Elliptic curve search results

Results (25 matches)

 

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
1785.d3	1785m3	1785.d	1785m	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 17 \)	\( 3^{2} \cdot 5^{2} \cdot 7^{4} \cdot 17^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.24.0.6	2Cs	$14280$	$192$	$1$	$1$	$1$		$2$	$2048$	$0.774677$	$369543396484081/45120132225$	$1.10652$	$4.48010$	$[1, 0, 0, -1495, -19888]$	\(y^2+xy=x^3-1495x-19888\)	2.6.0.a.1, 4.24.0-4.b.1.1, 60.48.0-60.c.1.2, 168.48.0.?, 280.48.0.?, $\ldots$	$[]$
5355.n3	5355d4	5355.n	5355d	$6$	$8$	\( 3^{2} \cdot 5 \cdot 7 \cdot 17 \)	\( 3^{8} \cdot 5^{2} \cdot 7^{4} \cdot 17^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$14280$	$192$	$1$	$1$	$1$		$2$	$16384$	$1.323982$	$369543396484081/45120132225$	$1.10652$	$4.67458$	$[1, -1, 0, -13455, 536976]$	\(y^2+xy=x^3-x^2-13455x+536976\)	2.6.0.a.1, 4.12.0.b.1, 12.24.0-4.b.1.1, 20.24.0-4.b.1.2, 56.24.0-4.b.1.2, $\ldots$	$[]$
8925.w3	8925h3	8925.w	8925h	$6$	$8$	\( 3 \cdot 5^{2} \cdot 7 \cdot 17 \)	\( 3^{2} \cdot 5^{8} \cdot 7^{4} \cdot 17^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$14280$	$192$	$1$	$1$	$1$		$2$	$49152$	$1.579395$	$369543396484081/45120132225$	$1.10652$	$4.74901$	$[1, 1, 0, -37375, -2486000]$	\(y^2+xy=x^3+x^2-37375x-2486000\)	2.6.0.a.1, 4.12.0.b.1, 12.24.0-4.b.1.2, 20.24.0-4.b.1.1, 56.24.0-4.b.1.2, $\ldots$	$[]$
12495.b3	12495a4	12495.b	12495a	$6$	$8$	\( 3 \cdot 5 \cdot 7^{2} \cdot 17 \)	\( 3^{2} \cdot 5^{2} \cdot 7^{10} \cdot 17^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$14280$	$192$	$1$	$1$	$1$		$2$	$98304$	$1.747631$	$369543396484081/45120132225$	$1.10652$	$4.79363$	$[1, 1, 1, -73256, 6748328]$	\(y^2+xy+y=x^3+x^2-73256x+6748328\)	2.6.0.a.1, 4.12.0.b.1, 24.24.0-4.b.1.2, 28.24.0-4.b.1.1, 40.24.0-4.b.1.2, $\ldots$	$[]$
26775.p3	26775bq3	26775.p	26775bq	$6$	$8$	\( 3^{2} \cdot 5^{2} \cdot 7 \cdot 17 \)	\( 3^{8} \cdot 5^{8} \cdot 7^{4} \cdot 17^{4} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.24.0.3	2Cs	$14280$	$192$	$1$	$1.163806048$	$1$		$34$	$393216$	$2.128700$	$369543396484081/45120132225$	$1.10652$	$4.88382$	$[1, -1, 1, -336380, 66785622]$	\(y^2+xy+y=x^3-x^2-336380x+66785622\)	2.6.0.a.1, 4.24.0-4.b.1.2, 60.48.0-60.c.1.1, 168.48.0.?, 280.48.0.?, $\ldots$	$[(614, 9255), (155, 4206)]$
28560.bq3	28560dc3	28560.bq	28560dc	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \)	\( 2^{12} \cdot 3^{2} \cdot 5^{2} \cdot 7^{4} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.24.0.5	2Cs	$14280$	$192$	$1$	$2.524774964$	$1$		$15$	$131072$	$1.467825$	$369543396484081/45120132225$	$1.10652$	$4.08012$	$[0, -1, 0, -23920, 1272832]$	\(y^2=x^3-x^2-23920x+1272832\)	2.6.0.a.1, 4.24.0-4.b.1.3, 60.48.0-60.c.1.7, 168.48.0.?, 280.48.0.?, $\ldots$	$[(-56, 1560)]$
