Elliptic curves over $\Q$ of conductor 12482

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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
12482.a1	12482d3	12482.a	12482d	$3$	$9$	\( 2 \cdot 79^{2} \)	\( 2^{18} \cdot 79^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$2844$	$144$	$3$	$1$	$1$		$0$	$748800$	$2.864582$	$15698803397448457/20709376$	$1.00146$	$6.73333$	$[1, 1, 0, -32556306, 71485491508]$	\(y^2+xy=x^3+x^2-32556306x+71485491508\)	3.4.0.a.1, 9.12.0.a.1, 12.8.0-3.a.1.4, 36.24.0-9.a.1.3, 237.8.0.?, $\ldots$	$[ ]$
12482.a2	12482d2	12482.a	12482d	$3$	$9$	\( 2 \cdot 79^{2} \)	\( 2^{6} \cdot 79^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.12.0.1	3Cs	$2844$	$144$	$3$	$1$	$1$		$0$	$249600$	$2.315277$	$59914169497/31554496$	$0.96798$	$5.41058$	$[1, 1, 0, -508771, 41675213]$	\(y^2+xy=x^3+x^2-508771x+41675213\)	3.12.0.a.1, 12.24.0-3.a.1.2, 237.24.0.?, 316.2.0.?, 711.72.0.?, $\ldots$	$[ ]$
12482.a3	12482d1	12482.a	12482d	$3$	$9$	\( 2 \cdot 79^{2} \)	\( 2^{2} \cdot 79^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$2844$	$144$	$3$	$1$	$1$		$0$	$83200$	$1.765970$	$11134383337/316$	$0.90937$	$5.23216$	$[1, 1, 0, -290336, -60333932]$	\(y^2+xy=x^3+x^2-290336x-60333932\)	3.4.0.a.1, 9.12.0.a.1, 12.8.0-3.a.1.3, 36.24.0-9.a.1.4, 237.8.0.?, $\ldots$	$[ ]$
12482.b1	12482b1	12482.b	12482b	$1$	$1$	\( 2 \cdot 79^{2} \)	\( 2^{19} \cdot 79^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.2		$8$	$2$	$0$	$1$	$1$		$0$	$8892$	$0.516834$	$973784889/524288$	$1.07245$	$3.12081$	$[1, -1, 0, -380, 848]$	\(y^2+xy=x^3-x^2-380x+848\)	8.2.0.b.1	$[ ]$
12482.c1	12482a1	12482.c	12482a	$1$	$1$	\( 2 \cdot 79^{2} \)	\( 2^{19} \cdot 79^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.2		$8$	$2$	$0$	$11.38627503$	$1$		$0$	$702468$	$2.701557$	$973784889/524288$	$1.07245$	$5.90034$	$[1, -1, 0, -2372750, -370649772]$	\(y^2+xy=x^3-x^2-2372750x-370649772\)	8.2.0.b.1	$[(-3483819/140, 18744494259/140)]$
12482.d1	12482c1	12482.d	12482c	$1$	$1$	\( 2 \cdot 79^{2} \)	\( 2^{2} \cdot 79^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$316$	$2$	$0$	$1$	$1$		$0$	$49920$	$1.414158$	$4826809/316$	$0.94063$	$4.41117$	$[1, 0, 1, -21974, -1182500]$	\(y^2+xy+y=x^3-21974x-1182500\)	316.2.0.?	$[ ]$
12482.e1	12482h2	12482.e	12482h	$2$	$2$	\( 2 \cdot 79^{2} \)	\( 2 \cdot 79^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$632$	$12$	$0$	$12.26308300$	$1$		$0$	$74880$	$1.694258$	$81182737/12482$	$0.85973$	$4.71042$	$[1, 0, 0, -56299, -4410657]$	\(y^2+xy=x^3-56299x-4410657\)	2.3.0.a.1, 8.6.0.b.1, 316.6.0.?, 632.12.0.?	$[(-10676151/304, 22548629517/304)]$
12482.e2	12482h1	12482.e	12482h	$2$	$2$	\( 2 \cdot 79^{2} \)	\( - 2^{2} \cdot 79^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$632$	$12$	$0$	$6.131541504$	$1$		$1$	$37440$	$1.347685$	$103823/316$	$0.80009$	$4.15777$	$[1, 0, 0, 6111, -378971]$	\(y^2+xy=x^3+6111x-378971\)	2.3.0.a.1, 8.6.0.c.1, 158.6.0.?, 632.12.0.?	$[(50959/30, 9670567/30)]$
