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
3192.i2	3192a2	3192.i	3192a	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{8} \cdot 3^{2} \cdot 7^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1596$	$48$	$0$	$1$	$1$		$3$	$1024$	$0.154619$	$340062928/159201$	$0.84722$	$3.12203$	$[0, -1, 0, -92, 180]$	\(y^2=x^3-x^2-92x+180\)	2.6.0.a.1, 12.12.0-2.a.1.1, 28.12.0-2.a.1.1, 76.12.0.?, 84.24.0.?, $\ldots$	$[]$
6384.bf2	6384k2	6384.bf	6384k	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{8} \cdot 3^{2} \cdot 7^{2} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1596$	$48$	$0$	$3.275171707$	$1$		$5$	$2048$	$0.154619$	$340062928/159201$	$0.84722$	$2.87504$	$[0, 1, 0, -92, -180]$	\(y^2=x^3+x^2-92x-180\)	2.6.0.a.1, 12.12.0-2.a.1.1, 28.12.0-2.a.1.1, 76.12.0.?, 84.24.0.?, $\ldots$	$[(523, 11970)]$
9576.c2	9576w2	9576.c	9576w	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{8} \cdot 3^{8} \cdot 7^{2} \cdot 19^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1596$	$48$	$0$	$1.400618188$	$1$		$33$	$8192$	$0.703925$	$340062928/159201$	$0.84722$	$3.46694$	$[0, 0, 0, -831, -4030]$	\(y^2=x^3-831x-4030\)	2.6.0.a.1, 4.12.0-2.a.1.1, 84.24.0.?, 228.24.0.?, 532.24.0.?, $\ldots$	$[(-7, 38), (-19, 70)]$
19152.l2	19152v2	19152.l	19152v	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{8} \cdot 3^{8} \cdot 7^{2} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1596$	$48$	$0$	$2.070662755$	$1$		$9$	$16384$	$0.703925$	$340062928/159201$	$0.84722$	$3.22322$	$[0, 0, 0, -831, 4030]$	\(y^2=x^3-831x+4030\)	2.6.0.a.1, 4.12.0-2.a.1.1, 84.24.0.?, 228.24.0.?, 532.24.0.?, $\ldots$	$[(33, 112)]$
22344.s2	22344u2	22344.s	22344u	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{8} \cdot 3^{2} \cdot 7^{8} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1596$	$48$	$0$	$5.035110592$	$1$		$3$	$49152$	$1.127575$	$340062928/159201$	$0.84722$	$3.68126$	$[0, 1, 0, -4524, -52704]$	\(y^2=x^3+x^2-4524x-52704\)	2.6.0.a.1, 4.12.0-2.a.1.1, 84.24.0.?, 228.24.0.?, 532.24.0.?, $\ldots$	$[(-75/2, 1287/2)]$
25536.o2	25536co2	25536.o	25536co	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{14} \cdot 3^{2} \cdot 7^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$3192$	$48$	$0$	$1$	$1$		$3$	$16384$	$0.501193$	$340062928/159201$	$0.84722$	$2.89211$	$[0, -1, 0, -369, -1071]$	\(y^2=x^3-x^2-369x-1071\)	2.6.0.a.1, 24.12.0-2.a.1.1, 56.12.0-2.a.1.1, 84.12.0.?, 152.12.0.?, $\ldots$	$[]$
25536.cc2	25536bc2	25536.cc	25536bc	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{14} \cdot 3^{2} \cdot 7^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$3192$	$48$	$0$	$1$	$1$		$3$	$16384$	$0.501193$	$340062928/159201$	$0.84722$	$2.89211$	$[0, 1, 0, -369, 1071]$	\(y^2=x^3+x^2-369x+1071\)	2.6.0.a.1, 24.12.0-2.a.1.1, 56.12.0-2.a.1.1, 84.12.0.?, 152.12.0.?, $\ldots$	$[]$
44688.f2	44688n2	44688.f	44688n	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{8} \cdot 3^{2} \cdot 7^{8} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1596$	$48$	$0$	$2.344055421$	$1$		$7$	$98304$	$1.127575$	$340062928/159201$	$0.84722$	$3.44295$	$[0, -1, 0, -4524, 52704]$	\(y^2=x^3-x^2-4524x+52704\)	2.6.0.a.1, 4.12.0-2.a.1.1, 84.24.0.?, 228.24.0.?, 532.24.0.?, $\ldots$	$[(-15, 342)]$
60648.bn2	60648bi2	60648.bn	60648bi	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{8} \cdot 3^{2} \cdot 7^{2} \cdot 19^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1596$	$48$	$0$	$1$	$4$	$2$	$3$	$368640$	$1.626839$	$340062928/159201$	$0.84722$	$3.89150$	$[0, 1, 0, -33332, -1034880]$	\(y^2=x^3+x^2-33332x-1034880\)	2.6.0.a.1, 4.12.0-2.a.1.1, 84.24.0.?, 228.24.0.?, 532.24.0.?, $\ldots$	$[]$
