Elliptic curves over $\Q$ of conductor 1848

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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
1848.a1	1848c1	1848.a	1848c	$1$	$1$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( - 2^{4} \cdot 3 \cdot 7 \cdot 11 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$462$	$2$	$0$	$0.252492919$	$1$		$6$	$160$	$-0.518612$	$-12967168/231$	$0.77180$	$2.55001$	$[0, -1, 0, -12, 21]$	\(y^2=x^3-x^2-12x+21\)	462.2.0.?	$[(2, 1)]$
1848.b1	1848a1	1848.b	1848a	$1$	$1$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( - 2^{4} \cdot 3^{3} \cdot 7 \cdot 11^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$462$	$2$	$0$	$1$	$1$		$0$	$288$	$0.140484$	$-91238612224/251559$	$0.90714$	$3.72436$	$[0, -1, 0, -236, -1323]$	\(y^2=x^3-x^2-236x-1323\)	462.2.0.?	$[ ]$
1848.c1	1848h2	1848.c	1848h	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( 2^{11} \cdot 3^{4} \cdot 7^{2} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$2.508793443$	$1$		$3$	$768$	$0.348568$	$4866277250/43659$	$0.89537$	$3.97910$	$[0, -1, 0, -448, -3476]$	\(y^2=x^3-x^2-448x-3476\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[(25, 18)]$
1848.c2	1848h1	1848.c	1848h	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( - 2^{10} \cdot 3^{2} \cdot 7 \cdot 11^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$1.254396721$	$1$		$7$	$384$	$0.001994$	$-62500/7623$	$0.98433$	$3.10161$	$[0, -1, 0, -8, -132]$	\(y^2=x^3-x^2-8x-132\)	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[(14, 48)]$
1848.d1	1848b3	1848.d	1848b	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( 2^{11} \cdot 3^{12} \cdot 7^{8} \cdot 11^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$264$	$48$	$0$	$1.374838482$	$1$		$3$	$46080$	$2.337139$	$14171198121996897746/4077720290568771$	$1.03437$	$6.87627$	$[0, -1, 0, -640232, -139597332]$	\(y^2=x^3-x^2-640232x-139597332\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 24.24.0-24.bb.1.16, 44.12.0-4.c.1.1, $\ldots$	$[(-479, 7546)]$
1848.d2	1848b2	1848.d	1848b	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( 2^{10} \cdot 3^{6} \cdot 7^{4} \cdot 11^{6} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$264$	$48$	$0$	$2.749676965$	$1$		$7$	$23040$	$1.990564$	$21843440425782779332/3100814593569$	$1.02507$	$6.84165$	$[0, -1, 0, -586992, -172882980]$	\(y^2=x^3-x^2-586992x-172882980\)	2.6.0.a.1, 8.12.0-2.a.1.1, 12.12.0-2.a.1.1, 24.24.0-24.a.1.3, 44.12.0-2.a.1.1, $\ldots$	$[(962, 12320)]$
1848.d3	1848b1	1848.d	1848b	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( 2^{8} \cdot 3^{3} \cdot 7^{2} \cdot 11^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$264$	$48$	$0$	$5.499353930$	$1$		$3$	$11520$	$1.643991$	$87364831012240243408/1760913$	$1.02507$	$6.84163$	$[0, -1, 0, -586972, -172895372]$	\(y^2=x^3-x^2-586972x-172895372\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 12.12.0-4.c.1.2, 24.24.0-24.bb.1.2, $\ldots$	$[(5958, 455840)]$
1848.d4	1848b4	1848.d	1848b	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( - 2^{11} \cdot 3^{3} \cdot 7^{2} \cdot 11^{12} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$264$	$48$	$0$	$5.499353930$	$1$		$1$	$46080$	$2.337139$	$-8226100326647904626/4152140742401883$	$1.03134$	$6.88734$	$[0, -1, 0, -534072, -205375860]$	\(y^2=x^3-x^2-534072x-205375860\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 12.12.0-4.c.1.1, 24.24.0-24.v.1.4, $\ldots$	$[(23861/5, 1548316/5)]$
