Elliptic curve search results

Results (23 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
3570.t5	3570t1	3570.t	3570t	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \)	\( - 2^{24} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17^{2} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.48.0.32	2B	$4080$	$192$	$1$	$1$	$1$		$3$	$9216$	$1.094938$	$3168685387909439/3563732336640$	$0.95941$	$4.36317$	$[1, 1, 1, 3060, 64557]$	\(y^2+xy+y=x^3+x^2+3060x+64557\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.e.2.7, 30.6.0.a.1, $\ldots$	$[ ]$
10710.a5	10710f1	10710.a	10710f	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 \)	\( - 2^{24} \cdot 3^{7} \cdot 5 \cdot 7^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$4080$	$192$	$1$	$1$	$1$		$1$	$73728$	$1.644245$	$3168685387909439/3563732336640$	$0.95941$	$4.55696$	$[1, -1, 0, 27540, -1715504]$	\(y^2+xy=x^3-x^2+27540x-1715504\)	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.e.2, $\ldots$	$[ ]$
17850.ba5	17850u1	17850.ba	17850u	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 \)	\( - 2^{24} \cdot 3 \cdot 5^{7} \cdot 7^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$4080$	$192$	$1$	$5.063589033$	$1$		$3$	$221184$	$1.899656$	$3168685387909439/3563732336640$	$0.95941$	$4.63226$	$[1, 0, 1, 76499, 7916648]$	\(y^2+xy+y=x^3+76499x+7916648\)	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.e.2, $\ldots$	$[(1932, 84871)]$
24990.ca5	24990by1	24990.ca	24990by	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17 \)	\( - 2^{24} \cdot 3 \cdot 5 \cdot 7^{8} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$28560$	$192$	$1$	$1$	$1$		$1$	$442368$	$2.067894$	$3168685387909439/3563732336640$	$0.95941$	$4.67771$	$[1, 0, 0, 149939, -21693295]$	\(y^2+xy=x^3+149939x-21693295\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 28.12.0-4.c.1.2, $\ldots$	$[ ]$
28560.ds5	28560ef1	28560.ds	28560ef	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \)	\( - 2^{36} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.48	2B	$4080$	$192$	$1$	$1$	$4$	$2$	$1$	$221184$	$1.788086$	$3168685387909439/3563732336640$	$0.95941$	$4.28956$	$[0, 1, 0, 48960, -4033740]$	\(y^2=x^3+x^2+48960x-4033740\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.e.2.5, 30.6.0.a.1, $\ldots$	$[ ]$
53550.du5	53550eb1	53550.du	53550eb	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 17 \)	\( - 2^{24} \cdot 3^{7} \cdot 5^{7} \cdot 7^{2} \cdot 17^{2} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.38	2B	$4080$	$192$	$1$	$0.838446074$	$1$		$17$	$1769472$	$2.448963$	$3168685387909439/3563732336640$	$0.95941$	$4.77026$	$[1, -1, 1, 688495, -213749503]$	\(y^2+xy+y=x^3-x^2+688495x-213749503\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.12, 16.48.0-16.e.2.10, 30.6.0.a.1, $\ldots$	$[(339, 7480)]$
60690.bv5	60690bw1	60690.bv	60690bw	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17^{2} \)	\( - 2^{24} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.94	2B	$4080$	$192$	$1$	$1$	$1$		$1$	$2654208$	$2.511543$	$3168685387909439/3563732336640$	$0.95941$	$4.78424$	$[1, 0, 0, 884334, 310979076]$	\(y^2+xy=x^3+884334x+310979076\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.1, 16.48.0-16.e.2.2, 30.6.0.a.1, $\ldots$	$[ ]$
74970.bd5	74970by1	74970.bd	74970by	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 17 \)	\( - 2^{24} \cdot 3^{7} \cdot 5 \cdot 7^{8} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$28560$	$192$	$1$	$4.173644526$	$1$		$3$	$3538944$	$2.617199$	$3168685387909439/3563732336640$	$0.95941$	$4.80713$	$[1, -1, 0, 1349451, 585718965]$	\(y^2+xy=x^3-x^2+1349451x+585718965\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 30.6.0.a.1, $\ldots$	$[(835, 47480)]$
