Elliptic curve search results

Results (12 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
10626.r1	10626p2	10626.r	10626p	$2$	$3$	\( 2 \cdot 3 \cdot 7 \cdot 11 \cdot 23 \)	\( - 2^{10} \cdot 3^{3} \cdot 7^{3} \cdot 11^{3} \cdot 23^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.2	3B.1.2	$21252$	$16$	$0$	$1$	$9$	$3$	$0$	$8981280$	$4.114464$	$-3133382230165522315000208250857964625/153574604080128$	$1.05971$	$9.06425$	$[1, 0, 0, -30485726893, -2048771311274671]$	\(y^2+xy=x^3-30485726893x-2048771311274671\)	3.8.0-3.a.1.1, 21252.16.0.?	$[]$
31878.n1	31878q2	31878.n	31878q	$2$	$3$	\( 2 \cdot 3^{2} \cdot 7 \cdot 11 \cdot 23 \)	\( - 2^{10} \cdot 3^{9} \cdot 7^{3} \cdot 11^{3} \cdot 23^{3} \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$21252$	$16$	$0$	$6.841400981$	$1$		$4$	$71850240$	$4.663773$	$-3133382230165522315000208250857964625/153574604080128$	$1.05971$	$8.73961$	$[1, -1, 0, -274371542037, 55316825404416117]$	\(y^2+xy=x^3-x^2-274371542037x+55316825404416117\)	3.8.0-3.a.1.2, 21252.16.0.?	$[(-461894, 289201475)]$
74382.bc1	74382u2	74382.bc	74382u	$2$	$3$	\( 2 \cdot 3 \cdot 7^{2} \cdot 11 \cdot 23 \)	\( - 2^{10} \cdot 3^{3} \cdot 7^{9} \cdot 11^{3} \cdot 23^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$21252$	$16$	$0$	$5.758221841$	$1$		$0$	$431101440$	$5.087418$	$-3133382230165522315000208250857964625/153574604080128$	$1.05971$	$8.53266$	$[1, 1, 1, -1493800617758, 702727065966594395]$	\(y^2+xy+y=x^3+x^2-1493800617758x+702727065966594395\)	3.4.0.a.1, 21.8.0-3.a.1.2, 3036.8.0.?, 21252.16.0.?	$[(6342817/3, 25292029/3)]$
85008.r1	85008bi2	85008.r	85008bi	$2$	$3$	\( 2^{4} \cdot 3 \cdot 7 \cdot 11 \cdot 23 \)	\( - 2^{22} \cdot 3^{3} \cdot 7^{3} \cdot 11^{3} \cdot 23^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$21252$	$16$	$0$	$1$	$1$		$0$	$215550720$	$4.807610$	$-3133382230165522315000208250857964625/153574604080128$	$1.05971$	$8.13646$	$[0, -1, 0, -487771630288, 131121363921578944]$	\(y^2=x^3-x^2-487771630288x+131121363921578944\)	3.4.0.a.1, 12.8.0-3.a.1.2, 10626.8.0.?, 21252.16.0.?	$[]$
116886.u1	116886j2	116886.u	116886j	$2$	$3$	\( 2 \cdot 3 \cdot 7 \cdot 11^{2} \cdot 23 \)	\( - 2^{10} \cdot 3^{3} \cdot 7^{3} \cdot 11^{9} \cdot 23^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$21252$	$16$	$0$	$17.27106184$	$1$		$0$	$1077753600$	$5.313416$	$-3133382230165522315000208250857964625/153574604080128$	$1.05971$	$8.43456$	$[1, 0, 1, -3688772954056, 2726910926533633046]$	\(y^2+xy+y=x^3-3688772954056x+2726910926533633046\)	3.4.0.a.1, 33.8.0-3.a.1.1, 1932.8.0.?, 21252.16.0.?	$[(40540448905/191, 26723536344757/191)]$
223146.bh1	223146di2	223146.bh	223146di	$2$	$3$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \cdot 23 \)	\( - 2^{10} \cdot 3^{9} \cdot 7^{9} \cdot 11^{3} \cdot 23^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$21252$	$16$	$0$	$11.89679113$	$1$		$0$	$3448811520$	$5.636726$	$-3133382230165522315000208250857964625/153574604080128$	$1.05971$	$8.30674$	$[1, -1, 0, -13444205559822, -18973644225303608492]$	\(y^2+xy=x^3-x^2-13444205559822x-18973644225303608492\)	3.4.0.a.1, 21.8.0-3.a.1.1, 3036.8.0.?, 21252.16.0.?	$[(48363827/2, 318555072625/2)]$
244398.bl1	244398bl2	244398.bl	244398bl	$2$	$3$	\( 2 \cdot 3 \cdot 7 \cdot 11 \cdot 23^{2} \)	\( - 2^{10} \cdot 3^{3} \cdot 7^{3} \cdot 11^{3} \cdot 23^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$21252$	$16$	$0$	$2.213913104$	$1$		$0$	$4742115840$	$5.682213$	$-3133382230165522315000208250857964625/153574604080128$	$1.05971$	$8.28982$	$[1, 0, 0, -16126949526408, 24927368290379869248]$	\(y^2+xy=x^3-16126949526408x+24927368290379869248\)	3.4.0.a.1, 69.8.0-3.a.1.1, 924.8.0.?, 21252.16.0.?	$[(391834056/13, -2546775360/13)]$
