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	Manin constant
2730.x2	2730x4	2730.x	2730x	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{8} \cdot 13 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.48.0.161	2B	$4368$	$192$	$1$	$0.975453197$	$1$		$12$	$24576$	$1.656696$	$4078208988807294650401/359723582400$	$1.00772$	$6.28913$	$[1, 1, 1, -332850, 73774335]$	\(y^2+xy+y=x^3+x^2-332850x+73774335\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.2.4, 112.96.0.?, 156.24.0.?, $\ldots$	$[(333, -157)]$	$1$
8190.i2	8190n3	8190.i	8190n	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( 2^{6} \cdot 3^{7} \cdot 5^{2} \cdot 7^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$4368$	$192$	$1$	$1$	$1$		$0$	$196608$	$2.206005$	$4078208988807294650401/359723582400$	$1.00772$	$6.25388$	$[1, -1, 0, -2995650, -1994902700]$	\(y^2+xy=x^3-x^2-2995650x-1994902700\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 12.12.0-4.c.1.2, 24.48.0-8.bb.2.5, $\ldots$	$[ ]$	$1$
13650.x2	13650z4	13650.x	13650z	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2^{6} \cdot 3 \cdot 5^{8} \cdot 7^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$21840$	$192$	$1$	$1$	$1$		$0$	$589824$	$2.461414$	$4078208988807294650401/359723582400$	$1.00772$	$6.24026$	$[1, 0, 1, -8321251, 9238434398]$	\(y^2+xy+y=x^3-8321251x+9238434398\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 20.12.0-4.c.1.2, 40.48.0-8.bb.2.4, $\ldots$	$[ ]$	$1$
19110.cn2	19110cp3	19110.cn	19110cp	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \)	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{14} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.123	2B	$4368$	$192$	$1$	$1$	$4$	$2$	$0$	$1179648$	$2.629654$	$4078208988807294650401/359723582400$	$1.00772$	$6.23206$	$[1, 0, 0, -16309651, -25353525919]$	\(y^2+xy=x^3-16309651x-25353525919\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 16.48.0-8.bb.2.6, 28.12.0-4.c.1.2, $\ldots$	$[ ]$	$1$
21840.cc2	21840cg4	21840.cc	21840cg	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 2^{18} \cdot 3 \cdot 5^{2} \cdot 7^{8} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.177	2B	$4368$	$192$	$1$	$8.960867652$	$4$	$2$	$3$	$589824$	$2.349846$	$4078208988807294650401/359723582400$	$1.00772$	$5.81271$	$[0, 1, 0, -5325600, -4732208652]$	\(y^2=x^3+x^2-5325600x-4732208652\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.bb.2.3, 112.96.0.?, 156.24.0.?, $\ldots$	$[(16091, 2018940)]$	$1$
35490.d2	35490a4	35490.d	35490a	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13^{2} \)	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{8} \cdot 13^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$4368$	$192$	$1$	$1.735636817$	$1$		$4$	$4128768$	$2.939171$	$4078208988807294650401/359723582400$	$1.00772$	$6.21835$	$[1, 1, 0, -56251653, 162363472653]$	\(y^2+xy=x^3+x^2-56251653x+162363472653\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 12.12.0-4.c.1.1, 24.48.0-8.bb.2.3, $\ldots$	$[(4594, 28123)]$	$1$
40950.dy2	40950ds4	40950.dy	40950ds	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2^{6} \cdot 3^{7} \cdot 5^{8} \cdot 7^{8} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$21840$	$192$	$1$	$3.537266144$	$1$		$6$	$4718592$	$3.010723$	$4078208988807294650401/359723582400$	$1.00772$	$6.21540$	$[1, -1, 1, -74891255, -249437728753]$	\(y^2+xy+y=x^3-x^2-74891255x-249437728753\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 60.12.0-4.c.1.2, 112.48.0.?, $\ldots$	$[(-4995, 2506)]$	$1$
57330.cr2	57330ci4	57330.cr	57330ci	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \)	\( 2^{6} \cdot 3^{7} \cdot 5^{2} \cdot 7^{14} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$4368$	$192$	$1$	$1$	$1$		$0$	$9437184$	$3.178959$	$4078208988807294650401/359723582400$	$1.00772$	$6.20879$	$[1, -1, 0, -146786859, 684545199813]$	\(y^2+xy=x^3-x^2-146786859x+684545199813\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 48.48.0-8.bb.2.4, 84.12.0.?, $\ldots$	$[ ]$	$1$
65520.e2	65520cv4	65520.e	65520cv	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( 2^{18} \cdot 3^{7} \cdot 5^{2} \cdot 7^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$4368$	$192$	$1$	$1$	$1$		$1$	$4718592$	$2.899151$	$4078208988807294650401/359723582400$	$1.00772$	$5.83127$	$[0, 0, 0, -47930403, 127721703202]$	\(y^2=x^3-47930403x+127721703202\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 12.12.0-4.c.1.1, 24.48.0-8.bb.2.6, $\ldots$	$[ ]$	$1$