67032.cc2	67032ce2	67032.cc	67032ce	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{8} \cdot 3^{8} \cdot 7^{8} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1596$	$48$	$0$	$1$	$1$		$3$	$393216$	$1.676880$	$340062928/159201$	$0.84722$	$3.91049$	$[0, 0, 0, -40719, 1382290]$	\(y^2=x^3-40719x+1382290\)	2.6.0.a.1, 12.12.0-2.a.1.1, 28.12.0-2.a.1.1, 76.12.0.?, 84.24.0.?, $\ldots$	$[]$
76608.em2	76608bc2	76608.em	76608bc	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{14} \cdot 3^{8} \cdot 7^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$3192$	$48$	$0$	$1$	$1$		$3$	$131072$	$1.050499$	$340062928/159201$	$0.84722$	$3.19571$	$[0, 0, 0, -3324, -32240]$	\(y^2=x^3-3324x-32240\)	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 168.24.0.?, 228.12.0.?, $\ldots$	$[]$
76608.et2	76608fm2	76608.et	76608fm	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{14} \cdot 3^{8} \cdot 7^{2} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$3192$	$48$	$0$	$2.699170366$	$1$		$7$	$131072$	$1.050499$	$340062928/159201$	$0.84722$	$3.19571$	$[0, 0, 0, -3324, 32240]$	\(y^2=x^3-3324x+32240\)	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 168.24.0.?, 228.12.0.?, $\ldots$	$[(2, 160)]$
79800.bw2	79800bt2	79800.bw	79800bt	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{8} \cdot 3^{2} \cdot 5^{6} \cdot 7^{2} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$7980$	$48$	$0$	$1.463022186$	$1$		$11$	$131072$	$0.959338$	$340062928/159201$	$0.84722$	$3.08723$	$[0, 1, 0, -2308, 17888]$	\(y^2=x^3+x^2-2308x+17888\)	2.6.0.a.1, 60.12.0-2.a.1.1, 84.12.0.?, 140.12.0.?, 228.12.0.?, $\ldots$	$[(-2, 150)]$
121296.bo2	121296s2	121296.bo	121296s	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{8} \cdot 3^{2} \cdot 7^{2} \cdot 19^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1596$	$48$	$0$	$9.205634888$	$1$		$3$	$737280$	$1.626839$	$340062928/159201$	$0.84722$	$3.66107$	$[0, -1, 0, -33332, 1034880]$	\(y^2=x^3-x^2-33332x+1034880\)	2.6.0.a.1, 4.12.0-2.a.1.1, 84.24.0.?, 228.24.0.?, 532.24.0.?, $\ldots$	$[(52060/3, 11871440/3)]$
134064.ff2	134064fb2	134064.ff	134064fb	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{8} \cdot 3^{8} \cdot 7^{8} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1596$	$48$	$0$	$1$	$4$	$2$	$3$	$786432$	$1.676880$	$340062928/159201$	$0.84722$	$3.68090$	$[0, 0, 0, -40719, -1382290]$	\(y^2=x^3-40719x-1382290\)	2.6.0.a.1, 12.12.0-2.a.1.1, 28.12.0-2.a.1.1, 76.12.0.?, 84.24.0.?, $\ldots$	$[]$
159600.f2	159600gr2	159600.f	159600gr	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{8} \cdot 3^{2} \cdot 5^{6} \cdot 7^{2} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$7980$	$48$	$0$	$1.774384469$	$1$		$11$	$262144$	$0.959338$	$340062928/159201$	$0.84722$	$2.90861$	$[0, -1, 0, -2308, -17888]$	\(y^2=x^3-x^2-2308x-17888\)	2.6.0.a.1, 60.12.0-2.a.1.1, 84.12.0.?, 140.12.0.?, 228.12.0.?, $\ldots$	$[(-23, 150)]$
178752.eb2	178752kc2	178752.eb	178752kc	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{14} \cdot 3^{2} \cdot 7^{8} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$3192$	$48$	$0$	$3.041259112$	$1$		$7$	$786432$	$1.474148$	$340062928/159201$	$0.84722$	$3.39218$	$[0, -1, 0, -18097, -403535]$	\(y^2=x^3-x^2-18097x-403535\)	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 168.24.0.?, 228.12.0.?, $\ldots$	$[(-71, 720)]$
178752.jq2	178752cl2	178752.jq	178752cl	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{14} \cdot 3^{2} \cdot 7^{8} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$3192$	$48$	$0$	$1$	$1$		$3$	$786432$	$1.474148$	$340062928/159201$	$0.84722$	$3.39218$	$[0, 1, 0, -18097, 403535]$	\(y^2=x^3+x^2-18097x+403535\)	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 168.24.0.?, 228.12.0.?, $\ldots$	$[]$
