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
8736.k3	8736n1	8736.k	8736n	$4$	$4$	\( 2^{5} \cdot 3 \cdot 7 \cdot 13 \)	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2184$	$48$	$0$	$1$	$1$		$3$	$1536$	$-0.028645$	$131096512/74529$	$0.92560$	$2.51788$	$[0, -1, 0, -42, 0]$	\(y^2=x^3-x^2-42x\)	2.6.0.a.1, 24.12.0-2.a.1.1, 28.12.0-2.a.1.1, 52.12.0-2.a.1.1, 168.24.0.?, $\ldots$	$[ ]$
8736.x3	8736j1	8736.x	8736j	$4$	$4$	\( 2^{5} \cdot 3 \cdot 7 \cdot 13 \)	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 13^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2184$	$48$	$0$	$2.759923106$	$1$		$5$	$1536$	$-0.028645$	$131096512/74529$	$0.92560$	$2.51788$	$[0, 1, 0, -42, 0]$	\(y^2=x^3+x^2-42x\)	2.6.0.a.1, 24.12.0-2.a.1.1, 28.12.0-2.a.1.1, 52.12.0-2.a.1.1, 168.24.0.?, $\ldots$	$[(56, 420)]$
17472.l2	17472n2	17472.l	17472n	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 13 \)	\( 2^{12} \cdot 3^{2} \cdot 7^{2} \cdot 13^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2184$	$48$	$0$	$1.316085778$	$1$		$11$	$6144$	$0.317929$	$131096512/74529$	$0.92560$	$2.76497$	$[0, -1, 0, -169, 169]$	\(y^2=x^3-x^2-169x+169\)	2.6.0.a.1, 12.12.0-2.a.1.1, 56.12.0-2.a.1.1, 104.12.0.?, 168.24.0.?, $\ldots$	$[(0, 13)]$
17472.bu2	17472bb2	17472.bu	17472bb	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 13 \)	\( 2^{12} \cdot 3^{2} \cdot 7^{2} \cdot 13^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2184$	$48$	$0$	$1.642165635$	$1$		$9$	$6144$	$0.317929$	$131096512/74529$	$0.92560$	$2.76497$	$[0, 1, 0, -169, -169]$	\(y^2=x^3+x^2-169x-169\)	2.6.0.a.1, 12.12.0-2.a.1.1, 56.12.0-2.a.1.1, 104.12.0.?, 168.24.0.?, $\ldots$	$[(-5, 24)]$
26208.i3	26208k1	26208.i	26208k	$4$	$4$	\( 2^{5} \cdot 3^{2} \cdot 7 \cdot 13 \)	\( 2^{6} \cdot 3^{8} \cdot 7^{2} \cdot 13^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$2184$	$48$	$0$	$2.910827331$	$1$		$21$	$12288$	$0.520661$	$131096512/74529$	$0.92560$	$2.89390$	$[0, 0, 0, -381, 380]$	\(y^2=x^3-381x+380\)	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 156.12.0.?, 168.24.0.?, $\ldots$	$[(-8, 54), (-13, 56)]$
26208.r3	26208bq1	26208.r	26208bq	$4$	$4$	\( 2^{5} \cdot 3^{2} \cdot 7 \cdot 13 \)	\( 2^{6} \cdot 3^{8} \cdot 7^{2} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$2184$	$48$	$0$	$1$	$1$		$3$	$12288$	$0.520661$	$131096512/74529$	$0.92560$	$2.89390$	$[0, 0, 0, -381, -380]$	\(y^2=x^3-381x-380\)	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 156.12.0.?, 168.24.0.?, $\ldots$	$[ ]$
52416.fe2	52416ca2	52416.fe	52416ca	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 13 \)	\( 2^{12} \cdot 3^{8} \cdot 7^{2} \cdot 13^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$2184$	$48$	$0$	$2.149670597$	$1$		$9$	$49152$	$0.867235$	$131096512/74529$	$0.92560$	$3.09202$	$[0, 0, 0, -1524, 3040]$	\(y^2=x^3-1524x+3040\)	2.6.0.a.1, 4.12.0-2.a.1.1, 168.24.0.?, 312.24.0.?, 364.24.0.?, $\ldots$	$[(77, 585)]$
