Elliptic curve search results

Results (15 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
105117.a1	105117a4	105117.a	105117a	$4$	$4$	\( 3 \cdot 37 \cdot 947 \)	\( 3^{15} \cdot 37^{4} \cdot 947^{2} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$888$	$48$	$0$	$1$	$529$	$23$	$2$	$3834064800$	$5.945709$	$35750015327789590863195632604819940505843644873/24117132814226841843$	$1.05522$	$9.27047$	$[1, 1, 0, -68630554334764, 218838796108963317073]$	\(y^2+xy=x^3+x^2-68630554334764x+218838796108963317073\)	2.3.0.a.1, 4.12.0-4.c.1.1, 12.24.0-12.h.1.2, 296.24.0.?, 888.48.0.?	$[]$
105117.a2	105117a3	105117.a	105117a	$4$	$4$	\( 3 \cdot 37 \cdot 947 \)	\( 3^{60} \cdot 37 \cdot 947^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$888$	$48$	$0$	$1$	$529$	$23$	$0$	$3834064800$	$5.945709$	$8729043897258866627620076007027982222826473/1406620573680619625525682424748557533$	$1.04462$	$8.55113$	$[1, 1, 0, -4289575555614, 3419077107941220627]$	\(y^2+xy=x^3+x^2-4289575555614x+3419077107941220627\)	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.ba.1.16, 74.6.0.?, 148.24.0.?, $\ldots$	$[]$
105117.a3	105117a2	105117.a	105117a	$4$	$4$	\( 3 \cdot 37 \cdot 947 \)	\( 3^{30} \cdot 37^{2} \cdot 947^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$444$	$48$	$0$	$1$	$529$	$23$	$2$	$1917032400$	$5.599136$	$8728031086049350630185661576267116242035033/226694511596718381171271067361$	$1.04462$	$8.55112$	$[1, 1, 0, -4289409645949, 3419354848717276480]$	\(y^2+xy=x^3+x^2-4289409645949x+3419354848717276480\)	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.1, 148.24.0.?, 444.48.0.?	$[]$
105117.a4	105117a1	105117.a	105117a	$4$	$4$	\( 3 \cdot 37 \cdot 947 \)	\( - 3^{15} \cdot 37 \cdot 947^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$888$	$48$	$0$	$1$	$529$	$23$	$1$	$958516200$	$5.252563$	$-2130619715770746733128519218686344041353/343415882572552805694607290035799$	$1.03234$	$7.83178$	$[1, 1, 0, -268077733544, 53431675391780595]$	\(y^2+xy=x^3+x^2-268077733544x+53431675391780595\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.2, 24.24.0-24.ba.1.4, $\ldots$	$[]$
240885.l1	240885l3	240885.l	240885l	$4$	$4$	\( 3^{2} \cdot 5 \cdot 53 \cdot 101 \)	\( 3^{8} \cdot 5^{7} \cdot 53^{16} \cdot 101 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.18	2B	$24240$	$192$	$3$	$1$	$529$	$23$	$0$	$11074732032$	$6.262848$	$241546784464320517468534794561141985838881/275275669262322797848958276546015625$	$1.04263$	$8.22135$	$[1, -1, 0, -11677100702130, -15343432289684969049]$	\(y^2+xy=x^3-x^2-11677100702130x-15343432289684969049\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 12.12.0-4.c.1.1, 16.24.0-8.o.1.2, $\ldots$	$[]$
240885.l2	240885l2	240885.l	240885l	$4$	$4$	\( 3^{2} \cdot 5 \cdot 53 \cdot 101 \)	\( 3^{10} \cdot 5^{14} \cdot 53^{8} \cdot 101^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.34	2Cs	$12120$	$192$	$3$	$1$	$529$	$23$	$2$	$5537366016$	$5.916267$	$241348524484789039743342517469216354588881/313989253251890737554931640625$	$1.04261$	$8.22128$	$[1, -1, 0, -11673904999005, -15352258084787078424]$	\(y^2+xy=x^3-x^2-11673904999005x-15352258084787078424\)	2.6.0.a.1, 4.12.0.a.1, 8.24.0-4.a.1.2, 12.24.0-4.a.1.1, 24.48.0-24.j.1.4, $\ldots$	$[]$
240885.l3	240885l1	240885.l	240885l	$4$	$4$	\( 3^{2} \cdot 5 \cdot 53 \cdot 101 \)	\( 3^{14} \cdot 5^{7} \cdot 53^{4} \cdot 101 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.18	2B	$24240$	$192$	$3$	$1$	$529$	$23$	$1$	$2768683008$	$5.569695$	$241348524258716777321981861762654349672961/408493283589140625$	$1.04261$	$8.22128$	$[1, -1, 0, -11673904995360, -15352258094853452325]$	\(y^2+xy=x^3-x^2-11673904995360x-15352258094853452325\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 12.12.0-4.c.1.2, 16.24.0-8.o.1.2, $\ldots$	$[]$
