85282$	$2.87359$	$2$	$[0, -1, 0, -47, -108]$	\(y^2=x^3-x^2-47x-108\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 28.12.0-4.c.1.2, 76.12.0.?, $\ldots$	$[ ]$	$1$
6384.bf3	6384k1	6384.bf	6384k	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{4} \cdot 3^{4} \cdot 7 \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1.637585853$	$1$		$3$	$1024$	$-0.191954$	$733001728/10773$	$0.85282$	$2.64625$	$2$	$[0, 1, 0, -47, 108]$	\(y^2=x^3+x^2-47x+108\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 28.12.0-4.c.1.1, 76.12.0.?, $\ldots$	$[(-8, 6)]$	$1$
9576.c3	9576w1	9576.c	9576w	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{4} \cdot 3^{10} \cdot 7 \cdot 19 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$3192$	$48$	$0$	$1.400618188$	$1$		$15$	$4096$	$0.357352$	$733001728/10773$	$0.85282$	$3.24827$	$2$	$[0, 0, 0, -426, 3341]$	\(y^2=x^3-426x+3341\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 84.12.0.?, 168.24.0.?, $\ldots$	$[(10, 9), (1, 54)]$	$1$
19152.l3	19152v1	19152.l	19152v	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{4} \cdot 3^{10} \cdot 7 \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$3192$	$48$	$0$	$4.141325510$	$1$		$3$	$8192$	$0.357352$	$733001728/10773$	$0.85282$	$3.01992$	$2$	$[0, 0, 0, -426, -3341]$	\(y^2=x^3-426x-3341\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 84.12.0.?, 168.24.0.?, $\ldots$	$[(51, 328)]$	$1$
22344.s3	22344u1	22344.s	22344u	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{4} \cdot 7^{7} \cdot 19 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$3192$	$48$	$0$	$2.517555296$	$1$		$7$	$24576$	$0.781001$	$733001728/10773$	$0.85282$	$3.48109$	$1$	$[0, 1, 0, -2319, 41670]$	\(y^2=x^3+x^2-2319x+41670\)	2.3.0.a.1, 4.12.0-4.c.1.1, 168.24.0.?, 266.6.0.?, 456.24.0.?, $\ldots$	$[(18, 78)]$	$1$
25536.o3	25536co1	25536.o	25536co	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{4} \cdot 7 \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$8192$	$0.154619$	$733001728/10773$	$0.85282$	$2.69458$	$2$	$[0, -1, 0, -189, 1053]$	\(y^2=x^3-x^2-189x+1053\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.6, 56.12.0-4.c.1.2, 152.12.0.?, $\ldots$	$[ ]$	$1$
25536.cc3	25536bc1	25536.cc	25536bc	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{4} \cdot 7 \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$8192$	$0.154619$	$733001728/10773$	$0.85282$	$2.69458$	$2$	$[0, 1, 0, -189, -1053]$	\(y^2=x^3+x^2-189x-1053\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.6, 56.12.0-4.c.1.1, 152.12.0.?, $\ldots$	$[ ]$	$1$
44688.f3	44688n1	44688.f	44688n	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{4} \cdot 7^{7} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$3192$	$48$	$0$	$4.688110842$	$1$		$1$	$49152$	$0.781001$	$733001728/10773$	$0.85282$	$3.25574$	$2$	$[0, -1, 0, -2319, -41670]$	\(y^2=x^3-x^2-2319x-41670\)	2.3.0.a.1, 4.12.0-4.c.1.2, 168.24.0.?, 266.6.0.?, 456.24.0.?, $\ldots$	$[(514/3, 2548/3)]$	$1$
60648.bn3	60648bi1	60648.bn	60648bi	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{4} \cdot 3^{4} \cdot 7 \cdot 19^{7} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$3192$	$48$	$0$	$1$	$4$	$2$	$3$	$184320$	$1.280266$	$733001728/10773$	$0.85282$	$3.70948$	$1$	$[0, 1, 0, -17087, 843042]$	\(y^2=x^3+x^2-17087x+843042\)	2.3.0.a.1, 4.12.0-4.c.1.1, 168.24.0.?, 266.6.0.?, 456.24.0.?, $\ldots$	$[ ]$	$1$
