Elliptic curve search results

Results (34 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
975.d1	975e1	975.d	975e	$1$	$1$	\( 3 \cdot 5^{2} \cdot 13 \)	\( - 3^{2} \cdot 5^{8} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$720$	$0.660023$	$-417267265/19773$	$0.90540$	$4.76625$	$[1, 1, 1, -1138, -15844]$	\(y^2+xy+y=x^3+x^2-1138x-15844\)	52.2.0.a.1	$[]$
975.k1	975h1	975.k	975h	$1$	$1$	\( 3 \cdot 5^{2} \cdot 13 \)	\( - 3^{2} \cdot 5^{2} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$0.574557957$	$1$		$4$	$144$	$-0.144697$	$-417267265/19773$	$0.90540$	$3.36317$	$[1, 0, 1, -46, -127]$	\(y^2+xy+y=x^3-46x-127\)	52.2.0.a.1	$[(13, 32)]$
2925.b1	2925j1	2925.b	2925j	$1$	$1$	\( 3^{2} \cdot 5^{2} \cdot 13 \)	\( - 3^{8} \cdot 5^{2} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$0.194406897$	$1$		$6$	$1152$	$0.404610$	$-417267265/19773$	$0.90540$	$3.72614$	$[1, -1, 1, -410, 3422]$	\(y^2+xy+y=x^3-x^2-410x+3422\)	52.2.0.a.1	$[(0, 58)]$
2925.o1	2925q1	2925.o	2925q	$1$	$1$	\( 3^{2} \cdot 5^{2} \cdot 13 \)	\( - 3^{8} \cdot 5^{8} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$0.936281594$	$1$		$2$	$5760$	$1.209328$	$-417267265/19773$	$0.90540$	$4.93608$	$[1, -1, 0, -10242, 417541]$	\(y^2+xy=x^3-x^2-10242x+417541\)	52.2.0.a.1	$[(44, 203)]$
12675.p1	12675z1	12675.p	12675z	$1$	$1$	\( 3 \cdot 5^{2} \cdot 13^{2} \)	\( - 3^{2} \cdot 5^{2} \cdot 13^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$24192$	$1.137777$	$-417267265/19773$	$0.90540$	$4.07907$	$[1, 0, 0, -7693, -270778]$	\(y^2+xy=x^3-7693x-270778\)	52.2.0.a.1	$[]$
12675.x1	12675r1	12675.x	12675r	$1$	$1$	\( 3 \cdot 5^{2} \cdot 13^{2} \)	\( - 3^{2} \cdot 5^{8} \cdot 13^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$120960$	$1.942497$	$-417267265/19773$	$0.90540$	$5.10121$	$[1, 1, 0, -192325, -33847250]$	\(y^2+xy=x^3+x^2-192325x-33847250\)	52.2.0.a.1	$[]$
15600.bd1	15600bl1	15600.bd	15600bl	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13 \)	\( - 2^{12} \cdot 3^{2} \cdot 5^{2} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$0.276046627$	$1$		$6$	$9216$	$0.548450$	$-417267265/19773$	$0.90540$	$3.25888$	$[0, -1, 0, -728, 8112]$	\(y^2=x^3-x^2-728x+8112\)	52.2.0.a.1	$[(26, 78)]$
15600.bw1	15600cp1	15600.bw	15600cp	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13 \)	\( - 2^{12} \cdot 3^{2} \cdot 5^{8} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$46080$	$1.353170$	$-417267265/19773$	$0.90540$	$4.25905$	$[0, 1, 0, -18208, 977588]$	\(y^2=x^3+x^2-18208x+977588\)	52.2.0.a.1	$[]$
38025.p1	38025ck1	38025.p	38025ck	$1$	$1$	\( 3^{2} \cdot 5^{2} \cdot 13^{2} \)	\( - 3^{8} \cdot 5^{8} \cdot 13^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$3.097613246$	$1$		$2$	$967680$	$2.491802$	$-417267265/19773$	$0.90540$	$5.19484$	$[1, -1, 1, -1730930, 912144822]$	\(y^2+xy+y=x^3-x^2-1730930x+912144822\)	52.2.0.a.1	$[(920, 9426)]$
