Elliptic curves over $\Q$ of conductor 6699

Results (18 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
6699.a1	6699d4	6699.a	6699d	$4$	$4$	\( 3 \cdot 7 \cdot 11 \cdot 29 \)	\( 3^{6} \cdot 7 \cdot 11 \cdot 29 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$17864$	$48$	$0$	$5.204451561$	$1$		$0$	$82944$	$2.137047$	$72371679832051361738355457/1627857$	$1.00712$	$6.75889$	$[1, 1, 1, -8681904, 9842626320]$	\(y^2+xy+y=x^3+x^2-8681904x+9842626320\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 28.12.0-4.c.1.1, 56.24.0-56.z.1.10, $\ldots$	$[(27237/4, -47361/4)]$
6699.a2	6699d3	6699.a	6699d	$4$	$4$	\( 3 \cdot 7 \cdot 11 \cdot 29 \)	\( 3^{24} \cdot 7^{4} \cdot 11 \cdot 29 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$17864$	$48$	$0$	$5.204451561$	$1$		$0$	$82944$	$2.137047$	$17825137625614555960417/216318148151991039$	$0.98174$	$5.81573$	$[1, 1, 1, -544214, 152670836]$	\(y^2+xy+y=x^3+x^2-544214x+152670836\)	2.3.0.a.1, 4.12.0-4.c.1.2, 56.24.0-56.z.1.12, 1276.24.0.?, 17864.48.0.?	$[(1495/2, 8791/2)]$
6699.a3	6699d2	6699.a	6699d	$4$	$4$	\( 3 \cdot 7 \cdot 11 \cdot 29 \)	\( 3^{12} \cdot 7^{2} \cdot 11^{2} \cdot 29^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$8932$	$48$	$0$	$2.602225780$	$1$		$4$	$41472$	$1.790474$	$17668869054438249282097/2649918412449$	$0.98151$	$5.81473$	$[1, 1, 1, -542619, 153621456]$	\(y^2+xy+y=x^3+x^2-542619x+153621456\)	2.6.0.a.1, 4.12.0-2.a.1.1, 28.24.0-28.b.1.1, 1276.24.0.?, 8932.48.0.?	$[(381, 1349)]$
6699.a4	6699d1	6699.a	6699d	$4$	$4$	\( 3 \cdot 7 \cdot 11 \cdot 29 \)	\( - 3^{6} \cdot 7 \cdot 11^{4} \cdot 29^{4} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$17864$	$48$	$0$	$1.301112890$	$1$		$7$	$20736$	$1.443899$	$-4275768267198290017/52843101620463$	$0.94825$	$4.87197$	$[1, 1, 1, -33814, 2404610]$	\(y^2+xy+y=x^3+x^2-33814x+2404610\)	2.3.0.a.1, 4.12.0-4.c.1.1, 14.6.0.b.1, 28.24.0-28.g.1.2, 2552.24.0.?, $\ldots$	$[(62, 711)]$
6699.b1	6699c1	6699.b	6699c	$1$	$1$	\( 3 \cdot 7 \cdot 11 \cdot 29 \)	\( - 3^{3} \cdot 7 \cdot 11 \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$13398$	$2$	$0$	$1.404784454$	$1$		$2$	$432$	$-0.403872$	$-1/60291$	$0.98548$	$2.09560$	$[1, 1, 1, 0, -12]$	\(y^2+xy+y=x^3+x^2-12\)	13398.2.0.?	$[(2, 0)]$
6699.c1	6699a3	6699.c	6699a	$4$	$4$	\( 3 \cdot 7 \cdot 11 \cdot 29 \)	\( 3^{12} \cdot 7 \cdot 11 \cdot 29 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$53592$	$48$	$0$	$6.548206615$	$1$		$0$	$6144$	$0.926445$	$187519537050946633/1186707753$	$0.93261$	$4.51464$	$[1, 1, 0, -11924, 496227]$	\(y^2+xy=x^3+x^2-11924x+496227\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 44.12.0-4.c.1.1, 264.24.0.?, $\ldots$	$[(19229/4, 2618747/4)]$
6699.c2	6699a2	6699.c	6699a	$4$	$4$	\( 3 \cdot 7 \cdot 11 \cdot 29 \)	\( 3^{6} \cdot 7^{2} \cdot 11^{2} \cdot 29^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.6.0.1	2Cs	$26796$	$48$	$0$	$3.274103307$	$1$		$4$	$3072$	$0.579872$	$48455467135993/3635004681$	$0.88285$	$3.57692$	$[1, 1, 0, -759, 7200]$	\(y^2+xy=x^3+x^2-759x+7200\)	2.6.0.a.1, 12.12.0-2.a.1.1, 44.12.0-2.a.1.1, 132.24.0.?, 812.12.0.?, $\ldots$	$[(47/2, 23/2)]$
6699.c3	6699a1	6699.c	6699a	$4$	$4$	\( 3 \cdot 7 \cdot 11 \cdot 29 \)	\( 3^{3} \cdot 7 \cdot 11^{4} \cdot 29 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$53592$	$48$	$0$	$6.548206615$	$1$		$1$	$1536$	$0.233298$	$408023180713/80247321$	$0.84673$	$3.03467$	$[1, 1, 0, -154, -665]$	\(y^2+xy=x^3+x^2-154x-665\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 88.12.0.?, 264.24.0.?, $\ldots$	$[(-615/8, -895/8)]$
6699.c4	6699a4	6699.c	6699a	$4$	$4$	\( 3 \cdot 7 \cdot 11 \cdot 29 \)	\( - 3^{3} \cdot 7^{4} \cdot 11 \cdot 29^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$53592$	$48$	$0$	$6.548206615$	$1$		$0$	$6144$	$0.926445$	$42227808999767/504359959257$	$0.92634$	$3.89929$	$[1, 1, 0, 726, 33633]$	\(y^2+xy=x^3+x^2+726x+33633\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 44.12.0-4.c.1.2, 132.24.0.?, $\ldots$	$[(4799/2, 327911/2)]$