181944.c2	181944bi2	181944.c	181944bi	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{8} \cdot 3^{8} \cdot 7^{2} \cdot 19^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1596$	$48$	$0$	$4.025929320$	$1$		$7$	$2949120$	$2.176144$	$340062928/159201$	$0.84722$	$4.08276$	$[0, 0, 0, -299991, 27641770]$	\(y^2=x^3-299991x+27641770\)	2.6.0.a.1, 12.12.0-2.a.1.1, 28.12.0-2.a.1.2, 76.12.0.?, 84.24.0.?, $\ldots$	$[(-13, 5616)]$
239400.ct2	239400ct2	239400.ct	239400ct	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{8} \cdot 3^{8} \cdot 5^{6} \cdot 7^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$7980$	$48$	$0$	$1$	$1$		$3$	$1048576$	$1.508644$	$340062928/159201$	$0.84722$	$3.34559$	$[0, 0, 0, -20775, -503750]$	\(y^2=x^3-20775x-503750\)	2.6.0.a.1, 20.12.0-2.a.1.1, 84.12.0.?, 228.12.0.?, 420.24.0.?, $\ldots$	$[]$
363888.z2	363888z2	363888.z	363888z	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{8} \cdot 3^{8} \cdot 7^{2} \cdot 19^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1596$	$48$	$0$	$1$	$4$	$2$	$3$	$5898240$	$2.176144$	$340062928/159201$	$0.84722$	$3.86175$	$[0, 0, 0, -299991, -27641770]$	\(y^2=x^3-299991x-27641770\)	2.6.0.a.1, 12.12.0-2.a.1.1, 28.12.0-2.a.1.2, 76.12.0.?, 84.24.0.?, $\ldots$	$[]$
386232.bb2	386232bb2	386232.bb	386232bb	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11^{2} \cdot 19 \)	\( 2^{8} \cdot 3^{2} \cdot 7^{2} \cdot 11^{6} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$17556$	$48$	$0$	$1$	$1$		$3$	$1310720$	$1.353567$	$340062928/159201$	$0.84722$	$3.07654$	$[0, -1, 0, -11172, -194940]$	\(y^2=x^3-x^2-11172x-194940\)	2.6.0.a.1, 84.12.0.?, 132.12.0.?, 228.12.0.?, 308.12.0.?, $\ldots$	$[]$
424536.n2	424536n2	424536.n	424536n	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 19^{2} \)	\( 2^{8} \cdot 3^{2} \cdot 7^{8} \cdot 19^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1596$	$48$	$0$	$1$	$1$		$3$	$17694720$	$2.599792$	$340062928/159201$	$0.84722$	$4.20811$	$[0, -1, 0, -1633284, 351697284]$	\(y^2=x^3-x^2-1633284x+351697284\)	2.6.0.a.1, 12.12.0-2.a.1.2, 28.12.0-2.a.1.1, 76.12.0.?, 84.24.0.?, $\ldots$	$[]$
478800.hb2	478800hb2	478800.hb	478800hb	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{8} \cdot 3^{8} \cdot 5^{6} \cdot 7^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$7980$	$48$	$0$	$1$	$1$		$3$	$2097152$	$1.508644$	$340062928/159201$	$0.84722$	$3.16828$	$[0, 0, 0, -20775, 503750]$	\(y^2=x^3-20775x+503750\)	2.6.0.a.1, 20.12.0-2.a.1.1, 84.12.0.?, 228.12.0.?, 420.24.0.?, $\ldots$	$[]$
485184.n2	485184n2	485184.n	485184n	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{14} \cdot 3^{2} \cdot 7^{2} \cdot 19^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$3192$	$48$	$0$	$1$	$1$		$3$	$5898240$	$1.973412$	$340062928/159201$	$0.84722$	$3.59107$	$[0, -1, 0, -133329, -8145711]$	\(y^2=x^3-x^2-133329x-8145711\)	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 168.24.0.?, 228.12.0.?, $\ldots$	$[]$
485184.fu2	485184fu2	485184.fu	485184fu	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{14} \cdot 3^{2} \cdot 7^{2} \cdot 19^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$3192$	$48$	$0$	$6.819871282$	$1$		$3$	$5898240$	$1.973412$	$340062928/159201$	$0.84722$	$3.59107$	$[0, 1, 0, -133329, 8145711]$	\(y^2=x^3+x^2-133329x+8145711\)	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 168.24.0.?, 228.12.0.?, $\ldots$	$[(-401/3, 101024/3)]$

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