Elliptic curves over $\Q$ of conductor 4284

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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
4284.a1	4284a2	4284.a	4284a	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)	\( 2^{8} \cdot 3^{9} \cdot 7^{10} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1428$	$12$	$0$	$1$	$1$		$1$	$31680$	$1.896271$	$79708988544624/4802079233$	$1.06636$	$5.67310$	$[0, 0, 0, -153711, -21955050]$	\(y^2=x^3-153711x-21955050\)	2.3.0.a.1, 84.6.0.?, 204.6.0.?, 476.6.0.?, 1428.12.0.?	$[ ]$
4284.a2	4284a1	4284.a	4284a	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)	\( 2^{4} \cdot 3^{9} \cdot 7^{5} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1428$	$12$	$0$	$1$	$1$		$1$	$15840$	$1.549698$	$1219067475001344/4857223$	$1.18836$	$5.66770$	$[0, 0, 0, -151416, -22677975]$	\(y^2=x^3-151416x-22677975\)	2.3.0.a.1, 42.6.0.a.1, 204.6.0.?, 476.6.0.?, 1428.12.0.?	$[ ]$
4284.b1	4284e1	4284.b	4284e	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)	\( 2^{4} \cdot 3^{7} \cdot 7^{3} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1428$	$12$	$0$	$1$	$1$		$1$	$2880$	$0.744648$	$265327034368/297381$	$1.02684$	$4.26522$	$[0, 0, 0, -3036, 64325]$	\(y^2=x^3-3036x+64325\)	2.3.0.a.1, 42.6.0.a.1, 68.6.0.b.1, 1428.12.0.?	$[ ]$
4284.b2	4284e2	4284.b	4284e	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)	\( - 2^{8} \cdot 3^{8} \cdot 7^{6} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1428$	$12$	$0$	$1$	$1$		$1$	$5760$	$1.091221$	$-6940769488/18000297$	$0.99965$	$4.36452$	$[0, 0, 0, -2271, 97526]$	\(y^2=x^3-2271x+97526\)	2.3.0.a.1, 68.6.0.a.1, 84.6.0.?, 1428.12.0.?	$[ ]$
4284.c1	4284i1	4284.c	4284i	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)	\( 2^{4} \cdot 3^{9} \cdot 7 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1428$	$12$	$0$	$0.347202502$	$1$		$9$	$1728$	$0.454145$	$1302642688/54621$	$0.89951$	$3.62947$	$[0, 0, 0, -516, 4345]$	\(y^2=x^3-516x+4345\)	2.3.0.a.1, 42.6.0.a.1, 68.6.0.b.1, 1428.12.0.?	$[(8, 27)]$
4284.c2	4284i2	4284.c	4284i	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)	\( - 2^{8} \cdot 3^{12} \cdot 7^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1428$	$12$	$0$	$0.694405005$	$1$		$9$	$3456$	$0.800718$	$9148592/607257$	$0.90063$	$3.93411$	$[0, 0, 0, 249, 16126]$	\(y^2=x^3+249x+16126\)	2.3.0.a.1, 68.6.0.a.1, 84.6.0.?, 1428.12.0.?	$[(-1, 126)]$
4284.d1	4284c2	4284.d	4284c	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)	\( 2^{8} \cdot 3^{9} \cdot 7^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1428$	$12$	$0$	$1.690943462$	$1$		$5$	$2880$	$0.725688$	$347482224/833$	$0.80931$	$4.19711$	$[0, 0, 0, -2511, -48330]$	\(y^2=x^3-2511x-48330\)	2.3.0.a.1, 84.6.0.?, 204.6.0.?, 476.6.0.?, 1428.12.0.?	$[(-29, 10)]$
4284.d2	4284c1	4284.d	4284c	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)	\( 2^{4} \cdot 3^{9} \cdot 7 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1428$	$12$	$0$	$0.845471731$	$1$		$7$	$1440$	$0.379115$	$3538944/2023$	$1.07666$	$3.31707$	$[0, 0, 0, -216, -135]$	\(y^2=x^3-216x-135\)	2.3.0.a.1, 42.6.0.a.1, 204.6.0.?, 476.6.0.?, 1428.12.0.?	$[(-2, 17)]$
