Elliptic curve search results

Results (26 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
1290.m2	1290m2	1290.m	1290m	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{4} \cdot 3^{10} \cdot 5 \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$2580$	$12$	$0$	$0.196537535$	$1$		$10$	$1280$	$0.588867$	$1009328859791/8734528080$	$0.96292$	$4.22708$	$[1, 0, 0, 209, 4361]$	\(y^2+xy=x^3+209x+4361\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(8, 77)]$
3870.f2	3870h2	3870.f	3870h	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 43 \)	\( - 2^{4} \cdot 3^{16} \cdot 5 \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1.679529698$	$1$		$4$	$10240$	$1.138174$	$1009328859791/8734528080$	$0.96292$	$4.46286$	$[1, -1, 0, 1881, -117747]$	\(y^2+xy=x^3-x^2+1881x-117747\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(69, 546)]$
6450.i2	6450e2	6450.i	6450e	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 43 \)	\( - 2^{4} \cdot 3^{10} \cdot 5^{7} \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$0$	$30720$	$1.393587$	$1009328859791/8734528080$	$0.96292$	$4.55237$	$[1, 1, 0, 5225, 545125]$	\(y^2+xy=x^3+x^2+5225x+545125\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[]$
10320.i2	10320r2	10320.i	10320r	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{16} \cdot 3^{10} \cdot 5 \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$6.154246740$	$1$		$1$	$30720$	$1.282015$	$1009328859791/8734528080$	$0.96292$	$4.17599$	$[0, -1, 0, 3344, -279104]$	\(y^2=x^3-x^2+3344x-279104\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(466/3, 4690/3)]$
19350.cu2	19350ci2	19350.cu	19350ci	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 43 \)	\( - 2^{4} \cdot 3^{16} \cdot 5^{7} \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$0$	$245760$	$1.942892$	$1009328859791/8734528080$	$0.96292$	$4.71350$	$[1, -1, 1, 47020, -14671353]$	\(y^2+xy+y=x^3-x^2+47020x-14671353\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[]$
30960.ca2	30960cb2	30960.ca	30960cb	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 43 \)	\( - 2^{16} \cdot 3^{16} \cdot 5 \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$6.046319183$	$1$		$3$	$245760$	$1.831322$	$1009328859791/8734528080$	$0.96292$	$4.36978$	$[0, 0, 0, 30093, 7505714]$	\(y^2=x^3+30093x+7505714\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(695, 19082)]$
41280.y2	41280x2	41280.y	41280x	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{22} \cdot 3^{10} \cdot 5 \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$7.205961012$	$1$		$3$	$245760$	$1.628588$	$1009328859791/8734528080$	$0.96292$	$4.02260$	$[0, -1, 0, 13375, 2219457]$	\(y^2=x^3-x^2+13375x+2219457\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(2607, 133224)]$
41280.do2	41280di2	41280.do	41280di	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{22} \cdot 3^{10} \cdot 5 \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$1$	$245760$	$1.628588$	$1009328859791/8734528080$	$0.96292$	$4.02260$	$[0, 1, 0, 13375, -2219457]$	\(y^2=x^3+x^2+13375x-2219457\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[]$
51600.cb2	51600cy2	51600.cb	51600cy	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 43 \)	\( - 2^{16} \cdot 3^{10} \cdot 5^{7} \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$2.508564677$	$1$		$5$	$737280$	$2.086735$	$1009328859791/8734528080$	$0.96292$	$4.44652$	$[0, 1, 0, 83592, -34720812]$	\(y^2=x^3+x^2+83592x-34720812\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(468, 10350)]$
55470.e2	55470e2	55470.e	55470e	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 43^{2} \)	\( - 2^{4} \cdot 3^{10} \cdot 5 \cdot 43^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$10.57126136$	$1$		$0$	$2365440$	$2.469467$	$1009328859791/8734528080$	$0.96292$	$4.83753$	$[1, 1, 0, 386403, -345184371]$	\(y^2+xy=x^3+x^2+386403x-345184371\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(8003395/77, 23141703626/77)]$
63210.bs2	63210br2	63210.bs	63210br	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 43 \)	\( - 2^{4} \cdot 3^{10} \cdot 5 \cdot 7^{6} \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$0$	$368640$	$1.561823$	$1009328859791/8734528080$	$0.96292$	$3.79507$	$[1, 1, 1, 10240, -1485583]$	\(y^2+xy+y=x^3+x^2+10240x-1485583\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[]$
123840.d2	123840ch2	123840.d	123840ch	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 43 \)	\( - 2^{22} \cdot 3^{16} \cdot 5 \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$11.27022533$	$1$		$1$	$1966080$	$2.177895$	$1009328859791/8734528080$	$0.96292$	$4.20785$	$[0, 0, 0, 120372, -60045712]$	\(y^2=x^3+120372x-60045712\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(124136/11, 45003364/11)]$
123840.dm2	123840ev2	123840.dm	123840ev	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 43 \)	\( - 2^{22} \cdot 3^{16} \cdot 5 \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$5.724380101$	$1$		$3$	$1966080$	$2.177895$	$1009328859791/8734528080$	$0.96292$	$4.20785$	$[0, 0, 0, 120372, 60045712]$	\(y^2=x^3+120372x+60045712\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(-276, 2408)]$
