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	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
2730.b3	2730c4	2730.b	2730c	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{3} \cdot 3^{5} \cdot 5^{20} \cdot 7^{4} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.7	2B	$840$	$48$	$0$	$1$	$4$	$2$	$0$	$460800$	$3.083145$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$7.64860$	$[1, 1, 0, -8216883, 16006788837]$	\(y^2+xy=x^3+x^2-8216883x+16006788837\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 12.12.0-4.c.1.1, 24.24.0-24.v.1.4, $\ldots$	$[ ]$
8190.bn3	8190bp4	8190.bn	8190bp	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{3} \cdot 3^{11} \cdot 5^{20} \cdot 7^{4} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$840$	$48$	$0$	$2.173254326$	$1$		$4$	$3686400$	$3.632450$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$7.44759$	$[1, -1, 1, -73951952, -432257250549]$	\(y^2+xy+y=x^3-x^2-73951952x-432257250549\)	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.v.1.1, 280.24.0.?, 840.48.0.?	$[(13451, 996549)]$
13650.dh3	13650cs4	13650.dh	13650cs	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{3} \cdot 3^{5} \cdot 5^{26} \cdot 7^{4} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$840$	$48$	$0$	$1$	$1$		$0$	$11059200$	$3.887863$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$7.36993$	$[1, 0, 0, -205422088, 2001259448792]$	\(y^2+xy=x^3-205422088x+2001259448792\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 40.12.0-4.c.1.1, 56.12.0-4.c.1.5, $\ldots$	$[ ]$
19110.bj3	19110be4	19110.bj	19110be	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{3} \cdot 3^{5} \cdot 5^{20} \cdot 7^{10} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$840$	$48$	$0$	$1$	$1$		$0$	$22118400$	$4.056099$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$7.32317$	$[1, 0, 1, -402627293, -5491536452944]$	\(y^2+xy+y=x^3-402627293x-5491536452944\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 40.12.0-4.c.1.5, 56.12.0-4.c.1.2, $\ldots$	$[ ]$
21840.bp3	21840cb3	21840.bp	21840cb	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{15} \cdot 3^{5} \cdot 5^{20} \cdot 7^{4} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$840$	$48$	$0$	$6.736471366$	$1$		$3$	$11059200$	$3.776291$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$6.88925$	$[0, 1, 0, -131470136, -1024697425836]$	\(y^2=x^3+x^2-131470136x-1024697425836\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 12.12.0-4.c.1.2, 24.24.0-24.v.1.3, $\ldots$	$[(15100, 658242)]$
35490.cs3	35490cv3	35490.cs	35490cv	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13^{2} \)	\( - 2^{3} \cdot 3^{5} \cdot 5^{20} \cdot 7^{4} \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$10920$	$48$	$0$	$1$	$1$		$0$	$77414400$	$4.365623$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$7.24499$	$[1, 1, 1, -1388653315, 35173858341305]$	\(y^2+xy+y=x^3+x^2-1388653315x+35173858341305\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 104.12.0.?, 156.12.0.?, $\ldots$	$[ ]$
40950.br3	40950bn3	40950.br	40950bn	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{3} \cdot 3^{11} \cdot 5^{26} \cdot 7^{4} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$840$	$48$	$0$	$10.16446585$	$1$		$2$	$88473600$	$4.437172$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$7.22822$	$[1, -1, 0, -1848798792, -54034005117384]$	\(y^2+xy=x^3-x^2-1848798792x-54034005117384\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 24.12.0.v.1, 56.12.0-4.c.1.6, $\ldots$	$[(6589749, 16912561863)]$
57330.de3	57330ec3	57330.de	57330ec	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{3} \cdot 3^{11} \cdot 5^{20} \cdot 7^{10} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$840$	$48$	$0$	$1$	$1$		$0$	$176947200$	$4.605408$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$7.19050$	$[1, -1, 1, -3623645633, 148271484229481]$	\(y^2+xy+y=x^3-x^2-3623645633x+148271484229481\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 28.12.0-4.c.1.1, 40.12.0-4.c.1.6, $\ldots$	$[ ]$
65520.ek3	65520en3	65520.ek	65520en	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{15} \cdot 3^{11} \cdot 5^{20} \cdot 7^{4} \cdot 13^{2} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$840$	$48$	$0$	$1$	$1$		$3$	$88473600$	$4.325600$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$6.80116$	$[0, 0, 0, -1183231227, 27665647266346]$	\(y^2=x^3-1183231227x+27665647266346\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.v.1.2, 280.24.0.?, 840.48.0.?	$[ ]$
