Elliptic curve search results

Results (20 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
4290.bc5	4290bc1	4290.bc	4290bc	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{24} \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 13 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.48.0.30	2B	$34320$	$192$	$1$	$1$	$1$		$3$	$7680$	$1.011240$	$2533309721804161/1187575234560$	$0.95627$	$4.24057$	$[1, 0, 0, -2840, 25152]$	\(y^2+xy=x^3-2840x+25152\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.f.2.3, 130.6.0.?, $\ldots$	$[ ]$
12870.f5	12870k1	12870.f	12870k	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{24} \cdot 3^{8} \cdot 5 \cdot 11^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.6	2B	$34320$	$192$	$1$	$4.007853418$	$1$		$3$	$61440$	$1.560547$	$2533309721804161/1187575234560$	$0.95627$	$4.44484$	$[1, -1, 0, -25560, -679104]$	\(y^2+xy=x^3-x^2-25560x-679104\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.2, 16.24.0.f.2, $\ldots$	$[(-63, 855)]$
21450.k5	21450f1	21450.k	21450f	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13 \)	\( 2^{24} \cdot 3^{2} \cdot 5^{7} \cdot 11^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.6	2B	$34320$	$192$	$1$	$1$	$1$		$1$	$184320$	$1.815960$	$2533309721804161/1187575234560$	$0.95627$	$4.52449$	$[1, 1, 0, -71000, 3144000]$	\(y^2+xy=x^3+x^2-71000x+3144000\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.2, 20.12.0-4.c.1.2, $\ldots$	$[ ]$
34320.u5	34320bh1	34320.u	34320bh	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{36} \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.47	2B	$34320$	$192$	$1$	$1$	$1$		$1$	$184320$	$1.704388$	$2533309721804161/1187575234560$	$0.95627$	$4.19267$	$[0, -1, 0, -45440, -1609728]$	\(y^2=x^3-x^2-45440x-1609728\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.f.2.11, 130.6.0.?, $\ldots$	$[ ]$
47190.bi5	47190bg1	47190.bi	47190bg	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 11^{2} \cdot 13 \)	\( 2^{24} \cdot 3^{2} \cdot 5 \cdot 11^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.6	2B	$34320$	$192$	$1$	$1$	$4$	$2$	$1$	$921600$	$2.210186$	$2533309721804161/1187575234560$	$0.95627$	$4.63259$	$[1, 0, 1, -343643, -33820954]$	\(y^2+xy+y=x^3-343643x-33820954\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.2, 24.24.0-8.n.1.8, $\ldots$	$[ ]$
55770.y5	55770u1	55770.y	55770u	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13^{2} \)	\( 2^{24} \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.6	2B	$34320$	$192$	$1$	$1$	$1$		$1$	$1290240$	$2.293716$	$2533309721804161/1187575234560$	$0.95627$	$4.65349$	$[1, 0, 1, -479964, 55738906]$	\(y^2+xy+y=x^3-479964x+55738906\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.2, 20.12.0-4.c.1.2, $\ldots$	$[ ]$
64350.dr5	64350dj1	64350.dr	64350dj	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 13 \)	\( 2^{24} \cdot 3^{8} \cdot 5^{7} \cdot 11^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.6	2B	$34320$	$192$	$1$	$0.605594022$	$1$		$9$	$1474560$	$2.365265$	$2533309721804161/1187575234560$	$0.95627$	$4.67090$	$[1, -1, 1, -639005, -85527003]$	\(y^2+xy+y=x^3-x^2-639005x-85527003\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.2, 60.12.0-4.c.1.2, $\ldots$	$[(-361, 10080)]$
102960.bl5	102960dt1	102960.bl	102960dt	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{36} \cdot 3^{8} \cdot 5 \cdot 11^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.6	2B	$34320$	$192$	$1$	$6.174047536$	$1$		$3$	$1474560$	$2.253693$	$2533309721804161/1187575234560$	$0.95627$	$4.36470$	$[0, 0, 0, -408963, 43871618]$	\(y^2=x^3-408963x+43871618\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.1, 16.24.0.f.2, $\ldots$	$[(4546, 303534)]$
137280.n5	137280ha1	137280.n	137280ha	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{42} \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.196	2B	$34320$	$192$	$1$	$4.757316428$	$1$		$3$	$1474560$	$2.050961$	$2533309721804161/1187575234560$	$0.95627$	$4.05290$	$[0, -1, 0, -181761, 13059585]$	\(y^2=x^3-x^2-181761x+13059585\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.11, 16.48.0-16.f.2.12, 130.6.0.?, $\ldots$	$[(-456, 957)]$
137280.ez5	137280bg1	137280.ez	137280bg	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{42} \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.182	2B	$34320$	$192$	$1$	$1$	$4$	$2$	$1$	$1474560$	$2.050961$	$2533309721804161/1187575234560$	$0.95627$	$4.05290$	$[0, 1, 0, -181761, -13059585]$	\(y^2=x^3+x^2-181761x-13059585\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.9, 16.48.0-16.f.2.4, 130.6.0.?, $\ldots$	$[ ]$