154800.k2	154800bm2	154800.k	154800bm	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 43 \)	\( - 2^{16} \cdot 3^{16} \cdot 5^{7} \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$2.817122276$	$1$		$5$	$5898240$	$2.636040$	$1009328859791/8734528080$	$0.96292$	$4.58934$	$[0, 0, 0, 752325, 938214250]$	\(y^2=x^3+752325x+938214250\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(-1, 30618)]$
156090.o2	156090bq2	156090.o	156090bq	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 11^{2} \cdot 43 \)	\( - 2^{4} \cdot 3^{10} \cdot 5 \cdot 11^{6} \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$0$	$1792000$	$1.787815$	$1009328859791/8734528080$	$0.96292$	$3.73497$	$[1, 0, 1, 25286, -5779204]$	\(y^2+xy+y=x^3+25286x-5779204\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[]$
166410.ck2	166410t2	166410.ck	166410t	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 43^{2} \)	\( - 2^{4} \cdot 3^{16} \cdot 5 \cdot 43^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$4$	$2$	$0$	$18923520$	$3.018772$	$1009328859791/8734528080$	$0.96292$	$4.94376$	$[1, -1, 1, 3477622, 9323455641]$	\(y^2+xy+y=x^3-x^2+3477622x+9323455641\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[]$
189630.ba2	189630du2	189630.ba	189630du	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 43 \)	\( - 2^{4} \cdot 3^{16} \cdot 5 \cdot 7^{6} \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1.760952271$	$1$		$6$	$2949120$	$2.111130$	$1009328859791/8734528080$	$0.96292$	$3.99439$	$[1, -1, 0, 92160, 40202896]$	\(y^2+xy=x^3-x^2+92160x+40202896\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(-180, 4304)]$
206400.d2	206400dr2	206400.d	206400dr	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 43 \)	\( - 2^{22} \cdot 3^{10} \cdot 5^{7} \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1.766124581$	$1$		$7$	$5898240$	$2.433308$	$1009328859791/8734528080$	$0.96292$	$4.28266$	$[0, -1, 0, 334367, -278100863]$	\(y^2=x^3-x^2+334367x-278100863\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(973, 31104)]$
206400.ko2	206400hy2	206400.ko	206400hy	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 43 \)	\( - 2^{22} \cdot 3^{10} \cdot 5^{7} \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$1$	$5898240$	$2.433308$	$1009328859791/8734528080$	$0.96292$	$4.28266$	$[0, 1, 0, 334367, 278100863]$	\(y^2=x^3+x^2+334367x+278100863\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[]$
218010.bh2	218010bm2	218010.bh	218010bm	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 13^{2} \cdot 43 \)	\( - 2^{4} \cdot 3^{10} \cdot 5 \cdot 13^{6} \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1.764833667$	$1$		$4$	$2457600$	$1.871342$	$1009328859791/8734528080$	$0.96292$	$3.71499$	$[1, 0, 1, 35317, 9545798]$	\(y^2+xy+y=x^3+35317x+9545798\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(222, 5212)]$
277350.cu2	277350cu2	277350.cu	277350cu	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 43^{2} \)	\( - 2^{4} \cdot 3^{10} \cdot 5^{7} \cdot 43^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$0$	$56770560$	$3.274185$	$1009328859791/8734528080$	$0.96292$	$4.98681$	$[1, 0, 0, 9660062, -43167366508]$	\(y^2+xy=x^3+9660062x-43167366508\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[]$
316050.de2	316050de2	316050.de	316050de	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 43 \)	\( - 2^{4} \cdot 3^{10} \cdot 5^{7} \cdot 7^{6} \cdot 43^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$0.730372532$	$1$		$32$	$8847360$	$2.366543$	$1009328859791/8734528080$	$0.96292$	$4.07530$	$[1, 0, 1, 255999, -186209852]$	\(y^2+xy+y=x^3+255999x-186209852\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(662, 16206), (1607, 65346)]$
372810.cc2	372810cc2	372810.cc	372810cc	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 17^{2} \cdot 43 \)	\( - 2^{4} \cdot 3^{10} \cdot 5 \cdot 17^{6} \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$7.543912702$	$1$		$2$	$6307840$	$2.005474$	$1009328859791/8734528080$	$0.96292$	$3.68509$	$[1, 1, 1, 60395, 21365195]$	\(y^2+xy+y=x^3+x^2+60395x+21365195\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(2985, 162244)]$
443760.cp2	443760cp2	443760.cp	443760cp	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5 \cdot 43^{2} \)	\( - 2^{16} \cdot 3^{10} \cdot 5 \cdot 43^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$5.057530912$	$1$		$5$	$56770560$	$3.162613$	$1009328859791/8734528080$	$0.96292$	$4.70359$	$[0, 1, 0, 6182440, 22104164628]$	\(y^2=x^3+x^2+6182440x+22104164628\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(-2012, 39042)]$
465690.a2	465690a2	465690.a	465690a	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 19^{2} \cdot 43 \)	\( - 2^{4} \cdot 3^{10} \cdot 5 \cdot 19^{6} \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$0$	$9123840$	$2.061089$	$1009328859791/8734528080$	$0.96292$	$3.67341$	$[1, 1, 0, 75442, -29761212]$	\(y^2+xy=x^3+x^2+75442x-29761212\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[]$
468270.ee2	468270ee2	468270.ee	468270ee	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 43 \)	\( - 2^{4} \cdot 3^{16} \cdot 5 \cdot 11^{6} \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$4$	$2$	$0$	$14336000$	$2.337120$	$1009328859791/8734528080$	$0.96292$	$3.92555$	$[1, -1, 1, 227578, 156038501]$	\(y^2+xy+y=x^3-x^2+227578x+156038501\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[]$