85680.db5	85680el1	85680.db	85680el	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 \)	\( - 2^{36} \cdot 3^{7} \cdot 5 \cdot 7^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$4080$	$192$	$1$	$1$	$1$		$1$	$1769472$	$2.337391$	$3168685387909439/3563732336640$	$0.95941$	$4.45500$	$[0, 0, 0, 440637, 109351618]$	\(y^2=x^3+440637x+109351618\)	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.e.2, $\ldots$	$[ ]$
114240.cp5	114240gl1	114240.cp	114240gl	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \)	\( - 2^{42} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.185	2B	$4080$	$192$	$1$	$1$	$4$	$2$	$1$	$1769472$	$2.134659$	$3168685387909439/3563732336640$	$0.95941$	$4.13606$	$[0, -1, 0, 195839, -32465759]$	\(y^2=x^3-x^2+195839x-32465759\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.9, 16.48.0-16.e.2.8, 30.6.0.a.1, $\ldots$	$[ ]$
114240.fq5	114240dk1	114240.fq	114240dk	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \)	\( - 2^{42} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.194	2B	$4080$	$192$	$1$	$7.019781990$	$1$		$1$	$1769472$	$2.134659$	$3168685387909439/3563732336640$	$0.95941$	$4.13606$	$[0, 1, 0, 195839, 32465759]$	\(y^2=x^3+x^2+195839x+32465759\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.11, 16.48.0-16.e.2.6, 30.6.0.a.1, $\ldots$	$[(3373/2, 225981/2)]$
124950.ce5	124950bc1	124950.ce	124950bc	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{24} \cdot 3 \cdot 5^{7} \cdot 7^{8} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$28560$	$192$	$1$	$9.207051086$	$1$		$1$	$10616832$	$2.872612$	$3168685387909439/3563732336640$	$0.95941$	$4.85905$	$[1, 1, 0, 3748475, -2711661875]$	\(y^2+xy=x^3+x^2+3748475x-2711661875\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 30.6.0.a.1, $\ldots$	$[(1375625/8, 1614286825/8)]$
142800.b5	142800ei1	142800.b	142800ei	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 \)	\( - 2^{36} \cdot 3 \cdot 5^{7} \cdot 7^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$4080$	$192$	$1$	$1$	$1$		$1$	$5308416$	$2.592804$	$3168685387909439/3563732336640$	$0.95941$	$4.52149$	$[0, -1, 0, 1223992, -506665488]$	\(y^2=x^3-x^2+1223992x-506665488\)	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.e.2, $\ldots$	$[ ]$
182070.bw5	182070ct1	182070.bw	182070ct	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17^{2} \)	\( - 2^{24} \cdot 3^{7} \cdot 5 \cdot 7^{2} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$4080$	$192$	$1$	$1$	$4$	$2$	$1$	$21233664$	$3.060852$	$3168685387909439/3563732336640$	$0.95941$	$4.89451$	$[1, -1, 0, 7959006, -8396435052]$	\(y^2+xy=x^3-x^2+7959006x-8396435052\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 24.24.0-8.n.1.8, $\ldots$	$[ ]$
199920.c5	199920cy1	199920.c	199920cy	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17 \)	\( - 2^{36} \cdot 3 \cdot 5 \cdot 7^{8} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$28560$	$192$	$1$	$7.123502252$	$1$		$3$	$10616832$	$2.761040$	$3168685387909439/3563732336640$	$0.95941$	$4.56225$	$[0, -1, 0, 2399024, 1388370880]$	\(y^2=x^3-x^2+2399024x+1388370880\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 28.12.0-4.c.1.1, $\ldots$	$[(7761, 698152)]$
303450.b5	303450b1	303450.b	303450b	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17^{2} \)	\( - 2^{24} \cdot 3 \cdot 5^{7} \cdot 7^{2} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$4080$	$192$	$1$	$2.848801213$	$1$		$3$	$63700992$	$3.316265$	$3168685387909439/3563732336640$	$0.95941$	$4.93925$	$[1, 1, 0, 22108350, 38872384500]$	\(y^2+xy=x^3+x^2+22108350x+38872384500\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 24.24.0-8.n.1.8, $\ldots$	$[(5305, 550060)]$