30345.d3	30345g3	30345.d	30345g	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 17^{2} \)	\( 3^{2} \cdot 5^{2} \cdot 7^{4} \cdot 17^{10} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$14280$	$192$	$1$	$1$	$1$		$2$	$589824$	$2.191284$	$369543396484081/45120132225$	$1.10652$	$4.89735$	$[1, 1, 1, -432061, -97277686]$	\(y^2+xy+y=x^3+x^2-432061x-97277686\)	2.6.0.a.1, 4.12.0.b.1, 24.24.0-4.b.1.7, 40.24.0-4.b.1.2, 56.24.0-4.b.1.5, $\ldots$	$[]$
37485.bh3	37485bt3	37485.bh	37485bt	$6$	$8$	\( 3^{2} \cdot 5 \cdot 7^{2} \cdot 17 \)	\( 3^{8} \cdot 5^{2} \cdot 7^{10} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.17	2Cs	$14280$	$192$	$1$	$4.460797921$	$1$		$4$	$786432$	$2.296940$	$369543396484081/45120132225$	$1.10652$	$4.91948$	$[1, -1, 0, -659304, -182864165]$	\(y^2+xy=x^3-x^2-659304x-182864165\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.1, 60.24.0.c.1, 84.24.0.?, $\ldots$	$[(2690, 130955)]$
62475.cq3	62475cf3	62475.cq	62475cf	$6$	$8$	\( 3 \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( 3^{2} \cdot 5^{8} \cdot 7^{10} \cdot 17^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.17	2Cs	$14280$	$192$	$1$	$1$	$4$	$2$	$2$	$2359296$	$2.552349$	$369543396484081/45120132225$	$1.10652$	$4.96946$	$[1, 0, 1, -1831401, 847203823]$	\(y^2+xy+y=x^3-1831401x+847203823\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.1, 60.24.0.c.1, 84.24.0.?, $\ldots$	$[]$
85680.dc3	85680ek3	85680.dc	85680ek	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 \)	\( 2^{12} \cdot 3^{8} \cdot 5^{2} \cdot 7^{4} \cdot 17^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$14280$	$192$	$1$	$1$	$1$		$3$	$1048576$	$2.017132$	$369543396484081/45120132225$	$1.10652$	$4.26582$	$[0, 0, 0, -215283, -34151182]$	\(y^2=x^3-215283x-34151182\)	2.6.0.a.1, 4.12.0.b.1, 12.24.0-4.b.1.3, 20.24.0-4.b.1.2, 56.24.0-4.b.1.7, $\ldots$	$[]$
91035.bs3	91035br3	91035.bs	91035br	$6$	$8$	\( 3^{2} \cdot 5 \cdot 7 \cdot 17^{2} \)	\( 3^{8} \cdot 5^{2} \cdot 7^{4} \cdot 17^{10} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.11	2Cs	$14280$	$192$	$1$	$1$	$4$	$2$	$2$	$4718592$	$2.740589$	$369543396484081/45120132225$	$1.10652$	$5.00344$	$[1, -1, 0, -3888549, 2622608968]$	\(y^2+xy=x^3-x^2-3888549x+2622608968\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.8, 60.24.0.c.1, 120.48.0.?, $\ldots$	$[]$
114240.a3	114240q3	114240.a	114240q	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \)	\( 2^{18} \cdot 3^{2} \cdot 5^{2} \cdot 7^{4} \cdot 17^{4} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.20	2Cs	$14280$	$192$	$1$	$3.856333254$	$1$		$23$	$1048576$	$1.814398$	$369543396484081/45120132225$	$1.10652$	$3.95155$	$[0, -1, 0, -95681, -10086975]$	\(y^2=x^3-x^2-95681x-10086975\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.11, 60.24.0.c.1, 120.48.0.?, $\ldots$	$[(-191, 1088), (13103, 1499400)]$
114240.ih3	114240jk3	114240.ih	114240jk	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \)	\( 2^{18} \cdot 3^{2} \cdot 5^{2} \cdot 7^{4} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.21	2Cs	$14280$	$192$	$1$	$1.324311095$	$1$		$11$	$1048576$	$1.814398$	$369543396484081/45120132225$	$1.10652$	$3.95155$	$[0, 1, 0, -95681, 10086975]$	\(y^2=x^3+x^2-95681x+10086975\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.2, 60.24.0.c.1, 120.48.0.?, $\ldots$	$[(106, 1071)]$
