Elliptic curve search results

Results (29 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
663.a4	663b1	663.a	663b	$6$	$8$	\( 3 \cdot 13 \cdot 17 \)	\( 3^{2} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.48.0.31	2B	$3536$	$192$	$1$	$1.487906035$	$1$		$7$	$128$	$0.115435$	$17319700013617/25857$	$0.93528$	$4.69200$	$[1, 1, 1, -539, 4592]$	\(y^2+xy+y=x^3+x^2-539x+4592\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.f.1.4, 34.6.0.a.1, $\ldots$	$[(9, 19)]$
1989.e4	1989e1	1989.e	1989e	$6$	$8$	\( 3^{2} \cdot 13 \cdot 17 \)	\( 3^{8} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.7	2B	$10608$	$192$	$1$	$6.767931338$	$1$		$1$	$1024$	$0.664742$	$17319700013617/25857$	$0.93528$	$4.88119$	$[1, -1, 0, -4851, -128840]$	\(y^2+xy=x^3-x^2-4851x-128840\)	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.1, $\ldots$	$[(2136/5, 28876/5)]$
8619.i4	8619b1	8619.i	8619b	$6$	$8$	\( 3 \cdot 13^{2} \cdot 17 \)	\( 3^{2} \cdot 13^{8} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.88	2B	$3536$	$192$	$1$	$1$	$1$		$1$	$21504$	$1.397909$	$17319700013617/25857$	$0.93528$	$5.06223$	$[1, 1, 0, -91094, 10544487]$	\(y^2+xy=x^3+x^2-91094x+10544487\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.1, 16.48.0-16.f.1.1, 34.6.0.a.1, $\ldots$	$[ ]$
10608.p4	10608ba1	10608.p	10608ba	$6$	$8$	\( 2^{4} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{12} \cdot 3^{2} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.45	2B	$3536$	$192$	$1$	$2.326907997$	$1$		$3$	$8192$	$0.808582$	$17319700013617/25857$	$0.93528$	$4.18590$	$[0, 1, 0, -8624, -311148]$	\(y^2=x^3+x^2-8624x-311148\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.f.1.3, 34.6.0.a.1, $\ldots$	$[(202, 2496)]$
11271.e4	11271h1	11271.e	11271h	$6$	$8$	\( 3 \cdot 13 \cdot 17^{2} \)	\( 3^{2} \cdot 13^{2} \cdot 17^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.35	2B	$3536$	$192$	$1$	$4.904047116$	$1$		$3$	$36864$	$1.532042$	$17319700013617/25857$	$0.93528$	$5.08920$	$[1, 0, 0, -155777, 23651808]$	\(y^2+xy=x^3-155777x+23651808\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.12, 16.48.0-16.f.1.13, 34.6.0.a.1, $\ldots$	$[(9277/3, 822017/3)]$
16575.i4	16575f1	16575.i	16575f	$6$	$8$	\( 3 \cdot 5^{2} \cdot 13 \cdot 17 \)	\( 3^{2} \cdot 5^{6} \cdot 13^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.7	2B	$17680$	$192$	$1$	$1$	$1$		$1$	$16384$	$0.920155$	$17319700013617/25857$	$0.93528$	$4.13143$	$[1, 0, 1, -13476, 600973]$	\(y^2+xy+y=x^3-13476x+600973\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.1, 20.12.0-4.c.1.2, $\ldots$	$[ ]$
25857.f4	25857h1	25857.f	25857h	$6$	$8$	\( 3^{2} \cdot 13^{2} \cdot 17 \)	\( 3^{8} \cdot 13^{8} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.7	2B	$10608$	$192$	$1$	$1$	$4$	$2$	$1$	$172032$	$1.947216$	$17319700013617/25857$	$0.93528$	$5.16363$	$[1, -1, 1, -819851, -285520998]$	\(y^2+xy+y=x^3-x^2-819851x-285520998\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.1, 24.24.0-8.n.1.8, $\ldots$	$[ ]$
31824.bg4	31824bk1	31824.bg	31824bk	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 13 \cdot 17 \)	\( 2^{12} \cdot 3^{8} \cdot 13^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.7	2B	$10608$	$192$	$1$	$1$	$1$		$1$	$65536$	$1.357889$	$17319700013617/25857$	$0.93528$	$4.37813$	$[0, 0, 0, -77619, 8323378]$	\(y^2=x^3-77619x+8323378\)	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.1, $\ldots$	$[ ]$