38025.cr1	38025bf1	38025.cr	38025bf	$1$	$1$	\( 3^{2} \cdot 5^{2} \cdot 13^{2} \)	\( - 3^{8} \cdot 5^{2} \cdot 13^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$193536$	$1.687084$	$-417267265/19773$	$0.90540$	$4.27918$	$[1, -1, 0, -69237, 7311006]$	\(y^2+xy=x^3-x^2-69237x+7311006\)	52.2.0.a.1	$[]$
46800.x1	46800ex1	46800.x	46800ex	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 13 \)	\( - 2^{12} \cdot 3^{8} \cdot 5^{8} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$368640$	$1.902475$	$-417267265/19773$	$0.90540$	$4.43691$	$[0, 0, 0, -163875, -26558750]$	\(y^2=x^3-163875x-26558750\)	52.2.0.a.1	$[]$
46800.et1	46800ef1	46800.et	46800ef	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 13 \)	\( - 2^{12} \cdot 3^{8} \cdot 5^{2} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$73728$	$1.097757$	$-417267265/19773$	$0.90540$	$3.53892$	$[0, 0, 0, -6555, -212470]$	\(y^2=x^3-6555x-212470\)	52.2.0.a.1	$[]$
47775.z1	47775do1	47775.z	47775do	$1$	$1$	\( 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 3^{2} \cdot 5^{8} \cdot 7^{6} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$0.511077534$	$1$		$6$	$237600$	$1.632977$	$-417267265/19773$	$0.90540$	$4.12826$	$[1, 0, 0, -55763, 5267142]$	\(y^2+xy=x^3-55763x+5267142\)	52.2.0.a.1	$[(127, 424)]$
47775.co1	47775k1	47775.co	47775k	$1$	$1$	\( 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 3^{2} \cdot 5^{2} \cdot 7^{6} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$47520$	$0.828259$	$-417267265/19773$	$0.90540$	$3.23199$	$[1, 1, 0, -2230, 41245]$	\(y^2+xy=x^3+x^2-2230x+41245\)	52.2.0.a.1	$[]$
62400.bc1	62400fw1	62400.bc	62400fw	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 \)	\( - 2^{18} \cdot 3^{2} \cdot 5^{8} \cdot 13^{3} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$0.249510206$	$1$		$26$	$368640$	$1.699743$	$-417267265/19773$	$0.90540$	$4.10097$	$[0, -1, 0, -72833, 7893537]$	\(y^2=x^3-x^2-72833x+7893537\)	52.2.0.a.1	$[(517, 10400), (-133, 3900)]$
62400.bd1	62400q1	62400.bd	62400q	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 \)	\( - 2^{18} \cdot 3^{2} \cdot 5^{2} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$3.301959786$	$1$		$2$	$73728$	$0.895024$	$-417267265/19773$	$0.90540$	$3.22638$	$[0, -1, 0, -2913, -61983]$	\(y^2=x^3-x^2-2913x-61983\)	52.2.0.a.1	$[(63, 24)]$
62400.hc1	62400gp1	62400.hc	62400gp	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 \)	\( - 2^{18} \cdot 3^{2} \cdot 5^{2} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$0.985433036$	$1$		$4$	$73728$	$0.895024$	$-417267265/19773$	$0.90540$	$3.22638$	$[0, 1, 0, -2913, 61983]$	\(y^2=x^3+x^2-2913x+61983\)	52.2.0.a.1	$[(39, 96)]$
62400.hh1	62400dr1	62400.hh	62400dr	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 \)	\( - 2^{18} \cdot 3^{2} \cdot 5^{8} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$368640$	$1.699743$	$-417267265/19773$	$0.90540$	$4.10097$	$[0, 1, 0, -72833, -7893537]$	\(y^2=x^3+x^2-72833x-7893537\)	52.2.0.a.1	$[]$