52416.fi2	52416db2	52416.fi	52416db	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 13 \)	\( 2^{12} \cdot 3^{8} \cdot 7^{2} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$2184$	$48$	$0$	$1$	$1$		$3$	$49152$	$0.867235$	$131096512/74529$	$0.92560$	$3.09202$	$[0, 0, 0, -1524, -3040]$	\(y^2=x^3-1524x-3040\)	2.6.0.a.1, 4.12.0-2.a.1.1, 168.24.0.?, 312.24.0.?, 364.24.0.?, $\ldots$	$[ ]$
61152.d3	61152m1	61152.d	61152m	$4$	$4$	\( 2^{5} \cdot 3 \cdot 7^{2} \cdot 13 \)	\( 2^{6} \cdot 3^{2} \cdot 7^{8} \cdot 13^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$2184$	$48$	$0$	$2.010607031$	$1$		$9$	$73728$	$0.944310$	$131096512/74529$	$0.92560$	$3.13269$	$[0, -1, 0, -2074, -4136]$	\(y^2=x^3-x^2-2074x-4136\)	2.6.0.a.1, 4.12.0-2.a.1.1, 168.24.0.?, 312.24.0.?, 364.24.0.?, $\ldots$	$[(-5, 78)]$
61152.bl3	61152ce1	61152.bl	61152ce	$4$	$4$	\( 2^{5} \cdot 3 \cdot 7^{2} \cdot 13 \)	\( 2^{6} \cdot 3^{2} \cdot 7^{8} \cdot 13^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$2184$	$48$	$0$	$4.827017571$	$1$		$3$	$73728$	$0.944310$	$131096512/74529$	$0.92560$	$3.13269$	$[0, 1, 0, -2074, 4136]$	\(y^2=x^3+x^2-2074x+4136\)	2.6.0.a.1, 4.12.0-2.a.1.1, 168.24.0.?, 312.24.0.?, 364.24.0.?, $\ldots$	$[(-67/2, 1485/2)]$
113568.i3	113568u1	113568.i	113568u	$4$	$4$	\( 2^{5} \cdot 3 \cdot 7 \cdot 13^{2} \)	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 13^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$2184$	$48$	$0$	$1$	$1$		$3$	$258048$	$1.253830$	$131096512/74529$	$0.92560$	$3.28518$	$[0, -1, 0, -7154, -28536]$	\(y^2=x^3-x^2-7154x-28536\)	2.6.0.a.1, 4.12.0-2.a.1.1, 168.24.0.?, 312.24.0.?, 364.24.0.?, $\ldots$	$[ ]$
113568.bx3	113568co1	113568.bx	113568co	$4$	$4$	\( 2^{5} \cdot 3 \cdot 7 \cdot 13^{2} \)	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 13^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$2184$	$48$	$0$	$5.656556281$	$1$		$5$	$258048$	$1.253830$	$131096512/74529$	$0.92560$	$3.28518$	$[0, 1, 0, -7154, 28536]$	\(y^2=x^3+x^2-7154x+28536\)	2.6.0.a.1, 4.12.0-2.a.1.1, 168.24.0.?, 312.24.0.?, 364.24.0.?, $\ldots$	$[(-347/2, 495/2)]$
122304.db2	122304w2	122304.db	122304w	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 13 \)	\( 2^{12} \cdot 3^{2} \cdot 7^{8} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$2184$	$48$	$0$	$1$	$1$		$3$	$294912$	$1.290884$	$131096512/74529$	$0.92560$	$3.30236$	$[0, -1, 0, -8297, 41385]$	\(y^2=x^3-x^2-8297x+41385\)	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 156.12.0.?, 168.24.0.?, $\ldots$	$[ ]$
