Elliptic curves over $\Q$ of conductor 1014

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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
1014.a1	1014a1	1014.a	1014a	$1$	$1$	\( 2 \cdot 3 \cdot 13^{2} \)	\( - 2^{4} \cdot 3^{2} \cdot 13^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	4.2.0.1		$24$	$4$	$0$	$0.114266303$	$1$		$10$	$192$	$-0.051831$	$-169/144$	$1.17559$	$3.27740$	$[1, 1, 0, -3, -99]$	\(y^2+xy=x^3+x^2-3x-99\)	4.2.0.a.1, 24.4.0-4.a.1.1	$[(18, 69)]$
1014.b1	1014c4	1014.b	1014c	$4$	$10$	\( 2 \cdot 3 \cdot 13^{2} \)	\( 2^{10} \cdot 3^{2} \cdot 13^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$780$	$288$	$5$	$0.737226056$	$1$		$4$	$2400$	$1.170006$	$18013780041269221/9216$	$1.09234$	$6.51936$	$[1, 0, 1, -70997, 7275296]$	\(y^2+xy+y=x^3-70997x+7275296\)	2.3.0.a.1, 5.6.0.a.1, 10.36.0.b.1, 12.6.0.f.1, 26.6.0.b.1, $\ldots$	$[(147, 70)]$
1014.b2	1014c3	1014.b	1014c	$4$	$10$	\( 2 \cdot 3 \cdot 13^{2} \)	\( - 2^{20} \cdot 3 \cdot 13^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$780$	$288$	$5$	$1.474452113$	$1$		$3$	$1200$	$0.823432$	$-4395631034341/3145728$	$1.06506$	$5.31776$	$[1, 0, 1, -4437, 113440]$	\(y^2+xy+y=x^3-4437x+113440\)	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 12.6.0.f.1, 20.36.0.b.2, $\ldots$	$[(40, -1)]$
1014.b3	1014c2	1014.b	1014c	$4$	$10$	\( 2 \cdot 3 \cdot 13^{2} \)	\( 2^{2} \cdot 3^{10} \cdot 13^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$780$	$288$	$5$	$0.147445211$	$1$		$14$	$480$	$0.365287$	$476379541/236196$	$1.06546$	$3.99855$	$[1, 0, 1, -212, -466]$	\(y^2+xy+y=x^3-212x-466\)	2.3.0.a.1, 5.6.0.a.1, 10.36.0.b.2, 12.6.0.f.1, 26.6.0.b.1, $\ldots$	$[(-9, 31)]$
1014.b4	1014c1	1014.b	1014c	$4$	$10$	\( 2 \cdot 3 \cdot 13^{2} \)	\( - 2^{4} \cdot 3^{5} \cdot 13^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$780$	$288$	$5$	$0.294890422$	$1$		$13$	$240$	$0.018713$	$5735339/3888$	$1.16005$	$3.36003$	$[1, 0, 1, 48, -50]$	\(y^2+xy+y=x^3+48x-50\)	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 12.6.0.f.1, 20.36.0.b.1, $\ldots$	$[(5, 15)]$
1014.c1	1014b1	1014.c	1014b	$2$	$3$	\( 2 \cdot 3 \cdot 13^{2} \)	\( - 2^{8} \cdot 3^{6} \cdot 13^{8} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.2.0.1, 3.8.0.1	3B.1.1	$24$	$32$	$0$	$1$	$1$		$2$	$4992$	$1.415201$	$-156116857/186624$	$1.01025$	$5.85206$	$[1, 0, 1, -10482, 722308]$	\(y^2+xy+y=x^3-10482x+722308\)	3.8.0-3.a.1.2, 4.2.0.a.1, 12.16.0-12.a.1.6, 24.32.0-24.b.2.6	$[ ]$
1014.c2	1014b2	1014.c	1014b	$2$	$3$	\( 2 \cdot 3 \cdot 13^{2} \)	\( - 2^{24} \cdot 3^{2} \cdot 13^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.2.0.1, 3.8.0.2	3B.1.2	$24$	$32$	$0$	$1$	$1$		$0$	$14976$	$1.964508$	$93603087383/150994944$	$1.05810$	$6.69821$	$[1, 0, 1, 88383, -13514252]$	\(y^2+xy+y=x^3+88383x-13514252\)	3.8.0-3.a.1.1, 4.2.0.a.1, 12.16.0-12.a.1.5, 24.32.0-24.b.1.6	$[ ]$
1014.d1	1014e4	1014.d	1014e	$4$	$4$	\( 2 \cdot 3 \cdot 13^{2} \)	\( 2^{4} \cdot 3^{5} \cdot 13^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$312$	$48$	$0$	$1$	$1$		$0$	$26880$	$2.250553$	$986551739719628473/111045168$	$1.06555$	$8.20940$	$[1, 1, 1, -3504979, 2524207265]$	\(y^2+xy+y=x^3+x^2-3504979x+2524207265\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0.h.1, 24.24.0-12.h.1.6, $\ldots$	$[ ]$
1014.d2	1014e3	1014.d	1014e	$4$	$4$	\( 2 \cdot 3 \cdot 13^{2} \)	\( 2^{4} \cdot 3^{20} \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$312$	$48$	$0$	$1$	$1$		$0$	$26880$	$2.250553$	$1416134368422073/725251155408$	$1.07849$	$7.26364$	$[1, 1, 1, -395379, -32619423]$	\(y^2+xy+y=x^3+x^2-395379x-32619423\)	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.ba.1.1, 26.6.0.b.1, 52.24.0-52.g.1.1, $\ldots$	$[ ]$