1848.e1	1848e2	1848.e	1848e	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( 2^{11} \cdot 3^{8} \cdot 7^{2} \cdot 11^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$1$	$7680$	$1.369789$	$9791533777258802/427901859$	$0.99685$	$5.90877$	$[0, 1, 0, -56600, -5201616]$	\(y^2=x^3+x^2-56600x-5201616\)	2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.?	$[ ]$
1848.e2	1848e1	1848.e	1848e	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( - 2^{10} \cdot 3^{4} \cdot 7 \cdot 11^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$1$	$3840$	$1.023216$	$-4097989445764/1004475087$	$0.95402$	$4.82941$	$[0, 1, 0, -3360, -90576]$	\(y^2=x^3+x^2-3360x-90576\)	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[ ]$
1848.f1	1848l1	1848.f	1848l	$1$	$1$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( - 2^{4} \cdot 3^{7} \cdot 7^{3} \cdot 11 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$462$	$2$	$0$	$0.048426699$	$1$		$12$	$672$	$0.237277$	$-12967168/8251551$	$0.99302$	$3.47708$	$[0, 1, 0, -12, 549]$	\(y^2=x^3+x^2-12x+549\)	462.2.0.?	$[(-6, 21)]$
1848.g1	1848j5	1848.g	1848j	$6$	$8$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( 2^{11} \cdot 3^{2} \cdot 7^{8} \cdot 11^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.173	2B	$1232$	$192$	$1$	$4.720509114$	$1$		$1$	$6144$	$1.430304$	$5701568801608514/6277868289$	$0.99431$	$5.83687$	$[0, 1, 0, -47264, -3967008]$	\(y^2=x^3+x^2-47264x-3967008\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.r.1.6, 88.96.0.?, 112.96.0.?, $\ldots$	$[(-491/2, 105/2)]$
1848.g2	1848j3	1848.g	1848j	$6$	$8$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( 2^{10} \cdot 3^{4} \cdot 7^{4} \cdot 11^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.30	2Cs	$616$	$192$	$1$	$2.360254557$	$1$		$7$	$3072$	$1.083731$	$5489767279588/2847396321$	$0.98782$	$4.82133$	$[0, 1, 0, -3704, -29184]$	\(y^2=x^3+x^2-3704x-29184\)	2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.c.1.2, 56.96.0-56.e.2.1, 88.96.0.?, $\ldots$	$[(-32, 240)]$
1848.g3	1848j2	1848.g	1848j	$6$	$8$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( 2^{8} \cdot 3^{8} \cdot 7^{2} \cdot 11^{2} \)	$1$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.29	2Cs	$616$	$192$	$1$	$1.180127278$	$1$		$21$	$1536$	$0.737157$	$3911877700432/38900169$	$1.03181$	$4.59198$	$[0, 1, 0, -2084, 35616]$	\(y^2=x^3+x^2-2084x+35616\)	2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.h.1.9, 56.96.0-56.x.2.5, 88.96.0.?, $\ldots$	$[(31, 42)]$
1848.g4	1848j1	1848.g	1848j	$6$	$8$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( 2^{4} \cdot 3^{4} \cdot 7 \cdot 11 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.29	2B	$1232$	$192$	$1$	$2.360254557$	$1$		$7$	$768$	$0.390584$	$62140690757632/6237$	$0.98642$	$4.59102$	$[0, 1, 0, -2079, 35802]$	\(y^2=x^3+x^2-2079x+35802\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.h.1.2, 56.48.0-56.bu.2.6, $\ldots$	$[(42, 156)]$
1848.g5	1848j4	1848.g	1848j	$6$	$8$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( - 2^{10} \cdot 3^{16} \cdot 7 \cdot 11 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.29	2B	$1232$	$192$	$1$	$2.360254557$	$1$		$7$	$3072$	$1.083731$	$-17418812548/3314597517$	$1.01681$	$4.82737$	$[0, 1, 0, -544, 88592]$	\(y^2=x^3+x^2-544x+88592\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.h.1.2, 56.48.0-56.bv.2.7, $\ldots$	$[(-13, 306)]$