87360.dl3	87360fl3	87360.dl	87360fl	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{21} \cdot 3^{5} \cdot 5^{20} \cdot 7^{4} \cdot 13^{2} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$840$	$48$	$0$	$1$	$1$		$3$	$88473600$	$4.122864$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$6.41537$	$[0, -1, 0, -525880545, -8197053526143]$	\(y^2=x^3-x^2-525880545x-8197053526143\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.v.1.2, 280.24.0.?, 840.48.0.?	$[ ]$
87360.fn3	87360cx3	87360.fn	87360cx	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{21} \cdot 3^{5} \cdot 5^{20} \cdot 7^{4} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$840$	$48$	$0$	$0.584684178$	$1$		$11$	$88473600$	$4.122864$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$6.41537$	$[0, 1, 0, -525880545, 8197053526143]$	\(y^2=x^3+x^2-525880545x+8197053526143\)	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.v.1.1, 280.24.0.?, 840.48.0.?	$[(-16269, 3528000)]$
95550.ij3	95550hk3	95550.ij	95550hk	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{3} \cdot 3^{5} \cdot 5^{26} \cdot 7^{10} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$840$	$48$	$0$	$1$	$16$	$2$	$0$	$530841600$	$4.860817$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$7.13747$	$[1, 1, 1, -10065682313, -686442056617969]$	\(y^2+xy+y=x^3+x^2-10065682313x-686442056617969\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 24.24.0-24.v.1.6, 280.24.0.?, $\ldots$	$[ ]$
106470.br3	106470br3	106470.br	106470br	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13^{2} \)	\( - 2^{3} \cdot 3^{11} \cdot 5^{20} \cdot 7^{4} \cdot 13^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$10920$	$48$	$0$	$99.04118935$	$1$		$0$	$619315200$	$4.914925$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$7.12683$	$[1, -1, 0, -12497879835, -949706673095075]$	\(y^2+xy=x^3-x^2-12497879835x-949706673095075\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 52.12.0-4.c.1.1, 280.12.0.?, $\ldots$	$[(93243726700028584391529067138243200646185501/23464527090437393581, 545637730402170293932840300568479751137977192358701831578409951889/23464527090437393581)]$
109200.f3	109200da3	109200.f	109200da	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{15} \cdot 3^{5} \cdot 5^{26} \cdot 7^{4} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$840$	$48$	$0$	$1$	$9$	$3$	$1$	$265420800$	$4.581009$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$6.76588$	$[0, -1, 0, -3286753408, -128080604722688]$	\(y^2=x^3-x^2-3286753408x-128080604722688\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 40.12.0-4.c.1.2, 56.12.0-4.c.1.5, $\ldots$	$[ ]$
152880.cq3	152880db4	152880.cq	152880db	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{15} \cdot 3^{5} \cdot 5^{20} \cdot 7^{10} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$840$	$48$	$0$	$1$	$1$		$1$	$530841600$	$4.749245$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$6.74429$	$[0, -1, 0, -6442036680, 351458332988400]$	\(y^2=x^3-x^2-6442036680x+351458332988400\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 40.12.0-4.c.1.5, 56.12.0-4.c.1.1, $\ldots$	$[ ]$
177450.cu3	177450hg4	177450.cu	177450hg	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13^{2} \)	\( - 2^{3} \cdot 3^{5} \cdot 5^{26} \cdot 7^{4} \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$10920$	$48$	$0$	$1$	$4$	$2$	$0$	$1857945600$	$5.170341$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$7.07921$	$[1, 0, 1, -34716332876, 4396801725328898]$	\(y^2+xy+y=x^3-34716332876x+4396801725328898\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 280.12.0.?, 520.12.0.?, $\ldots$	$[ ]$
248430.ie3	248430ie3	248430.ie	248430ie	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{3} \cdot 3^{5} \cdot 5^{20} \cdot 7^{10} \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$10920$	$48$	$0$	$1$	$16$	$2$	$0$	$3715891200$	$5.338577$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$7.04998$	$[1, 0, 0, -68044012436, -12064837543104984]$	\(y^2+xy=x^3-68044012436x-12064837543104984\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 280.12.0.?, 520.12.0.?, $\ldots$	$[ ]$
