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
2730.u1	2730w5	2730.u	2730w	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 2 \cdot 3^{2} \cdot 5^{8} \cdot 7^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.55	2B	$21840$	$192$	$1$	$1$	$1$		$0$	$8192$	$1.248440$	$25306558948218234961/4478906250$	$0.98968$	$5.64677$	$2$	$[1, 1, 1, -61165, -5847895]$	\(y^2+xy+y=x^3+x^2-61165x-5847895\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 80.48.0.?, 104.48.0.?, $\ldots$	$[ ]$	$1$
8190.g1	8190k5	8190.g	8190k	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( 2 \cdot 3^{8} \cdot 5^{8} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$21840$	$192$	$1$	$2.394940853$	$1$		$4$	$65536$	$1.797745$	$25306558948218234961/4478906250$	$0.98968$	$5.68984$	$2$	$[1, -1, 0, -550485, 157342675]$	\(y^2+xy=x^3-x^2-550485x+157342675\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.1, 24.24.0-8.n.1.10, $\ldots$	$[(431, -130)]$	$1$
13650.bh1	13650be5	13650.bh	13650be	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2 \cdot 3^{2} \cdot 5^{14} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.3	2B	$21840$	$192$	$1$	$1.919699797$	$4$	$2$	$6$	$196608$	$2.053158$	$25306558948218234961/4478906250$	$0.98968$	$5.70648$	$2$	$[1, 0, 1, -1529126, -727928602]$	\(y^2+xy+y=x^3-1529126x-727928602\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.5, 20.12.0-4.c.1.1, $\ldots$	$[(-714, 367)]$	$1$
19110.cm1	19110co5	19110.cm	19110co	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \)	\( 2 \cdot 3^{2} \cdot 5^{8} \cdot 7^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$21840$	$192$	$1$	$1$	$4$	$2$	$0$	$393216$	$2.221394$	$25306558948218234961/4478906250$	$0.98968$	$5.71650$	$2$	$[1, 0, 0, -2997086, 1996836666]$	\(y^2+xy=x^3-2997086x+1996836666\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 24.24.0-8.n.1.4, 28.12.0-4.c.1.1, $\ldots$	$[ ]$	$1$
21840.cm1	21840ck6	21840.cm	21840ck	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 2^{13} \cdot 3^{2} \cdot 5^{8} \cdot 7^{2} \cdot 13 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.45	2B	$21840$	$192$	$1$	$1$	$1$		$3$	$196608$	$1.941586$	$25306558948218234961/4478906250$	$0.98968$	$5.30405$	$2$	$[0, 1, 0, -978640, 372307988]$	\(y^2=x^3+x^2-978640x+372307988\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 80.48.0.?, 104.48.0.?, $\ldots$	$[ ]$	$1$
35490.l1	35490i6	35490.l	35490i	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13^{2} \)	\( 2 \cdot 3^{2} \cdot 5^{8} \cdot 7^{2} \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.96	2B	$21840$	$192$	$1$	$1$	$4$	$2$	$0$	$1376256$	$2.530914$	$25306558948218234961/4478906250$	$0.98968$	$5.73325$	$2$	$[1, 1, 0, -10336888, -12796140482]$	\(y^2+xy=x^3+x^2-10336888x-12796140482\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.8, 52.12.0-4.c.1.1, 80.48.0.?, $\ldots$	$[ ]$	$1$
40950.ff1	40950ef6	40950.ff	40950ef	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2 \cdot 3^{8} \cdot 5^{14} \cdot 7^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$21840$	$192$	$1$	$1$	$4$	$2$	$0$	$1572864$	$2.602463$	$25306558948218234961/4478906250$	$0.98968$	$5.73684$	$2$	$[1, -1, 1, -13762130, 19654072247]$	\(y^2+xy+y=x^3-x^2-13762130x+19654072247\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 48.24.0-8.n.1.5, 60.12.0-4.c.1.1, $\ldots$	$[ ]$	$1$
57330.cs1	57330cg6	57330.cs	57330cg	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \)	\( 2 \cdot 3^{8} \cdot 5^{8} \cdot 7^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.93	2B	$21840$	$192$	$1$	$1$	$4$	$2$	$0$	$3145728$	$2.770699$	$25306558948218234961/4478906250$	$0.98968$	$5.74493$	$2$	$[1, -1, 0, -26973774, -53914589982]$	\(y^2+xy=x^3-x^2-26973774x-53914589982\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.5, 80.48.0.?, 84.12.0.?, $\ldots$	$[ ]$	$1$
65520.bh1	65520dg6	65520.bh	65520dg	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( 2^{13} \cdot 3^{8} \cdot 5^{8} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$21840$	$192$	$1$	$3.624243664$	$4$	$2$	$5$	$1572864$	$2.490891$	$25306558948218234961/4478906250$	$0.98968$	$5.37299$	$2$	$[0, 0, 0, -8807763, -10061123438]$	\(y^2=x^3-8807763x-10061123438\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.2, 24.24.0-8.n.1.12, $\ldots$	$[(-1713, 22)]$	$1$