1848.g6	1848j6	1848.g	1848j	$6$	$8$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( - 2^{11} \cdot 3^{2} \cdot 7^{2} \cdot 11^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.174	2B	$1232$	$192$	$1$	$4.720509114$	$1$		$3$	$6144$	$1.430304$	$146142660369886/94532266521$	$1.01155$	$5.34977$	$[0, 1, 0, 13936, -212640]$	\(y^2=x^3+x^2+13936x-212640\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.k.1.6, 56.96.0-56.bc.2.8, 176.96.0.?, $\ldots$	$[(115, 1710)]$
1848.h1	1848f1	1848.h	1848f	$1$	$1$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( - 2^{4} \cdot 3^{7} \cdot 7 \cdot 11^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$462$	$2$	$0$	$0.092711850$	$1$		$12$	$672$	$0.313465$	$575511296/20376279$	$0.95539$	$3.59495$	$[0, 1, 0, 44, -847]$	\(y^2=x^3+x^2+44x-847\)	462.2.0.?	$[(44, 297)]$
1848.i1	1848g1	1848.i	1848g	$1$	$1$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( - 2^{4} \cdot 3^{3} \cdot 7^{5} \cdot 11 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$462$	$2$	$0$	$0.064780648$	$1$		$10$	$480$	$0.201626$	$-1235663104/4991679$	$1.04005$	$3.42794$	$[0, 1, 0, -56, 441]$	\(y^2=x^3+x^2-56x+441\)	462.2.0.?	$[(28, 147)]$
1848.j1	1848i1	1848.j	1848i	$1$	$1$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( - 2^{4} \cdot 3 \cdot 7 \cdot 11 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$462$	$2$	$0$	$0.858509890$	$1$		$4$	$96$	$-0.636387$	$-256/231$	$0.83188$	$2.08331$	$[0, 1, 0, 0, -3]$	\(y^2=x^3+x^2-3\)	462.2.0.?	$[(2, 3)]$
1848.k1	1848d1	1848.k	1848d	$1$	$1$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( - 2^{4} \cdot 3 \cdot 7^{9} \cdot 11 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$462$	$2$	$0$	$1$	$1$		$0$	$1440$	$0.748445$	$-31636584484096/1331669031$	$0.95912$	$4.51061$	$[0, 1, 0, -1660, 26417]$	\(y^2=x^3+x^2-1660x+26417\)	462.2.0.?	$[ ]$
1848.l1	1848k3	1848.l	1848k	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( 2^{11} \cdot 3^{4} \cdot 7^{4} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$616$	$48$	$0$	$1$	$4$	$2$	$1$	$4096$	$1.161922$	$2970658109581346/2139291$	$1.06890$	$5.75020$	$[0, 1, 0, -38032, -2867488]$	\(y^2=x^3+x^2-38032x-2867488\)	2.3.0.a.1, 4.12.0-4.c.1.2, 56.24.0-56.z.1.12, 88.24.0.?, 616.48.0.?	$[ ]$
1848.l2	1848k4	1848.l	1848k	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( 2^{11} \cdot 3^{16} \cdot 7 \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$616$	$48$	$0$	$1$	$1$		$1$	$4096$	$1.161922$	$8849350367426/3314597517$	$0.97451$	$4.97696$	$[0, 1, 0, -5472, 90720]$	\(y^2=x^3+x^2-5472x+90720\)	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, $\ldots$	$[ ]$
1848.l3	1848k2	1848.l	1848k	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( 2^{10} \cdot 3^{8} \cdot 7^{2} \cdot 11^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$616$	$48$	$0$	$1$	$1$		$3$	$2048$	$0.815349$	$1478729816932/38900169$	$1.03465$	$4.64695$	$[0, 1, 0, -2392, -44800]$	\(y^2=x^3+x^2-2392x-44800\)	2.6.0.a.1, 4.12.0-2.a.1.1, 28.24.0-28.b.1.1, 88.24.0.?, 616.48.0.?	$[ ]$
1848.l4	1848k1	1848.l	1848k	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \)	\( - 2^{8} \cdot 3^{4} \cdot 7 \cdot 11^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$616$	$48$	$0$	$1$	$1$		$3$	$1024$	$0.468775$	$9148592/8301447$	$0.98816$	$3.84628$	$[0, 1, 0, 28, -2208]$	\(y^2=x^3+x^2+28x-2208\)	2.3.0.a.1, 4.12.0-4.c.1.1, 14.6.0.b.1, 28.24.0-28.g.1.2, 88.24.0.?, $\ldots$	$[ ]$

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