240885.l4	240885l4	240885.l	240885l	$4$	$4$	\( 3^{2} \cdot 5 \cdot 53 \cdot 101 \)	\( - 3^{8} \cdot 5^{28} \cdot 53^{4} \cdot 101^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.75	2B	$24240$	$192$	$3$	$1$	$529$	$23$	$0$	$11074732032$	$6.262848$	$-241150376637100011010604272072450358947201/275290740746480561792850494384765625$	$1.09756$	$8.22137$	$[1, -1, 0, -11670709354200, -15361083235641301875]$	\(y^2+xy=x^3-x^2-11670709354200x-15361083235641301875\)	2.3.0.a.1, 4.12.0.d.1, 8.24.0-4.d.1.4, 12.24.0-4.d.1.1, 24.48.0-24.z.1.2, $\ldots$	$[]$
328440.f1	328440f1	328440.f	328440f	$1$	$1$	\( 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 23 \)	\( - 2^{4} \cdot 3^{5} \cdot 5^{15} \cdot 7^{23} \cdot 17 \cdot 23^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$82110$	$2$	$0$	$1$	$529$	$23$	$0$	$14014396800$	$6.151947$	$-67363697007825315287516791404269719753984/41980121229590581887181268646240234375$	$1.05212$	$7.67702$	$[0, -1, 0, -2136030230276, -1731662395495550115]$	\(y^2=x^3-x^2-2136030230276x-1731662395495550115\)	82110.2.0.?	$[]$
343938.f1	343938f1	343938.f	343938f	$1$	$1$	\( 2 \cdot 3 \cdot 7 \cdot 19 \cdot 431 \)	\( - 2^{7} \cdot 3^{5} \cdot 7^{9} \cdot 19^{17} \cdot 431 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1375752$	$2$	$0$	$1$	$529$	$23$	$0$	$18266804640$	$5.854279$	$-724645288449829800761235614245590693276169/2964743255328339375522712182723610752$	$1.05389$	$7.56134$	$[1, 1, 0, -1871259077968, 988731638741956480]$	\(y^2+xy=x^3+x^2-1871259077968x+988731638741956480\)	1375752.2.0.?	$[]$
356454.n1	356454n1	356454.n	356454n	$1$	$1$	\( 2 \cdot 3^{3} \cdot 7 \cdot 23 \cdot 41 \)	\( - 2 \cdot 3^{9} \cdot 7 \cdot 23^{16} \cdot 41^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6888$	$2$	$0$	$1$	$529$	$23$	$0$	$12999716352$	$6.080238$	$28787515793477505534818898263850022125/16720929239014146552102781981226974$	$1.09421$	$7.52040$	$[1, -1, 0, 1723947052368, 52928879104616210]$	\(y^2+xy=x^3-x^2+1723947052368x+52928879104616210\)	6888.2.0.?	$[]$
493818.b1	493818b1	493818.b	493818b	$1$	$1$	\( 2 \cdot 3 \cdot 13^{2} \cdot 487 \)	\( - 2^{53} \cdot 3^{3} \cdot 13^{11} \cdot 487 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$151944$	$2$	$0$	$1$	$529$	$23$	$0$	$10833318720$	$5.823311$	$-8836877037250190041400193600040850593/43974332622477804378783744$	$1.04462$	$7.66303$	$[1, 1, 0, -7279112047821, -7559026998975481635]$	\(y^2+xy=x^3+x^2-7279112047821x-7559026998975481635\)	151944.2.0.?	$[]$
497070.bh1	497070bh1	497070.bh	497070bh	$1$	$1$	\( 2 \cdot 3^{3} \cdot 5 \cdot 7 \cdot 263 \)	\( - 2 \cdot 3^{5} \cdot 5^{5} \cdot 7^{3} \cdot 263 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$220920$	$2$	$0$	$1$	$529$	$23$	$0$	$135073440$	$3.593601$	$-27528904494860533787484920014203/563806250$	$1.01369$	$5.93801$	$[1, -1, 1, -3925459463, -94662802269219]$	\(y^2+xy+y=x^3-x^2-3925459463x-94662802269219\)	220920.2.0.?	$[]$
2116800.buh1	-	2116800.buh	-	$1$	$1$	\( 2^{6} \cdot 3^{3} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{65} \cdot 3^{5} \cdot 5^{8} \cdot 7^{11} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$168$	$2$	$0$	$1$	$529$	$23$	$0$	$60034867200$	$5.918961$	$-502229023208369508642555/2365374966787997696$	$1.08315$	$6.66662$	$[0, 0, 0, -2368958875500, -1409108667474130000]$	\(y^2=x^3-2368958875500x-1409108667474130000\)	168.2.0.?	$[]$
257120261.a1	-	257120261.a	-	$1$	$1$	\( 257120261 \)	\( -257120261 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1028481044$	$2$	$0$	$1$	$529$	$23$	$0$		$1.972464$	$-3003498643791062315843001/257120261$	$0.83266$	$2.91049$	$[1, -1, 0, -3005854, -2005105579]$	\(y^2+xy=x^3-x^2-3005854x-2005105579\)	1028481044.2.0.?	$[]$