87360.b2	87360ec4	87360.b	87360ec	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 2^{24} \cdot 3 \cdot 5^{2} \cdot 7^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.225	2B	$4368$	$192$	$1$	$1$	$4$	$2$	$1$	$4718592$	$2.696419$	$4078208988807294650401/359723582400$	$1.00772$	$5.47001$	$[0, -1, 0, -21302401, -37836366815]$	\(y^2=x^3-x^2-21302401x-37836366815\)	2.3.0.a.1, 4.6.0.c.1, 8.48.0-8.bb.2.2, 112.96.0.?, 156.12.0.?, $\ldots$	$[ ]$	$1$
87360.ff2	87360ck4	87360.ff	87360ck	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 2^{24} \cdot 3 \cdot 5^{2} \cdot 7^{8} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.210	2B	$4368$	$192$	$1$	$2.006874440$	$1$		$3$	$4718592$	$2.696419$	$4078208988807294650401/359723582400$	$1.00772$	$5.47001$	$[0, 1, 0, -21302401, 37836366815]$	\(y^2=x^3+x^2-21302401x+37836366815\)	2.3.0.a.1, 4.6.0.c.1, 8.48.0-8.bb.2.1, 112.96.0.?, 156.12.0.?, $\ldots$	$[(-3509, 263424)]$	$1$
95550.m2	95550bt4	95550.m	95550bt	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( 2^{6} \cdot 3 \cdot 5^{8} \cdot 7^{14} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$21840$	$192$	$1$	$12.38300773$	$1$		$2$	$28311552$	$3.434372$	$4078208988807294650401/359723582400$	$1.00772$	$6.19949$	$[1, 1, 0, -407741275, -3169190739875]$	\(y^2+xy=x^3+x^2-407741275x-3169190739875\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 80.48.0.?, 112.48.0.?, $\ldots$	$[(1181895, 1284118040)]$	$1$
106470.ex2	106470fi4	106470.ex	106470fi	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13^{2} \)	\( 2^{6} \cdot 3^{7} \cdot 5^{2} \cdot 7^{8} \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.183	2B	$4368$	$192$	$1$	$1$	$4$	$2$	$0$	$33030144$	$3.488480$	$4078208988807294650401/359723582400$	$1.00772$	$6.19762$	$[1, -1, 1, -506264882, -4384320026511]$	\(y^2+xy+y=x^3-x^2-506264882x-4384320026511\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.bb.2.6, 112.96.0.?, 156.24.0.?, $\ldots$	$[ ]$	$1$
109200.dm2	109200ds4	109200.dm	109200ds	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2^{18} \cdot 3 \cdot 5^{8} \cdot 7^{8} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$21840$	$192$	$1$	$9.502497535$	$1$		$1$	$14155776$	$3.154564$	$4078208988807294650401/359723582400$	$1.00772$	$5.83870$	$[0, -1, 0, -133140008, -591259801488]$	\(y^2=x^3-x^2-133140008x-591259801488\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 20.12.0-4.c.1.1, 40.48.0-8.bb.2.3, $\ldots$	$[(1674402/11, 618612750/11)]$	$1$
152880.ci2	152880ez3	152880.ci	152880ez	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \)	\( 2^{18} \cdot 3 \cdot 5^{2} \cdot 7^{14} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.128	2B	$4368$	$192$	$1$	$11.07433129$	$1$		$1$	$28311552$	$3.322800$	$4078208988807294650401/359723582400$	$1.00772$	$5.84324$	$[0, -1, 0, -260954416, 1622625658816]$	\(y^2=x^3-x^2-260954416x+1622625658816\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 16.48.0-8.bb.2.5, 28.12.0-4.c.1.1, $\ldots$	$[(505962/7, 58322342/7)]$	$1$
177450.kh2	177450bi3	177450.kh	177450bi	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13^{2} \)	\( 2^{6} \cdot 3 \cdot 5^{8} \cdot 7^{8} \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$21840$	$192$	$1$	$1$	$1$		$0$	$99090432$	$3.743893$	$4078208988807294650401/359723582400$	$1.00772$	$6.18927$	$[1, 0, 0, -1406291338, 20298246664292]$	\(y^2+xy=x^3-1406291338x+20298246664292\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 60.12.0-4.c.1.1, 112.48.0.?, $\ldots$	$[ ]$	$1$
248430.fd2	248430fd4	248430.fd	248430fd	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13^{2} \)	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{14} \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$4368$	$192$	$1$	$1$	$16$	$2$	$0$	$198180864$	$3.912128$	$4078208988807294650401/359723582400$	$1.00772$	$6.18414$	$[1, 0, 1, -2756331023, -55698940113022]$	\(y^2+xy+y=x^3-2756331023x-55698940113022\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 48.48.0-8.bb.2.7, 84.12.0.?, $\ldots$	$[ ]$	$1$