32487.f4	32487l1	32487.f	32487l	$6$	$8$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{2} \cdot 7^{6} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.7	2B	$24752$	$192$	$1$	$7.285358969$	$1$		$1$	$49152$	$1.088390$	$17319700013617/25857$	$0.93528$	$4.05814$	$[1, 0, 0, -26412, -1654353]$	\(y^2+xy=x^3-26412x-1654353\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.1, 28.12.0-4.c.1.2, $\ldots$	$[(15339/5, 1786878/5)]$
33813.i4	33813n1	33813.i	33813n	$6$	$8$	\( 3^{2} \cdot 13 \cdot 17^{2} \)	\( 3^{8} \cdot 13^{2} \cdot 17^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.7	2B	$10608$	$192$	$1$	$20.19760679$	$1$		$1$	$294912$	$2.081348$	$17319700013617/25857$	$0.93528$	$5.18515$	$[1, -1, 0, -1401993, -638598816]$	\(y^2+xy=x^3-x^2-1401993x-638598816\)	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.1, $\ldots$	$[(2124780340/99, 97835661555578/99)]$
42432.bb4	42432bl1	42432.bb	42432bl	$6$	$8$	\( 2^{6} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{18} \cdot 3^{2} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.184	2B	$3536$	$192$	$1$	$4.439113605$	$1$		$3$	$65536$	$1.155155$	$17319700013617/25857$	$0.93528$	$4.03162$	$[0, -1, 0, -34497, -2454687]$	\(y^2=x^3-x^2-34497x-2454687\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.9, 16.48.0-16.f.1.12, 34.6.0.a.1, $\ldots$	$[(951, 28704)]$
42432.cf4	42432s1	42432.cf	42432s	$6$	$8$	\( 2^{6} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{18} \cdot 3^{2} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.197	2B	$3536$	$192$	$1$	$1.796603525$	$1$		$3$	$65536$	$1.155155$	$17319700013617/25857$	$0.93528$	$4.03162$	$[0, 1, 0, -34497, 2454687]$	\(y^2=x^3+x^2-34497x+2454687\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.11, 16.48.0-16.f.1.11, 34.6.0.a.1, $\ldots$	$[(89, 312)]$
49725.f4	49725i1	49725.f	49725i	$6$	$8$	\( 3^{2} \cdot 5^{2} \cdot 13 \cdot 17 \)	\( 3^{8} \cdot 5^{6} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.7	2B	$53040$	$192$	$1$	$5.501105976$	$1$		$3$	$131072$	$1.469460$	$17319700013617/25857$	$0.93528$	$4.32125$	$[1, -1, 1, -121280, -16226278]$	\(y^2+xy+y=x^3-x^2-121280x-16226278\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.1, 34.6.0.a.1, $\ldots$	$[(1024, 30025)]$
80223.j4	80223c1	80223.j	80223c	$6$	$8$	\( 3 \cdot 11^{2} \cdot 13 \cdot 17 \)	\( 3^{2} \cdot 11^{6} \cdot 13^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.7	2B	$38896$	$192$	$1$	$1$	$1$		$1$	$163840$	$1.314383$	$17319700013617/25857$	$0.93528$	$3.97343$	$[1, 1, 0, -65221, -6438296]$	\(y^2+xy=x^3+x^2-65221x-6438296\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.1, 34.6.0.a.1, $\ldots$	$[ ]$
97461.q4	97461m1	97461.q	97461m	$6$	$8$	\( 3^{2} \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{8} \cdot 7^{6} \cdot 13^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.7	2B	$74256$	$192$	$1$	$1$	$1$		$1$	$393216$	$1.637697$	$17319700013617/25857$	$0.93528$	$4.24385$	$[1, -1, 0, -237708, 44667531]$	\(y^2+xy=x^3-x^2-237708x+44667531\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.1, 34.6.0.a.1, $\ldots$	$[ ]$