142800.ex3	142800ce3	142800.ex	142800ce	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 \)	\( 2^{12} \cdot 3^{2} \cdot 5^{8} \cdot 7^{4} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$14280$	$192$	$1$	$3.585669785$	$1$		$7$	$3145728$	$2.272545$	$369543396484081/45120132225$	$1.10652$	$4.34045$	$[0, 1, 0, -598008, 157907988]$	\(y^2=x^3+x^2-598008x+157907988\)	2.6.0.a.1, 4.12.0.b.1, 12.24.0-4.b.1.2, 20.24.0-4.b.1.3, 56.24.0-4.b.1.7, $\ldots$	$[(588, 3150)]$
151725.co3	151725cl4	151725.co	151725cl	$6$	$8$	\( 3 \cdot 5^{2} \cdot 7 \cdot 17^{2} \)	\( 3^{2} \cdot 5^{8} \cdot 7^{4} \cdot 17^{10} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.17	2Cs	$14280$	$192$	$1$	$47.83348727$	$1$		$2$	$14155776$	$2.996002$	$369543396484081/45120132225$	$1.10652$	$5.04611$	$[1, 0, 1, -10801526, -12138107677]$	\(y^2+xy+y=x^3-10801526x-12138107677\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.1, 60.24.0.c.1, 120.48.0.?, $\ldots$	$[(-7813/2, 318567/2), (450223/3, 300751652/3)]$
187425.bf3	187425bf4	187425.bf	187425bf	$6$	$8$	\( 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( 3^{8} \cdot 5^{8} \cdot 7^{10} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$14280$	$192$	$1$	$7.131216326$	$1$		$2$	$18874368$	$3.101658$	$369543396484081/45120132225$	$1.10652$	$5.06271$	$[1, -1, 1, -16482605, -22874503228]$	\(y^2+xy+y=x^3-x^2-16482605x-22874503228\)	2.6.0.a.1, 4.12.0.b.1, 24.24.0-4.b.1.2, 28.24.0-4.b.1.2, 40.24.0-4.b.1.2, $\ldots$	$[(147165/4, 49427947/4)]$
199920.eb3	199920bf4	199920.eb	199920bf	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17 \)	\( 2^{12} \cdot 3^{2} \cdot 5^{2} \cdot 7^{10} \cdot 17^{4} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$14280$	$192$	$1$	$12.06306088$	$1$		$17$	$6291456$	$2.440781$	$369543396484081/45120132225$	$1.10652$	$4.38620$	$[0, 1, 0, -1172096, -434237196]$	\(y^2=x^3+x^2-1172096x-434237196\)	2.6.0.a.1, 4.12.0.b.1, 24.24.0-4.b.1.7, 28.24.0-4.b.1.3, 40.24.0-4.b.1.7, $\ldots$	$[(-500, 5202), (8815, 821142)]$
212415.y3	212415l3	212415.y	212415l	$6$	$8$	\( 3 \cdot 5 \cdot 7^{2} \cdot 17^{2} \)	\( 3^{2} \cdot 5^{2} \cdot 7^{10} \cdot 17^{10} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.24	2Cs	$14280$	$192$	$1$	$26.37525410$	$1$		$6$	$28311552$	$3.164238$	$369543396484081/45120132225$	$1.10652$	$5.07227$	$[1, 0, 0, -21170990, 33302733267]$	\(y^2+xy=x^3-21170990x+33302733267\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.5, 60.24.0.c.1, 120.48.0.?, $\ldots$	$[(8754, 715923), (3394, 21703)]$
215985.ca3	215985bh3	215985.ca	215985bh	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 11^{2} \cdot 17 \)	\( 3^{2} \cdot 5^{2} \cdot 7^{4} \cdot 11^{6} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$157080$	$192$	$1$	$4.039060749$	$1$		$4$	$2621440$	$1.973625$	$369543396484081/45120132225$	$1.10652$	$3.90221$	$[1, 0, 1, -180898, 26290031]$	\(y^2+xy+y=x^3-180898x+26290031\)	2.6.0.a.1, 4.12.0.b.1, 44.24.0-4.b.1.1, 60.24.0.c.1, 168.24.0.?, $\ldots$	$[(-309, 7414)]$