262080.kc2	262080kc3	262080.kc	262080kc	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( 2^{24} \cdot 3^{7} \cdot 5^{2} \cdot 7^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$4368$	$192$	$1$	$1$	$4$	$2$	$1$	$37748736$	$3.245724$	$4078208988807294650401/359723582400$	$1.00772$	$5.51667$	$[0, 0, 0, -191721612, 1021773625616]$	\(y^2=x^3-191721612x+1021773625616\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 24.48.0-8.bb.2.1, 104.48.0.?, $\ldots$	$[ ]$	$1$
262080.ku2	262080ku4	262080.ku	262080ku	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( 2^{24} \cdot 3^{7} \cdot 5^{2} \cdot 7^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$4368$	$192$	$1$	$1$	$1$		$1$	$37748736$	$3.245724$	$4078208988807294650401/359723582400$	$1.00772$	$5.51667$	$[0, 0, 0, -191721612, -1021773625616]$	\(y^2=x^3-191721612x-1021773625616\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 24.48.0-8.bb.2.2, 104.48.0.?, $\ldots$	$[ ]$	$1$
283920.fl2	283920fl4	283920.fl	283920fl	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 13^{2} \)	\( 2^{18} \cdot 3 \cdot 5^{2} \cdot 7^{8} \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$4368$	$192$	$1$	$1$	$1$		$1$	$99090432$	$3.632320$	$4078208988807294650401/359723582400$	$1.00772$	$5.85097$	$[0, 1, 0, -900026456, -10393062302700]$	\(y^2=x^3+x^2-900026456x-10393062302700\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 12.12.0-4.c.1.2, 24.48.0-8.bb.2.4, $\ldots$	$[ ]$	$1$
286650.qs2	286650qs3	286650.qs	286650qs	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( 2^{6} \cdot 3^{7} \cdot 5^{8} \cdot 7^{14} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$21840$	$192$	$1$	$4.571322433$	$1$		$4$	$226492416$	$3.983677$	$4078208988807294650401/359723582400$	$1.00772$	$6.18205$	$[1, -1, 1, -3669671480, 85564480305147]$	\(y^2+xy+y=x^3-x^2-3669671480x+85564480305147\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 112.48.0.?, 156.12.0.?, $\ldots$	$[(34989, -13695)]$	$1$
327600.hm2	327600hm3	327600.hm	327600hm	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2^{18} \cdot 3^{7} \cdot 5^{8} \cdot 7^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$21840$	$192$	$1$	$1$	$1$		$1$	$113246208$	$3.703869$	$4078208988807294650401/359723582400$	$1.00772$	$5.85265$	$[0, 0, 0, -1198260075, 15965212900250]$	\(y^2=x^3-1198260075x+15965212900250\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 60.12.0-4.c.1.1, 112.48.0.?, $\ldots$	$[ ]$	$1$
330330.bc2	330330bc4	330330.bc	330330bc	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \cdot 13 \)	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{8} \cdot 11^{6} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$48048$	$192$	$1$	$5.592599198$	$4$	$2$	$2$	$31457280$	$2.855644$	$4078208988807294650401/359723582400$	$1.00772$	$5.04785$	$[1, 1, 0, -40274852, -98395014384]$	\(y^2+xy=x^3+x^2-40274852x-98395014384\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 44.12.0-4.c.1.2, 88.48.0.?, $\ldots$	$[(25747, 3978789)]$	$1$
436800.fb2	436800fb3	436800.fb	436800fb	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2^{24} \cdot 3 \cdot 5^{8} \cdot 7^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$21840$	$192$	$1$	$1$	$4$	$2$	$1$	$113246208$	$3.501137$	$4078208988807294650401/359723582400$	$1.00772$	$5.53569$	$[0, -1, 0, -532560033, 4730610971937]$	\(y^2=x^3-x^2-532560033x+4730610971937\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 40.48.0-8.bb.2.7, 112.48.0.?, $\ldots$	$[ ]$	$1$
436800.qi2	436800qi4	436800.qi	436800qi	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2^{24} \cdot 3 \cdot 5^{8} \cdot 7^{8} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$21840$	$192$	$1$	$20.25759995$	$1$		$1$	$113246208$	$3.501137$	$4078208988807294650401/359723582400$	$1.00772$	$5.53569$	$[0, 1, 0, -532560033, -4730610971937]$	\(y^2=x^3+x^2-532560033x-4730610971937\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 40.48.0-8.bb.2.8, 112.48.0.?, $\ldots$	$[(2181602177/268, 51352899611625/268)]$	$1$
458640.ib2	458640ib4	458640.ib	458640ib	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \)	\( 2^{18} \cdot 3^{7} \cdot 5^{2} \cdot 7^{14} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$4368$	$192$	$1$	$7.517916651$	$4$	$2$	$3$	$226492416$	$3.872105$	$4078208988807294650401/359723582400$	$1.00772$	$5.85645$	$[0, 0, 0, -2348589747, -43808544198286]$	\(y^2=x^3-2348589747x-43808544198286\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 48.48.0-8.bb.2.2, 84.12.0.?, $\ldots$	$[(-111943/2, 4075/2)]$	$1$

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