1014.d3	1014e2	1014.d	1014e	$4$	$4$	\( 2 \cdot 3 \cdot 13^{2} \)	\( 2^{8} \cdot 3^{10} \cdot 13^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$156$	$48$	$0$	$1$	$1$		$2$	$13440$	$1.903978$	$242702053576633/2554695936$	$1.10395$	$7.00880$	$[1, 1, 1, -219619, 39160961]$	\(y^2+xy+y=x^3+x^2-219619x+39160961\)	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.3, 52.24.0-52.b.1.2, 156.48.0.?	$[ ]$
1014.d4	1014e1	1014.d	1014e	$4$	$4$	\( 2 \cdot 3 \cdot 13^{2} \)	\( - 2^{16} \cdot 3^{5} \cdot 13^{7} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$312$	$48$	$0$	$1$	$1$		$3$	$6720$	$1.557405$	$-822656953/207028224$	$1.08584$	$6.06720$	$[1, 1, 1, -3299, 1521281]$	\(y^2+xy+y=x^3+x^2-3299x+1521281\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.ba.1.9, 78.6.0.?, 104.24.0.?, $\ldots$	$[ ]$
1014.e1	1014d1	1014.e	1014d	$1$	$1$	\( 2 \cdot 3 \cdot 13^{2} \)	\( - 2^{4} \cdot 3^{2} \cdot 13^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	4.2.0.1		$312$	$4$	$0$	$1$	$1$		$0$	$2496$	$1.230644$	$-169/144$	$1.17559$	$5.50081$	$[1, 1, 1, -595, -214687]$	\(y^2+xy+y=x^3+x^2-595x-214687\)	4.2.0.a.1, 312.4.0.?	$[ ]$
1014.f1	1014f1	1014.f	1014f	$2$	$3$	\( 2 \cdot 3 \cdot 13^{2} \)	\( - 2^{8} \cdot 3^{6} \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.2.0.1, 3.4.0.1	3B	$312$	$32$	$0$	$0.036626204$	$1$		$16$	$384$	$0.132727$	$-156116857/186624$	$1.01025$	$3.62865$	$[1, 0, 0, -62, 324]$	\(y^2+xy=x^3-62x+324\)	3.4.0.a.1, 4.2.0.a.1, 12.8.0.a.1, 24.16.0.b.2, 39.8.0-3.a.1.1, $\ldots$	$[(4, 10)]$
1014.f2	1014f2	1014.f	1014f	$2$	$3$	\( 2 \cdot 3 \cdot 13^{2} \)	\( - 2^{24} \cdot 3^{2} \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.2.0.1, 3.4.0.1	3B	$312$	$32$	$0$	$0.109878613$	$1$		$10$	$1152$	$0.682034$	$93603087383/150994944$	$1.05810$	$4.47480$	$[1, 0, 0, 523, -6111]$	\(y^2+xy=x^3+523x-6111\)	3.4.0.a.1, 4.2.0.a.1, 12.8.0.a.1, 24.16.0.b.1, 39.8.0-3.a.1.2, $\ldots$	$[(82, 727)]$
1014.g1	1014g4	1014.g	1014g	$4$	$10$	\( 2 \cdot 3 \cdot 13^{2} \)	\( 2^{10} \cdot 3^{2} \cdot 13^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$780$	$288$	$5$	$1$	$1$		$0$	$31200$	$2.452480$	$18013780041269221/9216$	$1.09234$	$8.74277$	$[1, 0, 0, -11998412, 15995824272]$	\(y^2+xy=x^3-11998412x+15995824272\)	2.3.0.a.1, 5.6.0.a.1, 10.36.0.b.1, 12.6.0.f.1, 26.6.0.b.1, $\ldots$	$[ ]$
1014.g2	1014g3	1014.g	1014g	$4$	$10$	\( 2 \cdot 3 \cdot 13^{2} \)	\( - 2^{20} \cdot 3 \cdot 13^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$780$	$288$	$5$	$1$	$1$		$1$	$15600$	$2.105907$	$-4395631034341/3145728$	$1.06506$	$7.54117$	$[1, 0, 0, -749772, 249978000]$	\(y^2+xy=x^3-749772x+249978000\)	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 12.6.0.f.1, 20.36.0.b.2, $\ldots$	$[ ]$
1014.g3	1014g2	1014.g	1014g	$4$	$10$	\( 2 \cdot 3 \cdot 13^{2} \)	\( 2^{2} \cdot 3^{10} \cdot 13^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$780$	$288$	$5$	$1$	$1$		$0$	$6240$	$1.647762$	$476379541/236196$	$1.06546$	$6.22196$	$[1, 0, 0, -35747, -987507]$	\(y^2+xy=x^3-35747x-987507\)	2.3.0.a.1, 5.6.0.a.1, 10.36.0.b.2, 12.6.0.f.1, 26.6.0.b.1, $\ldots$	$[ ]$
1014.g4	1014g1	1014.g	1014g	$4$	$10$	\( 2 \cdot 3 \cdot 13^{2} \)	\( - 2^{4} \cdot 3^{5} \cdot 13^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 5$	2.3.0.1, 5.6.0.1	2B, 5B	$780$	$288$	$5$	$1$	$1$		$1$	$3120$	$1.301188$	$5735339/3888$	$1.16005$	$5.58345$	$[1, 0, 0, 8193, -117495]$	\(y^2+xy=x^3+8193x-117495\)	2.3.0.a.1, 5.6.0.a.1, 10.18.0.a.1, 12.6.0.f.1, 20.36.0.b.1, $\ldots$	$[ ]$

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