87360.bc1	87360eq6	87360.bc	87360eq	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 2^{19} \cdot 3^{2} \cdot 5^{8} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.97	2B	$21840$	$192$	$1$	$3.116311721$	$1$		$5$	$1572864$	$2.288158$	$25306558948218234961/4478906250$	$0.98968$	$5.02332$	$2$	$[0, -1, 0, -3914561, 2982378465]$	\(y^2=x^3-x^2-3914561x+2982378465\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.11, 52.12.0-4.c.1.2, 80.48.0.?, $\ldots$	$[(1144, 77)]$	$1$
87360.eh1	87360bw6	87360.eh	87360bw	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 2^{19} \cdot 3^{2} \cdot 5^{8} \cdot 7^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.95	2B	$21840$	$192$	$1$	$1$	$4$	$2$	$1$	$1572864$	$2.288158$	$25306558948218234961/4478906250$	$0.98968$	$5.02332$	$2$	$[0, 1, 0, -3914561, -2982378465]$	\(y^2=x^3+x^2-3914561x-2982378465\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.9, 52.12.0-4.c.1.1, 80.48.0.?, $\ldots$	$[ ]$	$1$
95550.q1	95550br6	95550.q	95550br	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( 2 \cdot 3^{2} \cdot 5^{14} \cdot 7^{8} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$21840$	$192$	$1$	$4.532119064$	$1$		$2$	$9437184$	$3.026112$	$25306558948218234961/4478906250$	$0.98968$	$5.75629$	$2$	$[1, 1, 0, -74927150, 249604583250]$	\(y^2+xy=x^3+x^2-74927150x+249604583250\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 48.24.0-8.n.1.6, 80.24.0.?, $\ldots$	$[(5109, 11190)]$	$1$
106470.fo1	106470gb6	106470.fo	106470gb	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13^{2} \)	\( 2 \cdot 3^{8} \cdot 5^{8} \cdot 7^{2} \cdot 13^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$21840$	$192$	$1$	$4.011889458$	$1$		$0$	$11010048$	$3.080219$	$25306558948218234961/4478906250$	$0.98968$	$5.75857$	$2$	$[1, -1, 1, -93031997, 345402761019]$	\(y^2+xy+y=x^3-x^2-93031997x+345402761019\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 24.24.0-8.n.1.2, 56.24.0-8.n.1.4, $\ldots$	$[(22383/2, 5263/2)]$	$1$
109200.bj1	109200cy6	109200.bj	109200cy	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2^{13} \cdot 3^{2} \cdot 5^{14} \cdot 7^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.8	2B	$21840$	$192$	$1$	$1$	$1$		$1$	$4718592$	$2.746304$	$25306558948218234961/4478906250$	$0.98968$	$5.40060$	$2$	$[0, -1, 0, -24466008, 46587430512]$	\(y^2=x^3-x^2-24466008x+46587430512\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.2, 20.12.0-4.c.1.2, $\ldots$	$[ ]$	$1$
152880.ch1	152880ey6	152880.ch	152880ey	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \)	\( 2^{13} \cdot 3^{2} \cdot 5^{8} \cdot 7^{8} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$21840$	$192$	$1$	$12.80899701$	$1$		$1$	$9437184$	$2.914539$	$25306558948218234961/4478906250$	$0.98968$	$5.41749$	$2$	$[0, -1, 0, -47953376, -127797546624]$	\(y^2=x^3-x^2-47953376x-127797546624\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 24.24.0-8.n.1.8, 28.12.0-4.c.1.2, $\ldots$	$[(14912466/29, 52290303750/29)]$	$1$
177450.jb1	177450ce6	177450.jb	177450ce	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13^{2} \)	\( 2 \cdot 3^{2} \cdot 5^{14} \cdot 7^{2} \cdot 13^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.14	2B	$21840$	$192$	$1$	$25.62603550$	$1$		$0$	$33030144$	$3.335632$	$25306558948218234961/4478906250$	$0.98968$	$5.76877$	$2$	$[1, 0, 0, -258422213, -1599000715833]$	\(y^2+xy=x^3-258422213x-1599000715833\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.6, 40.24.0-8.n.1.11, $\ldots$	$[(14314517571273/16472, 51154602149144573697/16472)]$	$1$
248430.fa1	248430fa5	248430.fa	248430fa	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13^{2} \)	\( 2 \cdot 3^{2} \cdot 5^{8} \cdot 7^{8} \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$21840$	$192$	$1$	$1$	$1$		$0$	$66060288$	$3.503868$	$25306558948218234961/4478906250$	$0.98968$	$5.77503$	$2$	$[1, 0, 1, -506507538, 4387556662738]$	\(y^2+xy+y=x^3-506507538x+4387556662738\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 24.24.0-8.n.1.7, 56.24.0-8.n.1.12, $\ldots$	$[ ]$	$1$
262080.hk1	262080hk5	262080.hk	262080hk	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( 2^{19} \cdot 3^{8} \cdot 5^{8} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$21840$	$192$	$1$	$0.779747121$	$1$		$9$	$12582912$	$2.837467$	$25306558948218234961/4478906250$	$0.98968$	$5.10932$	$2$	$[0, 0, 0, -35231052, 80488987504]$	\(y^2=x^3-35231052x+80488987504\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 24.24.0-8.n.1.11, 56.24.0-8.n.1.4, $\ldots$	$[(3438, 1120)]$	$1$
