Elliptic curves over $\Q$ of conductor 3381

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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
3381.a1	3381f1	3381.a	3381f	$1$	$1$	\( 3 \cdot 7^{2} \cdot 23 \)	\( - 3 \cdot 7^{2} \cdot 23^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$276$	$2$	$0$	$0.211519757$	$1$		$6$	$576$	$-0.088861$	$-105484561/36501$	$0.86679$	$2.81009$	$[1, 1, 1, -36, 90]$	\(y^2+xy+y=x^3+x^2-36x+90\)	276.2.0.?	$[(-6, 14)]$
3381.b1	3381g1	3381.b	3381g	$1$	$1$	\( 3 \cdot 7^{2} \cdot 23 \)	\( - 3^{7} \cdot 7^{10} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$276$	$2$	$0$	$12.87261860$	$1$		$0$	$9408$	$1.388111$	$-14936239633/50301$	$0.93353$	$5.27841$	$[1, 1, 1, -33664, -2398306]$	\(y^2+xy+y=x^3+x^2-33664x-2398306\)	276.2.0.?	$[(371518/13, 223281586/13)]$
3381.c1	3381l1	3381.c	3381l	$1$	$1$	\( 3 \cdot 7^{2} \cdot 23 \)	\( - 3^{7} \cdot 7^{4} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$276$	$2$	$0$	$0.053532472$	$1$		$12$	$1344$	$0.415156$	$-14936239633/50301$	$0.93353$	$3.84159$	$[1, 0, 0, -687, 6894]$	\(y^2+xy=x^3-687x+6894\)	276.2.0.?	$[(-3, 96)]$
3381.d1	3381k1	3381.d	3381k	$1$	$1$	\( 3 \cdot 7^{2} \cdot 23 \)	\( - 3 \cdot 7^{8} \cdot 23^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$276$	$2$	$0$	$2.615507044$	$1$		$2$	$4032$	$0.884094$	$-105484561/36501$	$0.86679$	$4.24691$	$[1, 0, 0, -1765, -36226]$	\(y^2+xy=x^3-1765x-36226\)	276.2.0.?	$[(85, 613)]$
3381.e1	3381d1	3381.e	3381d	$1$	$1$	\( 3 \cdot 7^{2} \cdot 23 \)	\( - 3^{11} \cdot 7^{10} \cdot 23^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$6.645913051$	$1$		$0$	$14784$	$1.830883$	$1605632000/93710763$	$1.12164$	$5.56977$	$[0, -1, 1, 16007, -7794291]$	\(y^2+y=x^3-x^2+16007x-7794291\)	6.2.0.a.1	$[(2401/3, 105913/3)]$
3381.f1	3381e1	3381.f	3381e	$1$	$1$	\( 3 \cdot 7^{2} \cdot 23 \)	\( - 3 \cdot 7^{9} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$966$	$2$	$0$	$0.856147051$	$1$		$4$	$2016$	$0.611167$	$-4096000/69$	$0.84974$	$4.03245$	$[0, -1, 1, -1143, 15476]$	\(y^2+y=x^3-x^2-1143x+15476\)	966.2.0.?	$[(-16, 171)]$
3381.g1	3381a1	3381.g	3381a	$2$	$3$	\( 3 \cdot 7^{2} \cdot 23 \)	\( - 3^{3} \cdot 7^{2} \cdot 23^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$42$	$16$	$0$	$1$	$1$		$0$	$768$	$0.113669$	$-62992384000/14283$	$0.96759$	$3.53910$	$[0, -1, 1, -303, -1933]$	\(y^2+y=x^3-x^2-303x-1933\)	3.4.0.a.1, 6.8.0.b.1, 21.8.0-3.a.1.1, 42.16.0-6.b.1.1	$[]$
3381.g2	3381a2	3381.g	3381a	$2$	$3$	\( 3 \cdot 7^{2} \cdot 23 \)	\( - 3 \cdot 7^{2} \cdot 23^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$42$	$16$	$0$	$1$	$1$		$0$	$2304$	$0.662975$	$3584000000/444107667$	$1.15552$	$3.84614$	$[0, -1, 1, 117, -7120]$	\(y^2+y=x^3-x^2+117x-7120\)	3.4.0.a.1, 6.8.0.b.1, 21.8.0-3.a.1.2, 42.16.0-6.b.1.2	$[]$