67032.cc3	67032ce1	67032.cc	67032ce	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{10} \cdot 7^{7} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$196608$	$1.330307$	$733001728/10773$	$0.85282$	$3.73011$	$2$	$[0, 0, 0, -20874, -1145963]$	\(y^2=x^3-20874x-1145963\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 56.12.0-4.c.1.5, 152.12.0.?, $\ldots$	$[ ]$	$1$
76608.em3	76608bc1	76608.em	76608bc	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{10} \cdot 7 \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$65536$	$0.703925$	$733001728/10773$	$0.85282$	$3.01747$	$2$	$[0, 0, 0, -1704, 26728]$	\(y^2=x^3-1704x+26728\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 168.24.0.?, 266.6.0.?, $\ldots$	$[ ]$	$1$
76608.et3	76608fm1	76608.et	76608fm	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{10} \cdot 7 \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$3192$	$48$	$0$	$5.398340733$	$1$		$1$	$65536$	$0.703925$	$733001728/10773$	$0.85282$	$3.01747$	$2$	$[0, 0, 0, -1704, -26728]$	\(y^2=x^3-1704x-26728\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 168.24.0.?, 266.6.0.?, $\ldots$	$[(1609/4, 57915/4)]$	$1$
79800.bw3	79800bt1	79800.bw	79800bt	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{4} \cdot 3^{4} \cdot 5^{6} \cdot 7 \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$15960$	$48$	$0$	$2.926044373$	$1$		$3$	$65536$	$0.612764$	$733001728/10773$	$0.85282$	$2.90964$	$2$	$[0, 1, 0, -1183, -15862]$	\(y^2=x^3+x^2-1183x-15862\)	2.3.0.a.1, 4.6.0.c.1, 120.12.0.?, 140.12.0.?, 168.12.0.?, $\ldots$	$[(59, 351)]$	$1$
121296.bo3	121296s1	121296.bo	121296s	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{4} \cdot 3^{4} \cdot 7 \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$3192$	$48$	$0$	$18.41126977$	$1$		$1$	$368640$	$1.280266$	$733001728/10773$	$0.85282$	$3.48983$	$2$	$[0, -1, 0, -17087, -843042]$	\(y^2=x^3-x^2-17087x-843042\)	2.3.0.a.1, 4.12.0-4.c.1.2, 168.24.0.?, 266.6.0.?, 456.24.0.?, $\ldots$	$[(94188526/255, 909932897224/255)]$	$1$
134064.ff3	134064fb1	134064.ff	134064fb	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{10} \cdot 7^{7} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$4$	$2$	$1$	$393216$	$1.330307$	$733001728/10773$	$0.85282$	$3.51111$	$2$	$[0, 0, 0, -20874, 1145963]$	\(y^2=x^3-20874x+1145963\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 56.12.0-4.c.1.5, 152.12.0.?, $\ldots$	$[ ]$	$1$
159600.f3	159600gr1	159600.f	159600gr	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{4} \cdot 3^{4} \cdot 5^{6} \cdot 7 \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$15960$	$48$	$0$	$3.548768938$	$1$		$3$	$131072$	$0.612764$	$733001728/10773$	$0.85282$	$2.74129$	$2$	$[0, -1, 0, -1183, 15862]$	\(y^2=x^3-x^2-1183x+15862\)	2.3.0.a.1, 4.6.0.c.1, 120.12.0.?, 140.12.0.?, 168.12.0.?, $\ldots$	$[(38, 156)]$	$1$
178752.eb3	178752kc1	178752.eb	178752kc	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{4} \cdot 7^{7} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$3192$	$48$	$0$	$1.520629556$	$1$		$5$	$393216$	$1.127575$	$733001728/10773$	$0.85282$	$3.22642$	$2$	$[0, -1, 0, -9277, 342637]$	\(y^2=x^3-x^2-9277x+342637\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 168.24.0.?, 266.6.0.?, $\ldots$	$[(68, 147)]$	$1$
178752.jq3	178752cl1	178752.jq	178752cl	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{4} \cdot 7^{7} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$393216$	$1.127575$	$733001728/10773$	$0.85282$	$3.22642$	$2$	$[0, 1, 0, -9277, -342637]$	\(y^2=x^3+x^2-9277x-342637\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 168.24.0.?, 266.6.0.?, $\ldots$	$[ ]$	$1$
