Elliptic curve search results

Results (16 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
2445.c2	2445c2	2445.c	2445c	$4$	$4$	\( 3 \cdot 5 \cdot 163 \)	\( 3^{10} \cdot 5^{2} \cdot 163^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.6.0.1	2Cs	$9780$	$48$	$0$	$1$	$1$		$2$	$1920$	$0.730673$	$97393143178729/39221822025$	$0.92713$	$4.12851$	$1$	$[1, 0, 1, -959, -6379]$	\(y^2+xy+y=x^3-959x-6379\)	2.6.0.a.1, 12.12.0-2.a.1.1, 20.12.0-2.a.1.1, 60.24.0-60.a.1.3, 652.12.0.?, $\ldots$	$[ ]$	$1$
7335.c2	7335c2	7335.c	7335c	$4$	$4$	\( 3^{2} \cdot 5 \cdot 163 \)	\( 3^{16} \cdot 5^{2} \cdot 163^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$9780$	$48$	$0$	$5.040707867$	$1$		$4$	$15360$	$1.279978$	$97393143178729/39221822025$	$0.92713$	$4.35951$	$1$	$[1, -1, 1, -8627, 172226]$	\(y^2+xy+y=x^3-x^2-8627x+172226\)	2.6.0.a.1, 4.12.0-2.a.1.1, 60.24.0-60.a.1.2, 1956.24.0.?, 3260.24.0.?, $\ldots$	$[(79/2, 687/2)]$	$1$
12225.d2	12225b2	12225.d	12225b	$4$	$4$	\( 3 \cdot 5^{2} \cdot 163 \)	\( 3^{10} \cdot 5^{8} \cdot 163^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$9780$	$48$	$0$	$1$	$1$		$2$	$46080$	$1.535391$	$97393143178729/39221822025$	$0.92713$	$4.44855$	$1$	$[1, 1, 1, -23963, -797344]$	\(y^2+xy+y=x^3+x^2-23963x-797344\)	2.6.0.a.1, 4.12.0-2.a.1.1, 60.24.0-60.a.1.1, 1956.24.0.?, 3260.24.0.?, $\ldots$	$[ ]$	$1$
36675.i2	36675f2	36675.i	36675f	$4$	$4$	\( 3^{2} \cdot 5^{2} \cdot 163 \)	\( 3^{16} \cdot 5^{8} \cdot 163^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$9780$	$48$	$0$	$12.60355110$	$1$		$2$	$368640$	$2.084698$	$97393143178729/39221822025$	$0.92713$	$4.61073$	$1$	$[1, -1, 0, -215667, 21312616]$	\(y^2+xy=x^3-x^2-215667x+21312616\)	2.6.0.a.1, 12.12.0-2.a.1.1, 20.12.0-2.a.1.1, 60.24.0-60.a.1.4, 652.12.0.?, $\ldots$	$[(-879741/46, 627964243/46)]$	$1$
39120.f2	39120v2	39120.f	39120v	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 163 \)	\( 2^{12} \cdot 3^{10} \cdot 5^{2} \cdot 163^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$9780$	$48$	$0$	$4.597915951$	$1$		$7$	$122880$	$1.423820$	$97393143178729/39221822025$	$0.92713$	$3.83261$	$1$	$[0, -1, 0, -15336, 408240]$	\(y^2=x^3-x^2-15336x+408240\)	2.6.0.a.1, 12.12.0-2.a.1.1, 20.12.0-2.a.1.1, 60.24.0-60.a.1.4, 652.12.0.?, $\ldots$	$[(-134, 198)]$	$1$
117360.bo2	117360bx2	117360.bo	117360bx	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 163 \)	\( 2^{12} \cdot 3^{16} \cdot 5^{2} \cdot 163^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$9780$	$48$	$0$	$7.388992848$	$1$		$3$	$983040$	$1.973125$	$97393143178729/39221822025$	$0.92713$	$4.03660$	$1$	$[0, 0, 0, -138027, -10884454]$	\(y^2=x^3-138027x-10884454\)	2.6.0.a.1, 4.12.0-2.a.1.1, 60.24.0-60.a.1.1, 1956.24.0.?, 3260.24.0.?, $\ldots$	$[(5503/3, 311750/3)]$	$1$
119805.k2	119805h2	119805.k	119805h	$4$	$4$	\( 3 \cdot 5 \cdot 7^{2} \cdot 163 \)	\( 3^{10} \cdot 5^{2} \cdot 7^{6} \cdot 163^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$68460$	$48$	$0$	$8.214164161$	$1$		$2$	$737280$	$1.703627$	$97393143178729/39221822025$	$0.92713$	$3.75292$	$1$	$[1, 1, 0, -46967, 2140944]$	\(y^2+xy=x^3+x^2-46967x+2140944\)	2.6.0.a.1, 60.12.0.a.1, 84.12.0.?, 140.12.0.?, 420.24.0.?, $\ldots$	$[(-77/6, 323611/6)]$	$1$
156480.bi2	156480cy2	156480.bi	156480cy	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 163 \)	\( 2^{18} \cdot 3^{10} \cdot 5^{2} \cdot 163^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$19560$	$48$	$0$	$11.06215640$	$1$		$3$	$983040$	$1.770393$	$97393143178729/39221822025$	$0.92713$	$3.73611$	$1$	$[0, -1, 0, -61345, -3204575]$	\(y^2=x^3-x^2-61345x-3204575\)	2.6.0.a.1, 24.12.0-2.a.1.1, 40.12.0-2.a.1.1, 60.12.0.a.1, 120.24.0.?, $\ldots$	$[(262955/13, 133019700/13)]$	$1$
