Elliptic curves over $\Q$ of conductor 3800

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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
3800.a1	3800f1	3800.a	3800f	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 19 \)	\( - 2^{11} \cdot 5^{8} \cdot 19^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$152$	$2$	$0$	$1$	$1$		$0$	$11520$	$1.126575$	$-16241202/171475$	$0.93308$	$4.46956$	$[0, 0, 0, -1675, 115750]$	\(y^2=x^3-1675x+115750\)	152.2.0.?	$[]$
3800.b1	3800e2	3800.b	3800e	$2$	$2$	\( 2^{3} \cdot 5^{2} \cdot 19 \)	\( 2^{8} \cdot 5^{7} \cdot 19^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$0.334236190$	$1$		$31$	$3072$	$0.584636$	$3631696/1805$	$0.78833$	$3.67681$	$[0, 1, 0, -508, 1488]$	\(y^2=x^3+x^2-508x+1488\)	2.3.0.a.1, 10.6.0.a.1, 76.6.0.?, 380.12.0.?	$[(-2, 50), (22, 38)]$
3800.b2	3800e1	3800.b	3800e	$2$	$2$	\( 2^{3} \cdot 5^{2} \cdot 19 \)	\( - 2^{4} \cdot 5^{8} \cdot 19 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$1.336944762$	$1$		$19$	$1536$	$0.238062$	$702464/475$	$0.78481$	$3.14113$	$[0, 1, 0, 117, 238]$	\(y^2=x^3+x^2+117x+238\)	2.3.0.a.1, 20.6.0.c.1, 38.6.0.b.1, 380.12.0.?	$[(3, 25), (-1, 11)]$
3800.c1	3800b2	3800.c	3800b	$2$	$2$	\( 2^{3} \cdot 5^{2} \cdot 19 \)	\( 2^{8} \cdot 5^{9} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.2	2B	$760$	$48$	$1$	$1$	$1$		$1$	$17920$	$1.581814$	$3084800518928/361$	$0.95550$	$5.91885$	$[0, 1, 0, -240708, 45375088]$	\(y^2=x^3+x^2-240708x+45375088\)	2.3.0.a.1, 4.6.0.d.1, 10.6.0.a.1, 20.24.0-20.i.1.1, 152.12.0.?, $\ldots$	$[]$
3800.c2	3800b1	3800.c	3800b	$2$	$2$	\( 2^{3} \cdot 5^{2} \cdot 19 \)	\( 2^{4} \cdot 5^{9} \cdot 19^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.2	2B	$760$	$48$	$1$	$1$	$1$		$1$	$8960$	$1.235241$	$12144109568/130321$	$0.94080$	$4.91069$	$[0, 1, 0, -15083, 701338]$	\(y^2=x^3+x^2-15083x+701338\)	2.3.0.a.1, 4.6.0.d.1, 10.6.0.a.1, 20.24.0-20.i.1.2, 152.12.0.?, $\ldots$	$[]$
3800.d1	3800g1	3800.d	3800g	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 19 \)	\( - 2^{11} \cdot 5^{6} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$152$	$2$	$0$	$2.211913794$	$1$		$2$	$1152$	$0.387541$	$-31250/19$	$0.89957$	$3.43928$	$[0, -1, 0, -208, -1588]$	\(y^2=x^3-x^2-208x-1588\)	152.2.0.?	$[(37, 200)]$
3800.e1	3800a4	3800.e	3800a	$4$	$4$	\( 2^{3} \cdot 5^{2} \cdot 19 \)	\( 2^{10} \cdot 5^{7} \cdot 19 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$760$	$48$	$0$	$5.937430641$	$1$		$5$	$6144$	$1.190039$	$899466517764/95$	$0.96248$	$5.35175$	$[0, 0, 0, -50675, 4390750]$	\(y^2=x^3-50675x+4390750\)	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.z.1.4, 152.24.0.?, 380.24.0.?, $\ldots$	$[(454, 8658)]$
3800.e2	3800a3	3800.e	3800a	$4$	$4$	\( 2^{3} \cdot 5^{2} \cdot 19 \)	\( 2^{10} \cdot 5^{7} \cdot 19^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$760$	$48$	$0$	$1.484357660$	$1$		$5$	$6144$	$1.190039$	$1263284964/651605$	$0.94894$	$4.55492$	$[0, 0, 0, -5675, -54250]$	\(y^2=x^3-5675x-54250\)	2.3.0.a.1, 4.12.0-4.c.1.2, 10.6.0.a.1, 20.24.0-20.g.1.1, 152.24.0.?, $\ldots$	$[(-65, 200)]$