262080.ct3	262080ct3	262080.ct	262080ct	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{21} \cdot 3^{11} \cdot 5^{20} \cdot 7^{4} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$840$	$48$	$0$	$1$	$25$	$5$	$1$	$707788800$	$4.672173$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$6.37880$	$[0, 0, 0, -4732924908, -221325178130768]$	\(y^2=x^3-4732924908x-221325178130768\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 12.12.0-4.c.1.1, 24.24.0-24.v.1.4, $\ldots$	$[ ]$
262080.dz3	262080dz4	262080.dz	262080dz	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{21} \cdot 3^{11} \cdot 5^{20} \cdot 7^{4} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$840$	$48$	$0$	$1$	$1$		$1$	$707788800$	$4.672173$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$6.37880$	$[0, 0, 0, -4732924908, 221325178130768]$	\(y^2=x^3-4732924908x+221325178130768\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 12.12.0-4.c.1.2, 24.24.0-24.v.1.3, $\ldots$	$[ ]$
283920.he3	283920he3	283920.he	283920he	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 13^{2} \)	\( - 2^{15} \cdot 3^{5} \cdot 5^{20} \cdot 7^{4} \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$10920$	$48$	$0$	$1$	$1$		$1$	$1857945600$	$5.058769$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$6.70760$	$[0, 1, 0, -22218453040, -2251171370749612]$	\(y^2=x^3+x^2-22218453040x-2251171370749612\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 104.12.0.?, 156.12.0.?, $\ldots$	$[ ]$
286650.bm3	286650bm4	286650.bm	286650bm	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{3} \cdot 3^{11} \cdot 5^{26} \cdot 7^{10} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.13	2B	$840$	$48$	$0$	$1$	$16$	$2$	$0$	$4246732800$	$5.410126$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$7.03802$	$[1, -1, 0, -90591140817, 18533844937544341]$	\(y^2+xy=x^3-x^2-90591140817x+18533844937544341\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.6, 24.24.0-24.v.1.8, 140.12.0.?, $\ldots$	$[ ]$
327600.fp3	327600fp4	327600.fp	327600fp	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{15} \cdot 3^{11} \cdot 5^{26} \cdot 7^{4} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$840$	$48$	$0$	$36.61803765$	$1$		$1$	$2123366400$	$5.130318$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$6.69962$	$[0, 0, 0, -29580780675, 3458205908293250]$	\(y^2=x^3-29580780675x+3458205908293250\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 24.12.0.v.1, 56.12.0-4.c.1.6, $\ldots$	$[(307521137228425831/653369, 166413116454234076429521246/653369)]$
330330.ec3	330330ec3	330330.ec	330330ec	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \cdot 13 \)	\( - 2^{3} \cdot 3^{5} \cdot 5^{20} \cdot 7^{4} \cdot 11^{6} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$9$	$3$	$0$	$589824000$	$4.282097$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$5.89427$	$[1, 1, 1, -994242906, -21310007156481]$	\(y^2+xy+y=x^3+x^2-994242906x-21310007156481\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 88.12.0.?, 132.12.0.?, $\ldots$	$[ ]$
436800.gq3	436800gq4	436800.gq	436800gq	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{21} \cdot 3^{5} \cdot 5^{26} \cdot 7^{4} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$840$	$48$	$0$	$31.45272118$	$1$		$1$	$2123366400$	$4.927582$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$6.36390$	$[0, -1, 0, -13147013633, 1024657984795137]$	\(y^2=x^3-x^2-13147013633x+1024657984795137\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 24.12.0.v.1, 56.12.0-4.c.1.4, $\ldots$	$[(-748500066820824/72659, 2384791002841118614743/72659)]$
436800.or3	436800or3	436800.or	436800or	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{21} \cdot 3^{5} \cdot 5^{26} \cdot 7^{4} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$840$	$48$	$0$	$1$	$16$	$2$	$1$	$2123366400$	$4.927582$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$6.36390$	$[0, 1, 0, -13147013633, -1024657984795137]$	\(y^2=x^3+x^2-13147013633x-1024657984795137\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 24.12.0.v.1, 56.12.0-4.c.1.4, $\ldots$	$[ ]$
458640.fp3	458640fp3	458640.fp	458640fp	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{15} \cdot 3^{11} \cdot 5^{20} \cdot 7^{10} \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$840$	$48$	$0$	$1$	$16$	$2$	$1$	$4246732800$	$5.298553$	$-61354313914516350666047929/75227254486083984375000$	$1.04405$	$6.68157$	$[0, 0, 0, -57978330123, -9489317012356678]$	\(y^2=x^3-57978330123x-9489317012356678\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.v.1, 28.12.0-4.c.1.2, 40.12.0-4.c.1.6, $\ldots$	$[ ]$

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