156480.de2	156480g2	156480.de	156480g	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 163 \)	\( 2^{18} \cdot 3^{10} \cdot 5^{2} \cdot 163^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$19560$	$48$	$0$	$4.262827510$	$1$		$21$	$983040$	$1.770393$	$97393143178729/39221822025$	$0.92713$	$3.73611$	$1$	$[0, 1, 0, -61345, 3204575]$	\(y^2=x^3+x^2-61345x+3204575\)	2.6.0.a.1, 24.12.0-2.a.1.1, 40.12.0-2.a.1.1, 60.12.0.a.1, 120.24.0.?, $\ldots$	$[(53, 324), (23, 1344)]$	$1$
195600.cv2	195600x2	195600.cv	195600x	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 163 \)	\( 2^{12} \cdot 3^{10} \cdot 5^{8} \cdot 163^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$9780$	$48$	$0$	$2.397653147$	$1$		$9$	$2949120$	$2.228539$	$97393143178729/39221822025$	$0.92713$	$4.11892$	$1$	$[0, 1, 0, -383408, 50263188]$	\(y^2=x^3+x^2-383408x+50263188\)	2.6.0.a.1, 4.12.0-2.a.1.1, 60.24.0-60.a.1.2, 1956.24.0.?, 3260.24.0.?, $\ldots$	$[(-188, 10758)]$	$1$
295845.f2	295845f2	295845.f	295845f	$4$	$4$	\( 3 \cdot 5 \cdot 11^{2} \cdot 163 \)	\( 3^{10} \cdot 5^{2} \cdot 11^{6} \cdot 163^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$107580$	$48$	$0$	$1.868727733$	$1$		$8$	$2457600$	$1.929621$	$97393143178729/39221822025$	$0.92713$	$3.69889$	$1$	$[1, 0, 0, -115981, 8374136]$	\(y^2+xy=x^3-115981x+8374136\)	2.6.0.a.1, 60.12.0.a.1, 132.12.0.?, 220.12.0.?, 660.24.0.?, $\ldots$	$[(-100, 4406)]$	$1$
359415.j2	359415j2	359415.j	359415j	$4$	$4$	\( 3^{2} \cdot 5 \cdot 7^{2} \cdot 163 \)	\( 3^{16} \cdot 5^{2} \cdot 7^{6} \cdot 163^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$68460$	$48$	$0$	$4.686241286$	$1$		$6$	$5898240$	$2.252934$	$97393143178729/39221822025$	$0.92713$	$3.94590$	$1$	$[1, -1, 1, -422708, -58228194]$	\(y^2+xy+y=x^3-x^2-422708x-58228194\)	2.6.0.a.1, 28.12.0-2.a.1.1, 60.12.0.a.1, 420.24.0.?, 1956.12.0.?, $\ldots$	$[(-550, 3042)]$	$1$
398535.c2	398535c2	398535.c	398535c	$4$	$4$	\( 3 \cdot 5 \cdot 163^{2} \)	\( 3^{10} \cdot 5^{2} \cdot 163^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$9780$	$48$	$0$	$45.65972102$	$1$		$2$	$51010560$	$3.277546$	$97393143178729/39221822025$	$0.92713$	$4.86775$	$1$	$[1, 1, 1, -25466940, 27268217772]$	\(y^2+xy+y=x^3+x^2-25466940x+27268217772\)	2.6.0.a.1, 4.12.0-2.a.1.1, 60.24.0-60.a.1.6, 1956.24.0.?, 3260.24.0.?, $\ldots$	$[(-89690267697298527497/140519202, 622084793159290783842909832363/140519202)]$	$1$
413205.d2	413205d2	413205.d	413205d	$4$	$4$	\( 3 \cdot 5 \cdot 13^{2} \cdot 163 \)	\( 3^{10} \cdot 5^{2} \cdot 13^{6} \cdot 163^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$127140$	$48$	$0$	$1$	$1$		$2$	$4423680$	$2.013145$	$97393143178729/39221822025$	$0.92713$	$3.68084$	$1$	$[1, 0, 0, -161990, -13852125]$	\(y^2+xy=x^3-161990x-13852125\)	2.6.0.a.1, 60.12.0.a.1, 156.12.0.?, 260.12.0.?, 780.24.0.?, $\ldots$	$[ ]$	$1$
469440.bj2	469440bj2	469440.bj	469440bj	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 163 \)	\( 2^{18} \cdot 3^{16} \cdot 5^{2} \cdot 163^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$19560$	$48$	$0$	$6.216042916$	$1$		$5$	$7864320$	$2.319698$	$97393143178729/39221822025$	$0.92713$	$3.92656$	$1$	$[0, 0, 0, -552108, 87075632]$	\(y^2=x^3-552108x+87075632\)	2.6.0.a.1, 8.12.0-2.a.1.1, 60.12.0.a.1, 120.24.0.?, 1956.12.0.?, $\ldots$	$[(-412, 15640)]$	$1$
469440.bn2	469440bn2	469440.bn	469440bn	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 163 \)	\( 2^{18} \cdot 3^{16} \cdot 5^{2} \cdot 163^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$19560$	$48$	$0$	$12.56213684$	$1$		$3$	$7864320$	$2.319698$	$97393143178729/39221822025$	$0.92713$	$3.92656$	$1$	$[0, 0, 0, -552108, -87075632]$	\(y^2=x^3-552108x-87075632\)	2.6.0.a.1, 8.12.0-2.a.1.1, 60.12.0.a.1, 120.24.0.?, 1956.12.0.?, $\ldots$	$[(9488477/61, 27879007365/61)]$	$1$

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