4284.e1	4284h1	4284.e	4284h	$1$	$1$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)	\( - 2^{8} \cdot 3^{9} \cdot 7^{2} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$102$	$2$	$0$	$1.185943385$	$1$		$2$	$2304$	$0.532525$	$17997824/22491$	$0.86007$	$3.46667$	$[0, 0, 0, 312, -2284]$	\(y^2=x^3+312x-2284\)	102.2.0.?	$[(13, 63)]$
4284.f1	4284b2	4284.f	4284b	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)	\( 2^{8} \cdot 3^{3} \cdot 7^{10} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1428$	$12$	$0$	$6.203677341$	$1$		$1$	$10560$	$1.346966$	$79708988544624/4802079233$	$1.06636$	$4.88487$	$[0, 0, 0, -17079, 813150]$	\(y^2=x^3-17079x+813150\)	2.3.0.a.1, 84.6.0.?, 204.6.0.?, 476.6.0.?, 1428.12.0.?	$[(25/2, 6725/2)]$
4284.f2	4284b1	4284.f	4284b	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)	\( 2^{4} \cdot 3^{3} \cdot 7^{5} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1428$	$12$	$0$	$3.101838670$	$1$		$3$	$5280$	$1.000391$	$1219067475001344/4857223$	$1.18836$	$4.87947$	$[0, 0, 0, -16824, 839925]$	\(y^2=x^3-16824x+839925\)	2.3.0.a.1, 42.6.0.a.1, 204.6.0.?, 476.6.0.?, 1428.12.0.?	$[(7, 850)]$
4284.g1	4284d2	4284.g	4284d	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)	\( 2^{8} \cdot 3^{3} \cdot 7^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1428$	$12$	$0$	$1$	$1$		$1$	$960$	$0.176382$	$347482224/833$	$0.80931$	$3.40888$	$[0, 0, 0, -279, 1790]$	\(y^2=x^3-279x+1790\)	2.3.0.a.1, 84.6.0.?, 204.6.0.?, 476.6.0.?, 1428.12.0.?	$[ ]$
4284.g2	4284d1	4284.g	4284d	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)	\( 2^{4} \cdot 3^{3} \cdot 7 \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1428$	$12$	$0$	$1$	$1$		$1$	$480$	$-0.170192$	$3538944/2023$	$1.07666$	$2.52884$	$[0, 0, 0, -24, 5]$	\(y^2=x^3-24x+5\)	2.3.0.a.1, 42.6.0.a.1, 204.6.0.?, 476.6.0.?, 1428.12.0.?	$[ ]$
4284.h1	4284f1	4284.h	4284f	$1$	$1$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)	\( - 2^{8} \cdot 3^{15} \cdot 7^{2} \cdot 17^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$102$	$2$	$0$	$1$	$1$		$0$	$241920$	$2.872311$	$-6434900743458429657088/395758108932291$	$1.06283$	$7.45613$	$[0, 0, 0, -22144296, -40111047772]$	\(y^2=x^3-22144296x-40111047772\)	102.2.0.?	$[ ]$
4284.i1	4284g1	4284.i	4284g	$2$	$3$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)	\( - 2^{8} \cdot 3^{9} \cdot 7^{4} \cdot 17^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$102$	$16$	$0$	$1$	$1$		$0$	$13824$	$1.424240$	$-11632923639808/318495051$	$1.03083$	$5.05438$	$[0, 0, 0, -26976, -1745228]$	\(y^2=x^3-26976x-1745228\)	3.8.0-3.a.1.1, 102.16.0.?	$[ ]$
4284.i2	4284g2	4284.i	4284g	$2$	$3$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \)	\( - 2^{8} \cdot 3^{7} \cdot 7^{12} \cdot 17 \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$102$	$16$	$0$	$1$	$1$		$2$	$41472$	$1.973545$	$1021544365555712/705905647251$	$1.08891$	$5.58399$	$[0, 0, 0, 119904, -7040252]$	\(y^2=x^3+119904x-7040252\)	3.8.0-3.a.1.2, 102.16.0.?	$[ ]$

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