342720.ld5	342720ld1	342720.ld	342720ld	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 \)	\( - 2^{42} \cdot 3^{7} \cdot 5 \cdot 7^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$4080$	$192$	$1$	$5.117216781$	$1$		$3$	$14155776$	$2.683964$	$3168685387909439/3563732336640$	$0.95941$	$4.29673$	$[0, 0, 0, 1762548, -874812944]$	\(y^2=x^3+1762548x-874812944\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 24.24.0-8.n.1.9, $\ldots$	$[(13700, 1610784)]$
342720.md5	342720md1	342720.md	342720md	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 \)	\( - 2^{42} \cdot 3^{7} \cdot 5 \cdot 7^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$4080$	$192$	$1$	$9.441015628$	$1$		$1$	$14155776$	$2.683964$	$3168685387909439/3563732336640$	$0.95941$	$4.29673$	$[0, 0, 0, 1762548, 874812944]$	\(y^2=x^3+1762548x+874812944\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 24.24.0-8.n.1.11, $\ldots$	$[(-19895/8, 8821701/8)]$
374850.jf5	374850jf1	374850.jf	374850jf	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{24} \cdot 3^{7} \cdot 5^{7} \cdot 7^{8} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$28560$	$192$	$1$	$1$	$1$		$1$	$84934656$	$3.421917$	$3168685387909439/3563732336640$	$0.95941$	$4.95671$	$[1, -1, 1, 33736270, 73248606897]$	\(y^2+xy+y=x^3-x^2+33736270x+73248606897\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 28.12.0-4.c.1.2, $\ldots$	$[ ]$
424830.fi5	424830fi1	424830.fi	424830fi	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17^{2} \)	\( - 2^{24} \cdot 3 \cdot 5 \cdot 7^{8} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$28560$	$192$	$1$	$1$	$1$		$1$	$127401984$	$3.484501$	$3168685387909439/3563732336640$	$0.95941$	$4.96679$	$[1, 1, 1, 43332365, -106622490703]$	\(y^2+xy+y=x^3+x^2+43332365x-106622490703\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 30.6.0.a.1, $\ldots$	$[ ]$
428400.gi5	428400gi1	428400.gi	428400gi	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 17 \)	\( - 2^{36} \cdot 3^{7} \cdot 5^{7} \cdot 7^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.54	2B	$4080$	$192$	$1$	$1$	$1$		$1$	$42467328$	$3.142109$	$3168685387909439/3563732336640$	$0.95941$	$4.64675$	$[0, 0, 0, 11015925, 13668952250]$	\(y^2=x^3+11015925x+13668952250\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.10, 16.48.0-16.e.2.12, 30.6.0.a.1, $\ldots$	$[ ]$
431970.y5	431970y1	431970.y	431970y	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \cdot 17 \)	\( - 2^{24} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11^{6} \cdot 17^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$44880$	$192$	$1$	$20.28374186$	$1$		$7$	$11796480$	$2.293884$	$3168685387909439/3563732336640$	$0.95941$	$3.85936$	$[1, 1, 0, 370258, -84074316]$	\(y^2+xy=x^3+x^2+370258x-84074316\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 30.6.0.a.1, $\ldots$	$[(325, 8247), (4861/3, 439501/3)]$
485520.bg5	485520bg1	485520.bg	485520bg	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 17^{2} \)	\( - 2^{36} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.166	2B	$4080$	$192$	$1$	$1$	$4$	$2$	$1$	$63700992$	$3.204693$	$3168685387909439/3563732336640$	$0.95941$	$4.65968$	$[0, -1, 0, 14149344, -19902660864]$	\(y^2=x^3-x^2+14149344x-19902660864\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.5, 16.48.0-16.e.2.4, 30.6.0.a.1, $\ldots$	$[ ]$

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