Elliptic curve search results

Results (13 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
5270.e3	5270e2	5270.e	5270e	$4$	$4$	\( 2 \cdot 5 \cdot 17 \cdot 31 \)	\( 2^{4} \cdot 5^{2} \cdot 17^{4} \cdot 31^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$620$	$48$	$0$	$4.023814705$	$1$		$4$	$5120$	$0.783004$	$815853972965121/32105472400$	$0.98058$	$4.00655$	$[1, -1, 1, -1947, -31429]$	\(y^2+xy+y=x^3-x^2-1947x-31429\)	2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.b.1.2, 124.24.0.?, 620.48.0.?	$[(69, 364)]$
26350.e3	26350a2	26350.e	26350a	$4$	$4$	\( 2 \cdot 5^{2} \cdot 17 \cdot 31 \)	\( 2^{4} \cdot 5^{8} \cdot 17^{4} \cdot 31^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$620$	$48$	$0$	$1$	$1$		$2$	$122880$	$1.587723$	$815853972965121/32105472400$	$0.98058$	$4.32173$	$[1, -1, 0, -48667, -3977259]$	\(y^2+xy=x^3-x^2-48667x-3977259\)	2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.b.1.2, 124.24.0.?, 620.48.0.?	$[ ]$
42160.q3	42160t2	42160.q	42160t	$4$	$4$	\( 2^{4} \cdot 5 \cdot 17 \cdot 31 \)	\( 2^{16} \cdot 5^{2} \cdot 17^{4} \cdot 31^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$620$	$48$	$0$	$7.817622982$	$1$		$15$	$122880$	$1.476151$	$815853972965121/32105472400$	$0.98058$	$4.00527$	$[0, 0, 0, -31147, 2042586]$	\(y^2=x^3-31147x+2042586\)	2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.b.1.1, 124.24.0.?, 620.48.0.?	$[(85, 96), (-139, 1920)]$
47430.c3	47430j2	47430.c	47430j	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 17 \cdot 31 \)	\( 2^{4} \cdot 3^{6} \cdot 5^{2} \cdot 17^{4} \cdot 31^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1860$	$48$	$0$	$0.515559347$	$1$		$16$	$163840$	$1.332310$	$815853972965121/32105472400$	$0.98058$	$3.80114$	$[1, -1, 0, -17520, 866096]$	\(y^2+xy=x^3-x^2-17520x+866096\)	2.6.0.a.1, 12.12.0-2.a.1.1, 20.12.0.b.1, 60.24.0-20.b.1.2, 124.12.0.?, $\ldots$	$[(52, 280)]$
89590.m3	89590k2	89590.m	89590k	$4$	$4$	\( 2 \cdot 5 \cdot 17^{2} \cdot 31 \)	\( 2^{4} \cdot 5^{2} \cdot 17^{10} \cdot 31^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$10540$	$48$	$0$	$9.100681467$	$1$		$4$	$1474560$	$2.199612$	$815853972965121/32105472400$	$0.98058$	$4.50185$	$[1, -1, 1, -562593, -156659743]$	\(y^2+xy+y=x^3-x^2-562593x-156659743\)	2.6.0.a.1, 20.12.0.b.1, 68.12.0-2.a.1.1, 124.12.0.?, 340.24.0.?, $\ldots$	$[(14641, 1761824)]$
163370.p3	163370e2	163370.p	163370e	$4$	$4$	\( 2 \cdot 5 \cdot 17 \cdot 31^{2} \)	\( 2^{4} \cdot 5^{2} \cdot 17^{4} \cdot 31^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$620$	$48$	$0$	$6.971416707$	$1$		$4$	$4915200$	$2.499996$	$815853972965121/32105472400$	$0.98058$	$4.57683$	$[1, -1, 1, -1870767, 951259559]$	\(y^2+xy+y=x^3-x^2-1870767x+951259559\)	2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.b.1.3, 124.24.0.?, 620.48.0.?	$[(1789, 56792)]$
168640.be3	168640ce2	168640.be	168640ce	$4$	$4$	\( 2^{6} \cdot 5 \cdot 17 \cdot 31 \)	\( 2^{22} \cdot 5^{2} \cdot 17^{4} \cdot 31^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$1240$	$48$	$0$	$12.80086453$	$1$		$3$	$983040$	$1.822723$	$815853972965121/32105472400$	$0.98058$	$3.88948$	$[0, 0, 0, -124588, -16340688]$	\(y^2=x^3-124588x-16340688\)	2.6.0.a.1, 8.12.0-2.a.1.1, 20.12.0.b.1, 40.24.0-20.b.1.1, 124.12.0.?, $\ldots$	$[(617976/23, 460474644/23)]$