3800.e3	3800a2	3800.e	3800a	$4$	$4$	\( 2^{3} \cdot 5^{2} \cdot 19 \)	\( 2^{8} \cdot 5^{8} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$380$	$48$	$0$	$2.968715320$	$1$		$7$	$3072$	$0.843465$	$884901456/9025$	$0.92560$	$4.34355$	$[0, 0, 0, -3175, 68250]$	\(y^2=x^3-3175x+68250\)	2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.b.1.2, 76.24.0.?, 380.48.0.?	$[(-46, 342)]$
3800.e4	3800a1	3800.e	3800a	$4$	$4$	\( 2^{3} \cdot 5^{2} \cdot 19 \)	\( - 2^{4} \cdot 5^{10} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$760$	$48$	$0$	$1.484357660$	$1$		$3$	$1536$	$0.496891$	$-55296/11875$	$1.13186$	$3.55085$	$[0, 0, 0, -50, 2625]$	\(y^2=x^3-50x+2625\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 20.12.0-4.c.1.2, 38.6.0.b.1, $\ldots$	$[(5, 50)]$
3800.f1	3800d2	3800.f	3800d	$2$	$2$	\( 2^{3} \cdot 5^{2} \cdot 19 \)	\( 2^{8} \cdot 5^{13} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$1$	$4$	$2$	$1$	$107520$	$2.427265$	$31248575021659890256/28203125$	$1.01626$	$7.29007$	$[0, -1, 0, -10416508, -12936440988]$	\(y^2=x^3-x^2-10416508x-12936440988\)	2.3.0.a.1, 10.6.0.a.1, 76.6.0.?, 380.12.0.?	$[]$
3800.f2	3800d1	3800.f	3800d	$2$	$2$	\( 2^{3} \cdot 5^{2} \cdot 19 \)	\( - 2^{4} \cdot 5^{20} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$1$	$16$	$2$	$1$	$53760$	$2.080692$	$-121981271658244096/115966796875$	$1.08046$	$6.28109$	$[0, -1, 0, -650883, -202065988]$	\(y^2=x^3-x^2-650883x-202065988\)	2.3.0.a.1, 20.6.0.c.1, 38.6.0.b.1, 380.12.0.?	$[]$
3800.g1	3800i2	3800.g	3800i	$2$	$2$	\( 2^{3} \cdot 5^{2} \cdot 19 \)	\( 2^{8} \cdot 5^{3} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.2	2B	$760$	$48$	$1$	$0.665191731$	$1$		$5$	$3584$	$0.777095$	$3084800518928/361$	$0.95550$	$4.74732$	$[0, -1, 0, -9628, 366852]$	\(y^2=x^3-x^2-9628x+366852\)	2.3.0.a.1, 4.6.0.d.1, 10.6.0.a.1, 20.24.0-20.i.1.1, 152.12.0.?, $\ldots$	$[(48, 114)]$
3800.g2	3800i1	3800.g	3800i	$2$	$2$	\( 2^{3} \cdot 5^{2} \cdot 19 \)	\( 2^{4} \cdot 5^{3} \cdot 19^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.2	2B	$760$	$48$	$1$	$1.330383463$	$1$		$3$	$1792$	$0.430521$	$12144109568/130321$	$0.94080$	$3.73916$	$[0, -1, 0, -603, 5852]$	\(y^2=x^3-x^2-603x+5852\)	2.3.0.a.1, 4.6.0.d.1, 10.6.0.a.1, 20.24.0-20.i.1.2, 152.12.0.?, $\ldots$	$[(17, 15)]$
3800.h1	3800h1	3800.h	3800h	$2$	$2$	\( 2^{3} \cdot 5^{2} \cdot 19 \)	\( 2^{4} \cdot 5^{9} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$0.951140329$	$1$		$3$	$2304$	$0.653500$	$304900096/45125$	$0.86112$	$3.87792$	$[0, -1, 0, -883, 9012]$	\(y^2=x^3-x^2-883x+9012\)	2.3.0.a.1, 10.6.0.a.1, 76.6.0.?, 380.12.0.?	$[(57, 375)]$
3800.h2	3800h2	3800.h	3800h	$2$	$2$	\( 2^{3} \cdot 5^{2} \cdot 19 \)	\( - 2^{8} \cdot 5^{12} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$1.902280658$	$1$		$3$	$4608$	$1.000072$	$91765424/296875$	$0.86089$	$4.25349$	$[0, -1, 0, 1492, 47012]$	\(y^2=x^3-x^2+1492x+47012\)	2.3.0.a.1, 20.6.0.c.1, 38.6.0.b.1, 380.12.0.?	$[(22, 300)]$
3800.i1	3800c1	3800.i	3800c	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 19 \)	\( - 2^{8} \cdot 5^{6} \cdot 19 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$1$	$1$		$0$	$1120$	$0.193240$	$-1024/19$	$0.79665$	$3.10960$	$[0, -1, 0, -33, 437]$	\(y^2=x^3-x^2-33x+437\)	38.2.0.a.1	$[]$

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