127296.u4	127296cg1	127296.u	127296cg	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 13 \cdot 17 \)	\( 2^{18} \cdot 3^{8} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.7	2B	$10608$	$192$	$1$	$1.491343459$	$1$		$5$	$524288$	$1.704462$	$17319700013617/25857$	$0.93528$	$4.21559$	$[0, 0, 0, -310476, 66587024]$	\(y^2=x^3-310476x+66587024\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.1, 24.24.0-8.n.1.11, $\ldots$	$[(320, 52)]$
127296.bb4	127296h1	127296.bb	127296h	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 13 \cdot 17 \)	\( 2^{18} \cdot 3^{8} \cdot 13^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.7	2B	$10608$	$192$	$1$	$1$	$1$		$1$	$524288$	$1.704462$	$17319700013617/25857$	$0.93528$	$4.21559$	$[0, 0, 0, -310476, -66587024]$	\(y^2=x^3-310476x-66587024\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.1, 24.24.0-8.n.1.9, $\ldots$	$[ ]$
137904.cv4	137904p1	137904.cv	137904p	$6$	$8$	\( 2^{4} \cdot 3 \cdot 13^{2} \cdot 17 \)	\( 2^{12} \cdot 3^{2} \cdot 13^{8} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.160	2B	$3536$	$192$	$1$	$1$	$4$	$2$	$1$	$1376256$	$2.091057$	$17319700013617/25857$	$0.93528$	$4.57909$	$[0, 1, 0, -1457512, -677762188]$	\(y^2=x^3+x^2-1457512x-677762188\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.5, 16.48.0-16.f.1.2, 34.6.0.a.1, $\ldots$	$[ ]$
146523.y4	146523s1	146523.y	146523s	$6$	$8$	\( 3 \cdot 13^{2} \cdot 17^{2} \)	\( 3^{2} \cdot 13^{8} \cdot 17^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.93	2B	$3536$	$192$	$1$	$1$	$1$		$1$	$6193152$	$2.814518$	$17319700013617/25857$	$0.93528$	$5.28560$	$[1, 0, 1, -26326317, 51989348491]$	\(y^2+xy+y=x^3-26326317x+51989348491\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.1, 16.48.0-16.f.1.16, 34.6.0.a.1, $\ldots$	$[ ]$
180336.bg4	180336bp1	180336.bg	180336bp	$6$	$8$	\( 2^{4} \cdot 3 \cdot 13 \cdot 17^{2} \)	\( 2^{12} \cdot 3^{2} \cdot 13^{2} \cdot 17^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.53	2B	$3536$	$192$	$1$	$4.287519403$	$1$		$3$	$2359296$	$2.225189$	$17319700013617/25857$	$0.93528$	$4.61058$	$[0, -1, 0, -2492432, -1513715712]$	\(y^2=x^3-x^2-2492432x-1513715712\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.10, 16.48.0-16.f.1.14, 34.6.0.a.1, $\ldots$	$[(16496, 2108544)]$
215475.t4	215475p1	215475.t	215475p	$6$	$8$	\( 3 \cdot 5^{2} \cdot 13^{2} \cdot 17 \)	\( 3^{2} \cdot 5^{6} \cdot 13^{8} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.7	2B	$17680$	$192$	$1$	$1$	$1$		$1$	$2752512$	$2.202629$	$17319700013617/25857$	$0.93528$	$4.52170$	$[1, 0, 0, -2277363, 1322615592]$	\(y^2+xy=x^3-2277363x+1322615592\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.1, 34.6.0.a.1, $\ldots$	$[ ]$
239343.f4	239343f1	239343.f	239343f	$6$	$8$	\( 3 \cdot 13 \cdot 17 \cdot 19^{2} \)	\( 3^{2} \cdot 13^{2} \cdot 17 \cdot 19^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.7	2B	$67184$	$192$	$1$	$1$	$4$	$2$	$1$	$884736$	$1.587654$	$17319700013617/25857$	$0.93528$	$3.88752$	$[1, 0, 1, -194587, -33054439]$	\(y^2+xy+y=x^3-194587x-33054439\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.1, 34.6.0.a.1, $\ldots$	$[ ]$