3381.h1	3381j1	3381.h	3381j	$1$	$1$	\( 3 \cdot 7^{2} \cdot 23 \)	\( - 3^{11} \cdot 7^{4} \cdot 23^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$0.202698446$	$1$		$8$	$2112$	$0.857928$	$1605632000/93710763$	$1.12164$	$4.13296$	$[0, 1, 1, 327, 22817]$	\(y^2+y=x^3+x^2+327x+22817\)	6.2.0.a.1	$[(39, 310)]$
3381.i1	3381m1	3381.i	3381m	$1$	$1$	\( 3 \cdot 7^{2} \cdot 23 \)	\( - 3 \cdot 7^{3} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$966$	$2$	$0$	$1$	$1$		$0$	$288$	$-0.361788$	$-4096000/69$	$0.84974$	$2.59564$	$[0, 1, 1, -23, -52]$	\(y^2+y=x^3+x^2-23x-52\)	966.2.0.?	$[]$
3381.j1	3381i1	3381.j	3381i	$2$	$3$	\( 3 \cdot 7^{2} \cdot 23 \)	\( - 3^{3} \cdot 7^{8} \cdot 23^{2} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$6$	$16$	$0$	$1$	$1$		$2$	$5376$	$1.086624$	$-62992384000/14283$	$0.96759$	$4.97592$	$[0, 1, 1, -14863, 692647]$	\(y^2+y=x^3+x^2-14863x+692647\)	3.8.0-3.a.1.2, 6.16.0-6.b.1.2	$[]$
3381.j2	3381i2	3381.j	3381i	$2$	$3$	\( 3 \cdot 7^{2} \cdot 23 \)	\( - 3 \cdot 7^{8} \cdot 23^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$6$	$16$	$0$	$1$	$1$		$0$	$16128$	$1.635931$	$3584000000/444107667$	$1.15552$	$5.28295$	$[0, 1, 1, 5717, 2430628]$	\(y^2+y=x^3+x^2+5717x+2430628\)	3.8.0-3.a.1.1, 6.16.0-6.b.1.1	$[]$
3381.k1	3381b2	3381.k	3381b	$2$	$2$	\( 3 \cdot 7^{2} \cdot 23 \)	\( 3 \cdot 7^{6} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$276$	$12$	$0$	$1$	$1$		$0$	$1440$	$0.445561$	$413493625/1587$	$0.92463$	$3.87840$	$[1, 1, 0, -760, 7729]$	\(y^2+xy=x^3+x^2-760x+7729\)	2.3.0.a.1, 12.6.0.a.1, 92.6.0.?, 276.12.0.?	$[]$
3381.k2	3381b1	3381.k	3381b	$2$	$2$	\( 3 \cdot 7^{2} \cdot 23 \)	\( - 3^{2} \cdot 7^{6} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$276$	$12$	$0$	$1$	$1$		$1$	$720$	$0.098988$	$-15625/207$	$0.99061$	$3.01574$	$[1, 1, 0, -25, 232]$	\(y^2+xy=x^3+x^2-25x+232\)	2.3.0.a.1, 12.6.0.b.1, 46.6.0.a.1, 276.12.0.?	$[]$
3381.l1	3381c1	3381.l	3381c	$1$	$1$	\( 3 \cdot 7^{2} \cdot 23 \)	\( - 3^{5} \cdot 7^{7} \cdot 23^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$966$	$2$	$0$	$1$	$1$		$0$	$14400$	$1.098476$	$-98867482624/20696067$	$1.05025$	$4.59040$	$[0, -1, 1, -4720, 147237]$	\(y^2+y=x^3-x^2-4720x+147237\)	966.2.0.?	$[]$
3381.m1	3381h1	3381.m	3381h	$1$	$1$	\( 3 \cdot 7^{2} \cdot 23 \)	\( - 3 \cdot 7^{7} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$966$	$2$	$0$	$1.287009699$	$1$		$0$	$960$	$0.175126$	$512000/483$	$0.74348$	$3.05461$	$[0, -1, 1, 82, -253]$	\(y^2+y=x^3-x^2+82x-253\)	966.2.0.?	$[(13/2, 45/2)]$

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