122304.hz2	122304dg2	122304.hz	122304dg	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 13 \)	\( 2^{12} \cdot 3^{2} \cdot 7^{8} \cdot 13^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$2184$	$48$	$0$	$5.146074666$	$1$		$5$	$294912$	$1.290884$	$131096512/74529$	$0.92560$	$3.30236$	$[0, 1, 0, -8297, -41385]$	\(y^2=x^3+x^2-8297x-41385\)	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 156.12.0.?, 168.24.0.?, $\ldots$	$[(2361, 114660)]$
183456.cz3	183456di1	183456.cz	183456di	$4$	$4$	\( 2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( 2^{6} \cdot 3^{8} \cdot 7^{8} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2184$	$48$	$0$	$1$	$1$		$3$	$589824$	$1.493616$	$131096512/74529$	$0.92560$	$3.39261$	$[0, 0, 0, -18669, -130340]$	\(y^2=x^3-18669x-130340\)	2.6.0.a.1, 12.12.0-2.a.1.1, 56.12.0-2.a.1.1, 104.12.0.?, 168.24.0.?, $\ldots$	$[ ]$
183456.dp3	183456bm1	183456.dp	183456bm	$4$	$4$	\( 2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( 2^{6} \cdot 3^{8} \cdot 7^{8} \cdot 13^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2184$	$48$	$0$	$5.464498289$	$1$		$3$	$589824$	$1.493616$	$131096512/74529$	$0.92560$	$3.39261$	$[0, 0, 0, -18669, 130340]$	\(y^2=x^3-18669x+130340\)	2.6.0.a.1, 12.12.0-2.a.1.1, 56.12.0-2.a.1.1, 104.12.0.?, 168.24.0.?, $\ldots$	$[(-335/2, 8415/2)]$
218400.g3	218400by1	218400.g	218400by	$4$	$4$	\( 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2^{6} \cdot 3^{2} \cdot 5^{6} \cdot 7^{2} \cdot 13^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$10920$	$48$	$0$	$1.657427458$	$1$		$9$	$196608$	$0.776074$	$131096512/74529$	$0.92560$	$2.64411$	$[0, -1, 0, -1058, 2112]$	\(y^2=x^3-x^2-1058x+2112\)	2.6.0.a.1, 120.12.0.?, 140.12.0.?, 168.12.0.?, 260.12.0.?, $\ldots$	$[(58, 364)]$
218400.fo3	218400di1	218400.fo	218400di	$4$	$4$	\( 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2^{6} \cdot 3^{2} \cdot 5^{6} \cdot 7^{2} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$10920$	$48$	$0$	$1$	$1$		$3$	$196608$	$0.776074$	$131096512/74529$	$0.92560$	$2.64411$	$[0, 1, 0, -1058, -2112]$	\(y^2=x^3+x^2-1058x-2112\)	2.6.0.a.1, 120.12.0.?, 140.12.0.?, 168.12.0.?, 260.12.0.?, $\ldots$	$[ ]$
227136.de2	227136ix2	227136.de	227136ix	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 13^{2} \)	\( 2^{12} \cdot 3^{2} \cdot 7^{2} \cdot 13^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$2184$	$48$	$0$	$2.927180706$	$1$		$9$	$1032192$	$1.600403$	$131096512/74529$	$0.92560$	$3.43776$	$[0, -1, 0, -28617, 256905]$	\(y^2=x^3-x^2-28617x+256905\)	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 156.12.0.?, 168.24.0.?, $\ldots$	$[(177, 840)]$
227136.iu2	227136gl2	227136.iu	227136gl	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 13^{2} \)	\( 2^{12} \cdot 3^{2} \cdot 7^{2} \cdot 13^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$2184$	$48$	$0$	$8.799980182$	$1$		$3$	$1032192$	$1.600403$	$131096512/74529$	$0.92560$	$3.43776$	$[0, 1, 0, -28617, -256905]$	\(y^2=x^3+x^2-28617x-256905\)	2.6.0.a.1, 8.12.0-2.a.1.1, 84.12.0.?, 156.12.0.?, 168.24.0.?, $\ldots$	$[(-31649/15, 3383576/15)]$