240669.p4	240669p1	240669.p	240669p	$6$	$8$	\( 3^{2} \cdot 11^{2} \cdot 13 \cdot 17 \)	\( 3^{8} \cdot 11^{6} \cdot 13^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.7	2B	$116688$	$192$	$1$	$1$	$1$		$1$	$1310720$	$1.863689$	$17319700013617/25857$	$0.93528$	$4.15311$	$[1, -1, 1, -586994, 173247000]$	\(y^2+xy+y=x^3-x^2-586994x+173247000\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.1, 34.6.0.a.1, $\ldots$	$[ ]$
265200.bo4	265200bo1	265200.bo	265200bo	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13 \cdot 17 \)	\( 2^{12} \cdot 3^{2} \cdot 5^{6} \cdot 13^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.7	2B	$17680$	$192$	$1$	$1$	$1$		$1$	$1048576$	$1.613302$	$17319700013617/25857$	$0.93528$	$3.88023$	$[0, -1, 0, -215608, -38462288]$	\(y^2=x^3-x^2-215608x-38462288\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.1, 20.12.0-4.c.1.1, $\ldots$	$[ ]$
281775.bm4	281775bm1	281775.bm	281775bm	$6$	$8$	\( 3 \cdot 5^{2} \cdot 13 \cdot 17^{2} \)	\( 3^{2} \cdot 5^{6} \cdot 13^{2} \cdot 17^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.7	2B	$17680$	$192$	$1$	$3.623971906$	$1$		$3$	$4718592$	$2.336761$	$17319700013617/25857$	$0.93528$	$4.55330$	$[1, 1, 0, -3894425, 2956476000]$	\(y^2+xy=x^3+x^2-3894425x+2956476000\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.1, 20.12.0-4.c.1.2, $\ldots$	$[(1040, 5180)]$
350727.c4	350727c1	350727.c	350727c	$6$	$8$	\( 3 \cdot 13 \cdot 17 \cdot 23^{2} \)	\( 3^{2} \cdot 13^{2} \cdot 17 \cdot 23^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.7	2B	$81328$	$192$	$1$	$9.979857052$	$1$		$1$	$1622016$	$1.683182$	$17319700013617/25857$	$0.93528$	$3.86096$	$[1, 1, 1, -285142, -58724446]$	\(y^2+xy+y=x^3+x^2-285142x-58724446\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.1, 34.6.0.a.1, $\ldots$	$[(70116/5, 18030374/5)]$
413712.bb4	413712bb1	413712.bb	413712bb	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 13^{2} \cdot 17 \)	\( 2^{12} \cdot 3^{8} \cdot 13^{8} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.7	2B	$10608$	$192$	$1$	$2.084096238$	$1$		$3$	$11010048$	$2.640362$	$17319700013617/25857$	$0.93528$	$4.69979$	$[0, 0, 0, -13117611, 18286461466]$	\(y^2=x^3-13117611x+18286461466\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.1, 24.24.0-8.n.1.4, $\ldots$	$[(2925, 70304)]$
422331.bq4	422331bq1	422331.bq	422331bq	$6$	$8$	\( 3 \cdot 7^{2} \cdot 13^{2} \cdot 17 \)	\( 3^{2} \cdot 7^{6} \cdot 13^{8} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.7	2B	$24752$	$192$	$1$	$12.48673966$	$1$		$1$	$8257536$	$2.370865$	$17319700013617/25857$	$0.93528$	$4.44265$	$[1, 0, 1, -4463632, -3630149911]$	\(y^2+xy+y=x^3-4463632x-3630149911\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.1, 34.6.0.a.1, $\ldots$	$[(-6148661/71, 193792990/71)]$
439569.z4	439569z1	439569.z	439569z	$6$	$8$	\( 3^{2} \cdot 13^{2} \cdot 17^{2} \)	\( 3^{8} \cdot 13^{8} \cdot 17^{7} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.7	2B	$10608$	$192$	$1$	$76.50167907$	$1$		$7$	$49545216$	$3.363823$	$17319700013617/25857$	$0.93528$	$5.34600$	$[1, -1, 1, -236936849, -1403712409264]$	\(y^2+xy+y=x^3-x^2-236936849x-1403712409264\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.f.1, 24.24.0-8.n.1.8, $\ldots$	$[(-8882, 5539), (54973893493570/21583, 403348365283456334509/21583)]$

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