301665.bx3	301665bx4	301665.bx	301665bx	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 13^{2} \cdot 17 \)	\( 3^{2} \cdot 5^{2} \cdot 7^{4} \cdot 13^{6} \cdot 17^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$185640$	$192$	$1$	$1$	$1$		$2$	$3932160$	$2.057152$	$369543396484081/45120132225$	$1.10652$	$3.87832$	$[1, 0, 1, -252659, -43441279]$	\(y^2+xy+y=x^3-252659x-43441279\)	2.6.0.a.1, 4.12.0.b.1, 52.24.0-4.b.1.1, 60.24.0.c.1, 168.24.0.?, $\ldots$	$[]$
342720.le3	342720le3	342720.le	342720le	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 \)	\( 2^{18} \cdot 3^{8} \cdot 5^{2} \cdot 7^{4} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$14280$	$192$	$1$	$4.793261653$	$1$		$5$	$8388608$	$2.363705$	$369543396484081/45120132225$	$1.10652$	$4.12813$	$[0, 0, 0, -861132, 273209456]$	\(y^2=x^3-861132x+273209456\)	2.6.0.a.1, 4.12.0.b.1, 24.24.0-4.b.1.11, 40.24.0-4.b.1.6, 56.24.0-4.b.1.8, $\ldots$	$[(757, 7425)]$
342720.mc3	342720mc4	342720.mc	342720mc	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 \)	\( 2^{18} \cdot 3^{8} \cdot 5^{2} \cdot 7^{4} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$14280$	$192$	$1$	$2.841750403$	$1$		$11$	$8388608$	$2.363705$	$369543396484081/45120132225$	$1.10652$	$4.12813$	$[0, 0, 0, -861132, -273209456]$	\(y^2=x^3-861132x-273209456\)	2.6.0.a.1, 4.12.0.b.1, 24.24.0-4.b.1.1, 40.24.0-4.b.1.6, 56.24.0-4.b.1.3, $\ldots$	$[(-387, 1445)]$
428400.gk3	428400gk4	428400.gk	428400gk	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 17 \)	\( 2^{12} \cdot 3^{8} \cdot 5^{8} \cdot 7^{4} \cdot 17^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.24.0.3	2Cs	$14280$	$192$	$1$	$1$	$1$		$3$	$25165824$	$2.821850$	$369543396484081/45120132225$	$1.10652$	$4.48105$	$[0, 0, 0, -5382075, -4268897750]$	\(y^2=x^3-5382075x-4268897750\)	2.6.0.a.1, 4.24.0-4.b.1.2, 60.48.0-60.c.1.8, 168.48.0.?, 280.48.0.?, $\ldots$	$[]$
455175.bo3	455175bo3	455175.bo	455175bo	$6$	$8$	\( 3^{2} \cdot 5^{2} \cdot 7 \cdot 17^{2} \)	\( 3^{8} \cdot 5^{8} \cdot 7^{4} \cdot 17^{10} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$14280$	$192$	$1$	$1$	$1$		$2$	$113246208$	$3.545307$	$369543396484081/45120132225$	$1.10652$	$5.12655$	$[1, -1, 1, -97213730, 327728907272]$	\(y^2+xy+y=x^3-x^2-97213730x+327728907272\)	2.6.0.a.1, 4.12.0.b.1, 24.24.0-4.b.1.2, 40.24.0-4.b.1.7, 56.24.0-4.b.1.10, $\ldots$	$[]$
485520.fk3	485520fk3	485520.fk	485520fk	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 17^{2} \)	\( 2^{12} \cdot 3^{2} \cdot 5^{2} \cdot 7^{4} \cdot 17^{10} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$14280$	$192$	$1$	$10.81199401$	$1$		$3$	$37748736$	$2.884430$	$369543396484081/45120132225$	$1.10652$	$4.49557$	$[0, 1, 0, -6912976, 6211945940]$	\(y^2=x^3+x^2-6912976x+6211945940\)	2.6.0.a.1, 4.12.0.b.1, 24.24.0-4.b.1.2, 40.24.0-4.b.1.7, 56.24.0-4.b.1.5, $\ldots$	$[(93916/7, 893178/7)]$