6699.d1	6699b3	6699.d	6699b	$4$	$4$	\( 3 \cdot 7 \cdot 11 \cdot 29 \)	\( 3 \cdot 7 \cdot 11 \cdot 29^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$53592$	$48$	$0$	$1$	$4$	$2$	$0$	$3328$	$0.508607$	$215751695207833/163381911$	$0.97684$	$3.74645$	$[1, 1, 0, -1249, -17510]$	\(y^2+xy=x^3+x^2-1249x-17510\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 232.12.0.?, 308.12.0.?, $\ldots$	$[]$
6699.d2	6699b2	6699.d	6699b	$4$	$4$	\( 3 \cdot 7 \cdot 11 \cdot 29 \)	\( 3^{2} \cdot 7^{2} \cdot 11^{2} \cdot 29^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.6.0.1	2Cs	$26796$	$48$	$0$	$1$	$1$		$2$	$1664$	$0.162033$	$93391282153/44876601$	$0.95512$	$2.86730$	$[1, 1, 0, -94, -185]$	\(y^2+xy=x^3+x^2-94x-185\)	2.6.0.a.1, 12.12.0-2.a.1.1, 116.12.0.?, 308.12.0.?, 348.24.0.?, $\ldots$	$[]$
6699.d3	6699b1	6699.d	6699b	$4$	$4$	\( 3 \cdot 7 \cdot 11 \cdot 29 \)	\( 3^{4} \cdot 7 \cdot 11 \cdot 29 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$53592$	$48$	$0$	$1$	$1$		$1$	$832$	$-0.184541$	$13430356633/180873$	$0.80625$	$2.64717$	$[1, 1, 0, -49, 112]$	\(y^2+xy=x^3+x^2-49x+112\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 116.12.0.?, 308.12.0.?, $\ldots$	$[]$
6699.d4	6699b4	6699.d	6699b	$4$	$4$	\( 3 \cdot 7 \cdot 11 \cdot 29 \)	\( - 3 \cdot 7^{4} \cdot 11^{4} \cdot 29 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$53592$	$48$	$0$	$1$	$1$		$0$	$3328$	$0.508607$	$4365111505607/3058314567$	$0.88834$	$3.30370$	$[1, 1, 0, 341, -968]$	\(y^2+xy=x^3+x^2+341x-968\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 116.12.0.?, 174.6.0.?, $\ldots$	$[]$
6699.e1	6699e1	6699.e	6699e	$1$	$1$	\( 3 \cdot 7 \cdot 11 \cdot 29 \)	\( - 3 \cdot 7^{5} \cdot 11^{3} \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$13398$	$2$	$0$	$2.904216921$	$1$		$2$	$6000$	$0.689258$	$-1484391946907017/1946200179$	$0.90472$	$3.96563$	$[1, 1, 0, -2376, -45633]$	\(y^2+xy=x^3+x^2-2376x-45633\)	13398.2.0.?	$[(58, 97)]$
6699.f1	6699f4	6699.f	6699f	$4$	$4$	\( 3 \cdot 7 \cdot 11 \cdot 29 \)	\( 3 \cdot 7^{2} \cdot 11 \cdot 29^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$7656$	$48$	$0$	$1$	$1$		$0$	$7168$	$0.871175$	$71366476613135257/1143673377$	$0.92746$	$4.40498$	$[1, 0, 1, -8642, 308471]$	\(y^2+xy+y=x^3-8642x+308471\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 44.12.0-4.c.1.1, 66.6.0.a.1, $\ldots$	$[]$
6699.f2	6699f3	6699.f	6699f	$4$	$4$	\( 3 \cdot 7 \cdot 11 \cdot 29 \)	\( 3^{4} \cdot 7^{8} \cdot 11 \cdot 29 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$7656$	$48$	$0$	$1$	$1$		$0$	$7168$	$0.871175$	$1101438820807417/148956693039$	$0.90591$	$3.93150$	$[1, 0, 1, -2152, -33805]$	\(y^2+xy+y=x^3-2152x-33805\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 44.12.0-4.c.1.2, 116.12.0.?, $\ldots$	$[]$
6699.f3	6699f2	6699.f	6699f	$4$	$4$	\( 3 \cdot 7 \cdot 11 \cdot 29 \)	\( 3^{2} \cdot 7^{4} \cdot 11^{2} \cdot 29^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.6.0.1	2Cs	$3828$	$48$	$0$	$1$	$1$		$2$	$3584$	$0.524601$	$19061979249097/2198953449$	$0.87684$	$3.47102$	$[1, 0, 1, -557, 4475]$	\(y^2+xy+y=x^3-557x+4475\)	2.6.0.a.1, 12.12.0-2.a.1.1, 44.12.0-2.a.1.1, 116.12.0.?, 132.24.0.?, $\ldots$	$[]$
6699.f4	6699f1	6699.f	6699f	$4$	$4$	\( 3 \cdot 7 \cdot 11 \cdot 29 \)	\( - 3 \cdot 7^{2} \cdot 11^{4} \cdot 29 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$7656$	$48$	$0$	$1$	$1$		$1$	$1792$	$0.178028$	$12600539783/62414583$	$0.84977$	$2.86954$	$[1, 0, 1, 48, 361]$	\(y^2+xy+y=x^3+48x+361\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 88.12.0.?, 116.12.0.?, $\ldots$	$[]$