181944.c3	181944bi1	181944.c	181944bi	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{4} \cdot 3^{10} \cdot 7 \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$2.012964660$	$1$		$3$	$1474560$	$1.829571$	$733001728/10773$	$0.85282$	$3.91725$	$2$	$[0, 0, 0, -153786, -22915919]$	\(y^2=x^3-153786x-22915919\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 56.12.0-4.c.1.3, 152.12.0.?, $\ldots$	$[(665, 12996)]$	$1$
239400.ct3	239400ct1	239400.ct	239400ct	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{4} \cdot 3^{10} \cdot 5^{6} \cdot 7 \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$15960$	$48$	$0$	$1$	$1$		$1$	$524288$	$1.162071$	$733001728/10773$	$0.85282$	$3.18375$	$2$	$[0, 0, 0, -10650, 417625]$	\(y^2=x^3-10650x+417625\)	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.5, 168.12.0.?, 266.6.0.?, $\ldots$	$[ ]$	$1$
363888.z3	363888z1	363888.z	363888z	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{4} \cdot 3^{10} \cdot 7 \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$4$	$2$	$1$	$2949120$	$1.829571$	$733001728/10773$	$0.85282$	$3.70520$	$2$	$[0, 0, 0, -153786, 22915919]$	\(y^2=x^3-153786x+22915919\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 56.12.0-4.c.1.3, 152.12.0.?, $\ldots$	$[ ]$	$1$
386232.bb3	386232bb1	386232.bb	386232bb	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{4} \cdot 7 \cdot 11^{6} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$35112$	$48$	$0$	$1$	$1$		$1$	$655360$	$1.006992$	$733001728/10773$	$0.85282$	$2.92071$	$2$	$[0, -1, 0, -5727, 166608]$	\(y^2=x^3-x^2-5727x+166608\)	2.3.0.a.1, 4.6.0.c.1, 168.12.0.?, 264.12.0.?, 266.6.0.?, $\ldots$	$[ ]$	$1$
424536.n3	424536n1	424536.n	424536n	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 19^{2} \)	\( 2^{4} \cdot 3^{4} \cdot 7^{7} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$8847360$	$2.253220$	$733001728/10773$	$0.85282$	$4.05343$	$2$	$[0, -1, 0, -837279, -290837952]$	\(y^2=x^3-x^2-837279x-290837952\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.5, 28.12.0-4.c.1.2, 76.12.0.?, $\ldots$	$[ ]$	$1$
478800.hb3	478800hb1	478800.hb	478800hb	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{4} \cdot 3^{10} \cdot 5^{6} \cdot 7 \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$15960$	$48$	$0$	$1$	$4$	$2$	$1$	$1048576$	$1.162071$	$733001728/10773$	$0.85282$	$3.01502$	$2$	$[0, 0, 0, -10650, -417625]$	\(y^2=x^3-10650x-417625\)	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.5, 168.12.0.?, 266.6.0.?, $\ldots$	$[ ]$	$1$
485184.n3	485184n1	485184.n	485184n	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{4} \cdot 7 \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$2949120$	$1.626839$	$733001728/10773$	$0.85282$	$3.43796$	$2$	$[0, -1, 0, -68349, 6812685]$	\(y^2=x^3-x^2-68349x+6812685\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 168.24.0.?, 266.6.0.?, $\ldots$	$[ ]$	$1$
485184.fu3	485184fu1	485184.fu	485184fu	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{4} \cdot 7 \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$3192$	$48$	$0$	$3.409935641$	$1$		$1$	$2949120$	$1.626839$	$733001728/10773$	$0.85282$	$3.43796$	$2$	$[0, 1, 0, -68349, -6812685]$	\(y^2=x^3+x^2-68349x-6812685\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 168.24.0.?, 266.6.0.?, $\ldots$	$[(2133/2, 83391/2)]$	$1$

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