12482.f1	12482e2	12482.f	12482e	$2$	$7$	\( 2 \cdot 79^{2} \)	\( 2^{7} \cdot 79^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 7$	8.2.0.2, 7.16.0.2	7B.2.3	$4424$	$96$	$2$	$1$	$1$		$0$	$431340$	$2.773830$	$1916782322625/128$	$1.04638$	$6.70451$	$[1, -1, 1, -29736415, -62406419129]$	\(y^2+xy+y=x^3-x^2-29736415x-62406419129\)	7.16.0-7.a.1.1, 8.2.0.b.1, 56.32.0-56.b.1.2, 553.48.0.?, 4424.96.2.?	$[ ]$
12482.f2	12482e1	12482.f	12482e	$2$	$7$	\( 2 \cdot 79^{2} \)	\( 2 \cdot 79^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 7$	8.2.0.2, 7.16.0.1	7B.2.1	$4424$	$96$	$2$	$1$	$1$		$0$	$61620$	$1.800877$	$266625/2$	$0.85839$	$5.03064$	$[1, -1, 1, -154075, 23165129]$	\(y^2+xy+y=x^3-x^2-154075x+23165129\)	7.16.0-7.a.1.2, 8.2.0.b.1, 56.32.0-56.b.1.1, 553.48.0.?, 4424.96.2.?	$[ ]$
12482.g1	12482f2	12482.g	12482f	$2$	$7$	\( 2 \cdot 79^{2} \)	\( 2^{7} \cdot 79^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 7$	8.2.0.2, 7.8.0.1	7B	$4424$	$96$	$2$	$0.480844128$	$1$		$2$	$5460$	$0.589108$	$1916782322625/128$	$1.04638$	$3.92498$	$[1, -1, 1, -4765, 127781]$	\(y^2+xy+y=x^3-x^2-4765x+127781\)	7.8.0.a.1, 8.2.0.b.1, 56.16.0.b.1, 553.48.0.?, 4424.96.2.?	$[(39, -8)]$
12482.g2	12482f1	12482.g	12482f	$2$	$7$	\( 2 \cdot 79^{2} \)	\( 2 \cdot 79^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 7$	8.2.0.2, 7.8.0.1	7B	$4424$	$96$	$2$	$3.365908900$	$1$		$0$	$780$	$-0.383847$	$266625/2$	$0.85839$	$2.25110$	$[1, -1, 1, -25, -41]$	\(y^2+xy+y=x^3-x^2-25x-41\)	7.8.0.a.1, 8.2.0.b.1, 56.16.0.b.1, 553.48.0.?, 4424.96.2.?	$[(-43/4, 87/4)]$
12482.h1	12482g2	12482.h	12482g	$2$	$5$	\( 2 \cdot 79^{2} \)	\( 2^{4} \cdot 79^{11} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.2	5B.4.2	$1580$	$48$	$1$	$8.381730576$	$1$		$0$	$1497600$	$3.326832$	$1413378216646643521/49232902384$	$1.01962$	$7.21044$	$[1, 0, 0, -145914710, 678384431924]$	\(y^2+xy=x^3-145914710x+678384431924\)	5.12.0.a.2, 20.24.0-5.a.2.4, 316.2.0.?, 395.24.0.?, 1580.48.1.?	$[(1418446/15, 310716986/15)]$
12482.h2	12482g1	12482.h	12482g	$2$	$5$	\( 2 \cdot 79^{2} \)	\( 2^{20} \cdot 79^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.1	5B.4.1	$1580$	$48$	$1$	$1.676346115$	$1$		$0$	$299520$	$2.522114$	$8194759433281/82837504$	$0.96131$	$5.93203$	$[1, 0, 0, -2621350, -1619450396]$	\(y^2+xy=x^3-2621350x-1619450396\)	5.12.0.a.1, 20.24.0-5.a.1.4, 316.2.0.?, 395.24.0.?, 1580.48.1.?	$[(-8276/3, 112270/3)]$
12482.i1	12482i1	12482.i	12482i	$1$	$1$	\( 2 \cdot 79^{2} \)	\( 2^{8} \cdot 79^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$316$	$2$	$0$	$0.989915754$	$1$		$0$	$199680$	$1.718147$	$72511713/20224$	$0.89606$	$4.69845$	$[1, -1, 1, -54219, -3483941]$	\(y^2+xy+y=x^3-x^2-54219x-3483941\)	316.2.0.?	$[(-689/3, 13502/3)]$

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