117975.v1	117975bl1	117975.v	117975bl	$1$	$1$	\( 3 \cdot 5^{2} \cdot 11^{2} \cdot 13 \)	\( - 3^{2} \cdot 5^{2} \cdot 11^{6} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$3.828066614$	$1$		$2$	$205920$	$1.054251$	$-417267265/19773$	$0.90540$	$3.21403$	$[1, 0, 0, -5508, 163197]$	\(y^2+xy=x^3-5508x+163197\)	52.2.0.a.1	$[(-9, 465)]$
117975.bs1	117975bd1	117975.bs	117975bd	$1$	$1$	\( 3 \cdot 5^{2} \cdot 11^{2} \cdot 13 \)	\( - 3^{2} \cdot 5^{8} \cdot 11^{6} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$1029600$	$1.858971$	$-417267265/19773$	$0.90540$	$4.04092$	$[1, 1, 0, -137700, 20399625]$	\(y^2+xy=x^3+x^2-137700x+20399625\)	52.2.0.a.1	$[]$
143325.bv1	143325bo1	143325.bv	143325bo	$1$	$1$	\( 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 3^{8} \cdot 5^{2} \cdot 7^{6} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$10.04572452$	$1$		$0$	$380160$	$1.377565$	$-417267265/19773$	$0.90540$	$3.48812$	$[1, -1, 1, -20075, -1133688]$	\(y^2+xy+y=x^3-x^2-20075x-1133688\)	52.2.0.a.1	$[(59228/11, 13386156/11)]$
143325.ey1	143325dz1	143325.ey	143325dz	$1$	$1$	\( 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 3^{8} \cdot 5^{8} \cdot 7^{6} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$17.92702283$	$1$		$0$	$1900800$	$2.182285$	$-417267265/19773$	$0.90540$	$4.30145$	$[1, -1, 0, -501867, -142212834]$	\(y^2+xy=x^3-x^2-501867x-142212834\)	52.2.0.a.1	$[(703917486/865, 9243607672764/865)]$
187200.co1	187200la1	187200.co	187200la	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 \)	\( - 2^{18} \cdot 3^{8} \cdot 5^{2} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$589824$	$1.444330$	$-417267265/19773$	$0.90540$	$3.47738$	$[0, 0, 0, -26220, 1699760]$	\(y^2=x^3-26220x+1699760\)	52.2.0.a.1	$[]$
187200.cr1	187200o1	187200.cr	187200o	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 \)	\( - 2^{18} \cdot 3^{8} \cdot 5^{8} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$2.368681716$	$1$		$4$	$2949120$	$2.249050$	$-417267265/19773$	$0.90540$	$4.27282$	$[0, 0, 0, -655500, -212470000]$	\(y^2=x^3-655500x-212470000\)	52.2.0.a.1	$[(946, 3744)]$
187200.nv1	187200kd1	187200.nv	187200kd	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 \)	\( - 2^{18} \cdot 3^{8} \cdot 5^{8} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$2949120$	$2.249050$	$-417267265/19773$	$0.90540$	$4.27282$	$[0, 0, 0, -655500, 212470000]$	\(y^2=x^3-655500x+212470000\)	52.2.0.a.1	$[]$
187200.oa1	187200fw1	187200.oa	187200fw	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 \)	\( - 2^{18} \cdot 3^{8} \cdot 5^{2} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$5.900786338$	$1$		$0$	$589824$	$1.444330$	$-417267265/19773$	$0.90540$	$3.47738$	$[0, 0, 0, -26220, -1699760]$	\(y^2=x^3-26220x-1699760\)	52.2.0.a.1	$[(2074/3, 57248/3)]$