141570.dg5	141570bs1	141570.dg	141570bs	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 13 \)	\( 2^{24} \cdot 3^{8} \cdot 5 \cdot 11^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.91	2B	$34320$	$192$	$1$	$1$	$1$		$1$	$7372800$	$2.759495$	$2533309721804161/1187575234560$	$0.95627$	$4.75925$	$[1, -1, 1, -3092783, 913165751]$	\(y^2+xy+y=x^3-x^2-3092783x+913165751\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.1, 16.48.0-16.f.2.2, 130.6.0.?, $\ldots$	$[ ]$
167310.fe5	167310k1	167310.fe	167310k	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13^{2} \)	\( 2^{24} \cdot 3^{8} \cdot 5 \cdot 11^{2} \cdot 13^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.6	2B	$34320$	$192$	$1$	$2.433757809$	$1$		$5$	$10321920$	$2.843021$	$2533309721804161/1187575234560$	$0.95627$	$4.77649$	$[1, -1, 1, -4319672, -1504950469]$	\(y^2+xy+y=x^3-x^2-4319672x-1504950469\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.2, 60.12.0-4.c.1.2, $\ldots$	$[(-851, 39849)]$
171600.fr5	171600bv1	171600.fr	171600bv	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13 \)	\( 2^{36} \cdot 3^{2} \cdot 5^{7} \cdot 11^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.6	2B	$34320$	$192$	$1$	$6.561555502$	$1$		$3$	$4423680$	$2.509106$	$2533309721804161/1187575234560$	$0.95627$	$4.43400$	$[0, 1, 0, -1136008, -203488012]$	\(y^2=x^3+x^2-1136008x-203488012\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.2, 20.12.0-4.c.1.1, $\ldots$	$[(-793, 14118)]$
210210.cx5	210210cr1	210210.cx	210210cr	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \cdot 13 \)	\( 2^{24} \cdot 3^{2} \cdot 5 \cdot 7^{6} \cdot 11^{2} \cdot 13 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.6	2B	$240240$	$192$	$1$	$0.678453157$	$1$		$29$	$2949120$	$1.984196$	$2533309721804161/1187575234560$	$0.95627$	$3.84663$	$[1, 1, 1, -139161, -8766297]$	\(y^2+xy+y=x^3+x^2-139161x-8766297\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.2, 28.12.0-4.c.1.2, $\ldots$	$[(559, 9128), (-81, 1448)]$
235950.fs5	235950fs1	235950.fs	235950fs	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11^{2} \cdot 13 \)	\( 2^{24} \cdot 3^{2} \cdot 5^{7} \cdot 11^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.6	2B	$34320$	$192$	$1$	$1$	$1$		$1$	$22118400$	$3.014908$	$2533309721804161/1187575234560$	$0.95627$	$4.81048$	$[1, 1, 1, -8591063, -4227619219]$	\(y^2+xy+y=x^3+x^2-8591063x-4227619219\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.2, 120.24.0.?, $\ldots$	$[ ]$
278850.fs5	278850fs1	278850.fs	278850fs	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13^{2} \)	\( 2^{24} \cdot 3^{2} \cdot 5^{7} \cdot 11^{2} \cdot 13^{7} \)	$2$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.37	2B	$34320$	$192$	$1$	$2.051875410$	$1$		$35$	$30965760$	$3.098434$	$2533309721804161/1187575234560$	$0.95627$	$4.82633$	$[1, 1, 1, -11999088, 6967363281]$	\(y^2+xy+y=x^3+x^2-11999088x+6967363281\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.12, 16.48.0-16.f.2.14, 130.6.0.?, $\ldots$	$[(421, 44405), (565, 18917)]$
377520.cn5	377520cn1	377520.cn	377520cn	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 13 \)	\( 2^{36} \cdot 3^{2} \cdot 5 \cdot 11^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.6	2B	$34320$	$192$	$1$	$1$	$1$		$1$	$22118400$	$2.903336$	$2533309721804161/1187575234560$	$0.95627$	$4.53016$	$[0, -1, 0, -5498280, 2164541040]$	\(y^2=x^3-x^2-5498280x+2164541040\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.2, 24.24.0-8.n.1.4, $\ldots$	$[ ]$
411840.jr5	411840jr1	411840.jr	411840jr	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{42} \cdot 3^{8} \cdot 5 \cdot 11^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.6	2B	$34320$	$192$	$1$	$1$	$1$		$1$	$11796480$	$2.600266$	$2533309721804161/1187575234560$	$0.95627$	$4.21836$	$[0, 0, 0, -1635852, 350972944]$	\(y^2=x^3-1635852x+350972944\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.2, 24.24.0-8.n.1.11, $\ldots$	$[ ]$
411840.km5	411840km1	411840.km	411840km	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{42} \cdot 3^{8} \cdot 5 \cdot 11^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.6	2B	$34320$	$192$	$1$	$1$	$4$	$2$	$1$	$11796480$	$2.600266$	$2533309721804161/1187575234560$	$0.95627$	$4.21836$	$[0, 0, 0, -1635852, -350972944]$	\(y^2=x^3-1635852x-350972944\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.2, 24.24.0-8.n.1.9, $\ldots$	$[ ]$
446160.be5	446160be1	446160.be	446160be	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 11 \cdot 13^{2} \)	\( 2^{36} \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 13^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.6	2B	$34320$	$192$	$1$	$8.885857929$	$1$		$1$	$30965760$	$2.986862$	$2533309721804161/1187575234560$	$0.95627$	$4.54903$	$[0, -1, 0, -7679416, -3567290000]$	\(y^2=x^3-x^2-7679416x-3567290000\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.2, 20.12.0-4.c.1.1, $\ldots$	$[(-4811/3, 529606/3)]$

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