262080.na1	262080na6	262080.na	262080na	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( 2^{19} \cdot 3^{8} \cdot 5^{8} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$21840$	$192$	$1$	$5.320611172$	$1$		$3$	$12582912$	$2.837467$	$25306558948218234961/4478906250$	$0.98968$	$5.10932$	$2$	$[0, 0, 0, -35231052, -80488987504]$	\(y^2=x^3-35231052x-80488987504\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 24.24.0-8.n.1.9, 56.24.0-8.n.1.3, $\ldots$	$[(8672, 515900)]$	$1$
283920.ek1	283920ek5	283920.ek	283920ek	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 13^{2} \)	\( 2^{13} \cdot 3^{2} \cdot 5^{8} \cdot 7^{2} \cdot 13^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.98	2B	$21840$	$192$	$1$	$6.266529219$	$1$		$3$	$33030144$	$3.224060$	$25306558948218234961/4478906250$	$0.98968$	$5.44621$	$2$	$[0, 1, 0, -165390216, 818622210420]$	\(y^2=x^3+x^2-165390216x+818622210420\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.4, 52.12.0-4.c.1.2, 80.48.0.?, $\ldots$	$[(27876, 4227366)]$	$1$
286650.ql1	286650ql6	286650.ql	286650ql	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( 2 \cdot 3^{8} \cdot 5^{14} \cdot 7^{8} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.4	2B	$21840$	$192$	$1$	$7.313186344$	$16$	$2$	$0$	$75497472$	$3.575420$	$25306558948218234961/4478906250$	$0.98968$	$5.77759$	$2$	$[1, -1, 1, -674344355, -6739998092103]$	\(y^2+xy+y=x^3-x^2-674344355x-6739998092103\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.8, 40.24.0-8.n.1.4, $\ldots$	$[(-239907/4, 540395/4)]$	$1$
327600.z1	327600z6	327600.z	327600z	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2^{13} \cdot 3^{8} \cdot 5^{14} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$21840$	$192$	$1$	$8.930886202$	$1$		$1$	$37748736$	$3.295612$	$25306558948218234961/4478906250$	$0.98968$	$5.45245$	$2$	$[0, 0, 0, -220194075, -1257640429750]$	\(y^2=x^3-220194075x-1257640429750\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 48.24.0-8.n.1.4, 60.12.0-4.c.1.2, $\ldots$	$[(-1036529/11, 550494/11)]$	$1$
330330.bg1	330330bg5	330330.bg	330330bg	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \cdot 13 \)	\( 2 \cdot 3^{2} \cdot 5^{8} \cdot 7^{2} \cdot 11^{6} \cdot 13 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$240240$	$192$	$1$	$1.018613548$	$1$		$16$	$10485760$	$2.447388$	$25306558948218234961/4478906250$	$0.98968$	$4.64791$	$2$	$[1, 1, 0, -7400967, 7746543171]$	\(y^2+xy=x^3+x^2-7400967x+7746543171\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 44.12.0-4.c.1.1, 80.24.0.?, $\ldots$	$[(1557, 129), (1601, 1317)]$	$1$
436800.jt1	436800jt6	436800.jt	436800jt	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2^{19} \cdot 3^{2} \cdot 5^{14} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.9	2B	$21840$	$192$	$1$	$9.958187589$	$1$		$1$	$37748736$	$3.092880$	$25306558948218234961/4478906250$	$0.98968$	$5.14435$	$2$	$[0, -1, 0, -97864033, -372601580063]$	\(y^2=x^3-x^2-97864033x-372601580063\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.4, 40.24.0-8.n.1.2, $\ldots$	$[(-965353/13, 443832/13)]$	$1$
436800.lg1	436800lg5	436800.lg	436800lg	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2^{19} \cdot 3^{2} \cdot 5^{14} \cdot 7^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.14	2B	$21840$	$192$	$1$	$1$	$1$		$1$	$37748736$	$3.092880$	$25306558948218234961/4478906250$	$0.98968$	$5.14435$	$2$	$[0, 1, 0, -97864033, 372601580063]$	\(y^2=x^3+x^2-97864033x+372601580063\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.6, 40.24.0-8.n.1.6, $\ldots$	$[ ]$	$1$
458640.ig1	458640ig5	458640.ig	458640ig	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \)	\( 2^{13} \cdot 3^{8} \cdot 5^{8} \cdot 7^{8} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.87	2B	$21840$	$192$	$1$	$4.228700624$	$1$		$3$	$75497472$	$3.463848$	$25306558948218234961/4478906250$	$0.98968$	$5.46658$	$2$	$[0, 0, 0, -431580387, 3450965339234]$	\(y^2=x^3-431580387x+3450965339234\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.1, 80.48.0.?, 84.12.0.?, $\ldots$	$[(14023, 395550)]$	$1$

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