202800.y1	202800et1	202800.y	202800et	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13^{2} \)	\( - 2^{12} \cdot 3^{2} \cdot 5^{2} \cdot 13^{9} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1.515231901$	$1$		$10$	$1548288$	$1.830925$	$-417267265/19773$	$0.90540$	$3.83424$	$[0, -1, 0, -123088, 17329792]$	\(y^2=x^3-x^2-123088x+17329792\)	52.2.0.a.1	$[(-342, 4394), (178, 1014)]$
202800.jq1	202800bc1	202800.jq	202800bc	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13^{2} \)	\( - 2^{12} \cdot 3^{2} \cdot 5^{8} \cdot 13^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$7741440$	$2.635643$	$-417267265/19773$	$0.90540$	$4.62447$	$[0, 1, 0, -3077208, 2160069588]$	\(y^2=x^3+x^2-3077208x+2160069588\)	52.2.0.a.1	$[]$
281775.q1	281775q1	281775.q	281775q	$1$	$1$	\( 3 \cdot 5^{2} \cdot 13 \cdot 17^{2} \)	\( - 3^{2} \cdot 5^{8} \cdot 13^{3} \cdot 17^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$6.046792440$	$1$		$2$	$3444480$	$2.076630$	$-417267265/19773$	$0.90540$	$3.96870$	$[1, 0, 0, -328888, -75538483]$	\(y^2+xy=x^3-328888x-75538483\)	52.2.0.a.1	$[(5927, 451124)]$
281775.br1	281775br1	281775.br	281775br	$1$	$1$	\( 3 \cdot 5^{2} \cdot 13 \cdot 17^{2} \)	\( - 3^{2} \cdot 5^{2} \cdot 13^{3} \cdot 17^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1$	$1$		$0$	$688896$	$1.271910$	$-417267265/19773$	$0.90540$	$3.19918$	$[1, 1, 0, -13155, -609570]$	\(y^2+xy=x^3+x^2-13155x-609570\)	52.2.0.a.1	$[]$
351975.g1	351975g1	351975.g	351975g	$1$	$1$	\( 3 \cdot 5^{2} \cdot 13 \cdot 19^{2} \)	\( - 3^{2} \cdot 5^{2} \cdot 13^{3} \cdot 19^{6} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1.235031688$	$1$		$12$	$870912$	$1.327522$	$-417267265/19773$	$0.90540$	$3.19571$	$[1, 1, 1, -16433, 836516]$	\(y^2+xy+y=x^3+x^2-16433x+836516\)	52.2.0.a.1	$[(36, 523), (74, 143)]$
351975.br1	351975br1	351975.br	351975br	$1$	$1$	\( 3 \cdot 5^{2} \cdot 13 \cdot 19^{2} \)	\( - 3^{2} \cdot 5^{8} \cdot 13^{3} \cdot 19^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$1.945316915$	$1$		$2$	$4354560$	$2.132240$	$-417267265/19773$	$0.90540$	$3.95183$	$[1, 0, 1, -410826, 105386173]$	\(y^2+xy+y=x^3-410826x+105386173\)	52.2.0.a.1	$[(733, 13712)]$
353925.u1	353925u1	353925.u	353925u	$1$	$1$	\( 3^{2} \cdot 5^{2} \cdot 11^{2} \cdot 13 \)	\( - 3^{8} \cdot 5^{8} \cdot 11^{6} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$3.628722112$	$1$		$2$	$8236800$	$2.408276$	$-417267265/19773$	$0.90540$	$4.20937$	$[1, -1, 1, -1239305, -552029178]$	\(y^2+xy+y=x^3-x^2-1239305x-552029178\)	52.2.0.a.1	$[(4694, 309165)]$
353925.dl1	353925dl1	353925.dl	353925dl	$1$	$1$	\( 3^{2} \cdot 5^{2} \cdot 11^{2} \cdot 13 \)	\( - 3^{8} \cdot 5^{2} \cdot 11^{6} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$52$	$2$	$0$	$33.38924178$	$1$		$0$	$1647360$	$1.603558$	$-417267265/19773$	$0.90540$	$3.45358$	$[1, -1, 0, -49572, -4406319]$	\(y^2+xy=x^3-x^2-49572x-4406319\)	52.2.0.a.1	$[(788457961742160/1118987, 20044076497775651058387/1118987)]$