340704.dq3	340704dq1	340704.dq	340704dq	$4$	$4$	\( 2^{5} \cdot 3^{2} \cdot 7 \cdot 13^{2} \)	\( 2^{6} \cdot 3^{8} \cdot 7^{2} \cdot 13^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2184$	$48$	$0$	$1$	$1$		$3$	$2064384$	$1.803135$	$131096512/74529$	$0.92560$	$3.51931$	$[0, 0, 0, -64389, -834860]$	\(y^2=x^3-64389x-834860\)	2.6.0.a.1, 12.12.0-2.a.1.1, 56.12.0-2.a.1.2, 104.12.0.?, 168.24.0.?, $\ldots$	$[ ]$
340704.el3	340704el1	340704.el	340704el	$4$	$4$	\( 2^{5} \cdot 3^{2} \cdot 7 \cdot 13^{2} \)	\( 2^{6} \cdot 3^{8} \cdot 7^{2} \cdot 13^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2184$	$48$	$0$	$1$	$4$	$2$	$3$	$2064384$	$1.803135$	$131096512/74529$	$0.92560$	$3.51931$	$[0, 0, 0, -64389, 834860]$	\(y^2=x^3-64389x+834860\)	2.6.0.a.1, 12.12.0-2.a.1.1, 56.12.0-2.a.1.2, 104.12.0.?, 168.24.0.?, $\ldots$	$[ ]$
366912.ct2	366912ct2	366912.ct	366912ct	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( 2^{12} \cdot 3^{8} \cdot 7^{8} \cdot 13^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2184$	$48$	$0$	$1.939986124$	$1$		$11$	$2359296$	$1.840189$	$131096512/74529$	$0.92560$	$3.53366$	$[0, 0, 0, -74676, 1042720]$	\(y^2=x^3-74676x+1042720\)	2.6.0.a.1, 24.12.0-2.a.1.1, 28.12.0-2.a.1.1, 52.12.0-2.a.1.2, 168.24.0.?, $\ldots$	$[(357, 4459)]$
366912.ep2	366912ep2	366912.ep	366912ep	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( 2^{12} \cdot 3^{8} \cdot 7^{8} \cdot 13^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2184$	$48$	$0$	$2.703224551$	$1$		$9$	$2359296$	$1.840189$	$131096512/74529$	$0.92560$	$3.53366$	$[0, 0, 0, -74676, -1042720]$	\(y^2=x^3-74676x-1042720\)	2.6.0.a.1, 24.12.0-2.a.1.1, 28.12.0-2.a.1.1, 52.12.0-2.a.1.2, 168.24.0.?, $\ldots$	$[(-70, 1960)]$
436800.ge2	436800ge2	436800.ge	436800ge	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2^{12} \cdot 3^{2} \cdot 5^{6} \cdot 7^{2} \cdot 13^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$10920$	$48$	$0$	$2.645724768$	$1$		$25$	$786432$	$1.122648$	$131096512/74529$	$0.92560$	$2.82322$	$[0, -1, 0, -4233, -12663]$	\(y^2=x^3-x^2-4233x-12663\)	2.6.0.a.1, 60.12.0-2.a.1.1, 168.12.0.?, 280.12.0.?, 312.12.0.?, $\ldots$	$[(-24, 273), (93, 624)]$
436800.of2	436800of2	436800.of	436800of	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2^{12} \cdot 3^{2} \cdot 5^{6} \cdot 7^{2} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$10920$	$48$	$0$	$1$	$1$		$3$	$786432$	$1.122648$	$131096512/74529$	$0.92560$	$2.82322$	$[0, 1, 0, -4233, 12663]$	\(y^2=x^3+x^2-4233x+12663\)	2.6.0.a.1, 60.12.0-2.a.1.1, 168.12.0.?, 280.12.0.?, 312.12.0.?, $\ldots$	$[ ]$

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