255024.ci1	255024ci2	255024.ci	255024ci	$2$	$3$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 11 \cdot 23 \)	\( - 2^{22} \cdot 3^{9} \cdot 7^{3} \cdot 11^{3} \cdot 23^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$21252$	$16$	$0$	$440.4247690$	$1$		$0$	$1724405760$	$5.356918$	$-3133382230165522315000208250857964625/153574604080128$	$1.05971$	$7.94793$	$[0, 0, 0, -4389944672595, -3540272435937958894]$	\(y^2=x^3-4389944672595x-3540272435937958894\)	3.4.0.a.1, 12.8.0-3.a.1.1, 10626.8.0.?, 21252.16.0.?	$[(1277476042753597597234494192601101177656240056981084162139145289988631939272260314955158055667093222534701204839177831640566839718008537049476107601595975246377441606887038615977028205529615182/80492365136852223075753497140026062305757709816748122210359198475042590381925971303022825521, 1443791645465612700217913382140575850306745401810082874550612922232846454838827531390279361776283429583777612316962153393816397572087434141246030856783915287773151737669817605651563204872371743815688033984490403250885175087894026373229482098216899383421684328449317754609746501992346999352/80492365136852223075753497140026062305757709816748122210359198475042590381925971303022825521)]$
265650.p1	265650p2	265650.p	265650p	$2$	$3$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \cdot 23 \)	\( - 2^{10} \cdot 3^{3} \cdot 5^{6} \cdot 7^{3} \cdot 11^{3} \cdot 23^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$106260$	$16$	$0$	$1$	$49$	$7$	$0$	$1293304320$	$4.919182$	$-3133382230165522315000208250857964625/153574604080128$	$1.05971$	$7.50138$	$[1, 1, 0, -762143172325, -256096413909333875]$	\(y^2+xy=x^3+x^2-762143172325x-256096413909333875\)	3.4.0.a.1, 15.8.0-3.a.1.1, 21252.8.0.?, 106260.16.0.?	$[]$
340032.bt1	340032bt2	340032.bt	340032bt	$2$	$3$	\( 2^{6} \cdot 3 \cdot 7 \cdot 11 \cdot 23 \)	\( - 2^{28} \cdot 3^{3} \cdot 7^{3} \cdot 11^{3} \cdot 23^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$42504$	$16$	$0$	$82.86676601$	$1$		$0$	$1724405760$	$5.154190$	$-3133382230165522315000208250857964625/153574604080128$	$1.05971$	$7.57740$	$[0, -1, 0, -1951086521153, -1048968960286110399]$	\(y^2=x^3-x^2-1951086521153x-1048968960286110399\)	3.4.0.a.1, 24.8.0-3.a.1.1, 21252.8.0.?, 42504.16.0.?	$[(117631376478677337554402646106325085337/7358880417284099, 887720799534822452300185057696987106230239226738143327232/7358880417284099)]$
340032.eq1	340032eq2	340032.eq	340032eq	$2$	$3$	\( 2^{6} \cdot 3 \cdot 7 \cdot 11 \cdot 23 \)	\( - 2^{28} \cdot 3^{3} \cdot 7^{3} \cdot 11^{3} \cdot 23^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$42504$	$16$	$0$	$1$	$1$		$0$	$1724405760$	$5.154190$	$-3133382230165522315000208250857964625/153574604080128$	$1.05971$	$7.57740$	$[0, 1, 0, -1951086521153, 1048968960286110399]$	\(y^2=x^3+x^2-1951086521153x+1048968960286110399\)	3.4.0.a.1, 24.8.0-3.a.1.3, 21252.8.0.?, 42504.16.0.?	$[]$
350658.dj1	350658dj2	350658.dj	350658dj	$2$	$3$	\( 2 \cdot 3^{2} \cdot 7 \cdot 11^{2} \cdot 23 \)	\( - 2^{10} \cdot 3^{9} \cdot 7^{3} \cdot 11^{9} \cdot 23^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$21252$	$16$	$0$	$49.63706330$	$1$		$0$	$8622028800$	$5.862717$	$-3133382230165522315000208250857964625/153574604080128$	$1.05971$	$8.22508$	$[1, -1, 1, -33198956586500, -73626595016408092249]$	\(y^2+xy+y=x^3-x^2-33198956586500x-73626595016408092249\)	3.4.0.a.1, 33.8.0-3.a.1.2, 1932.8.0.?, 21252.16.0.?	$[(2170252728153761234750937/52036361, 3197028750452741685430154868587260205/52036361)]$