168640.bh3	168640r2	168640.bh	168640r	$4$	$4$	\( 2^{6} \cdot 5 \cdot 17 \cdot 31 \)	\( 2^{22} \cdot 5^{2} \cdot 17^{4} \cdot 31^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$1240$	$48$	$0$	$8.760333749$	$1$		$5$	$983040$	$1.822723$	$815853972965121/32105472400$	$0.98058$	$3.88948$	$[0, 0, 0, -124588, 16340688]$	\(y^2=x^3-124588x+16340688\)	2.6.0.a.1, 8.12.0-2.a.1.1, 20.12.0.b.1, 40.24.0-20.b.1.2, 124.12.0.?, $\ldots$	$[(12716, 1433376)]$
210800.bd3	210800r2	210800.bd	210800r	$4$	$4$	\( 2^{4} \cdot 5^{2} \cdot 17 \cdot 31 \)	\( 2^{16} \cdot 5^{8} \cdot 17^{4} \cdot 31^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$620$	$48$	$0$	$1$	$1$		$3$	$2949120$	$2.280869$	$815853972965121/32105472400$	$0.98058$	$4.26716$	$[0, 0, 0, -778675, 255323250]$	\(y^2=x^3-778675x+255323250\)	2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.b.1.1, 124.24.0.?, 620.48.0.?	$[ ]$
237150.dl3	237150dl2	237150.dl	237150dl	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 17 \cdot 31 \)	\( 2^{4} \cdot 3^{6} \cdot 5^{8} \cdot 17^{4} \cdot 31^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1860$	$48$	$0$	$2.719814545$	$1$		$8$	$3932160$	$2.137028$	$815853972965121/32105472400$	$0.98058$	$4.08708$	$[1, -1, 1, -438005, 107823997]$	\(y^2+xy+y=x^3-x^2-438005x+107823997\)	2.6.0.a.1, 12.12.0-2.a.1.1, 20.12.0.b.1, 60.24.0-20.b.1.2, 124.12.0.?, $\ldots$	$[(253, 3500)]$
258230.bh3	258230bh2	258230.bh	258230bh	$4$	$4$	\( 2 \cdot 5 \cdot 7^{2} \cdot 17 \cdot 31 \)	\( 2^{4} \cdot 5^{2} \cdot 7^{6} \cdot 17^{4} \cdot 31^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$4340$	$48$	$0$	$1.935613637$	$1$		$8$	$1966080$	$1.755959$	$815853972965121/32105472400$	$0.98058$	$3.69220$	$[1, -1, 1, -95388, 10970831]$	\(y^2+xy+y=x^3-x^2-95388x+10970831\)	2.6.0.a.1, 20.12.0.b.1, 28.12.0-2.a.1.1, 124.12.0.?, 140.24.0.?, $\ldots$	$[(223, 755)]$
379440.bc3	379440bc2	379440.bc	379440bc	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 17 \cdot 31 \)	\( 2^{16} \cdot 3^{6} \cdot 5^{2} \cdot 17^{4} \cdot 31^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1860$	$48$	$0$	$2.538802420$	$1$		$7$	$3932160$	$2.025455$	$815853972965121/32105472400$	$0.98058$	$3.83333$	$[0, 0, 0, -280323, -55149822]$	\(y^2=x^3-280323x-55149822\)	2.6.0.a.1, 12.12.0-2.a.1.1, 20.12.0.b.1, 60.24.0-20.b.1.1, 124.12.0.?, $\ldots$	$[(1119, 32130)]$
447950.p3	447950p2	447950.p	447950p	$4$	$4$	\( 2 \cdot 5^{2} \cdot 17^{2} \cdot 31 \)	\( 2^{4} \cdot 5^{8} \cdot 17^{10} \cdot 31^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$10540$	$48$	$0$	$1$	$1$		$2$	$35389440$	$3.004330$	$815853972965121/32105472400$	$0.98058$	$4.68714$	$[1, -1, 0, -14064817, -19596532659]$	\(y^2+xy=x^3-x^2-14064817x-19596532659\)	2.6.0.a.1, 20.12.0.b.1, 68.12.0-2.a.1.1, 124.12.0.?, 340.24.0.?, $\ldots$	$[ ]$

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