Elliptic curves over $\Q$ of conductor 494

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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
494.a1	494a1	494.a	494a	$1$	$1$	\( 2 \cdot 13 \cdot 19 \)	\( - 2^{5} \cdot 13 \cdot 19^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$104$	$2$	$0$	$0.326323647$	$1$		$6$	$40$	$-0.318178$	$214921799/150176$	$0.86097$	$3.09322$	$[1, 1, 0, 13, 13]$	\(y^2+xy=x^3+x^2+13x+13\)	104.2.0.?	$[(3, 8)]$
494.b1	494b4	494.b	494b	$4$	$4$	\( 2 \cdot 13 \cdot 19 \)	\( 2 \cdot 13^{4} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.8	2B	$1976$	$48$	$0$	$1$	$1$		$0$	$136$	$0.072229$	$969417177273/1085318$	$0.93818$	$4.44979$	$[1, -1, 0, -206, 1190]$	\(y^2+xy=x^3-x^2-206x+1190\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 76.12.0.?, 104.24.0.?, $\ldots$	$[]$
494.b2	494b3	494.b	494b	$4$	$4$	\( 2 \cdot 13 \cdot 19 \)	\( 2 \cdot 13 \cdot 19^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.7	2B	$1976$	$48$	$0$	$1$	$1$		$0$	$136$	$0.072229$	$345505073913/3388346$	$0.97212$	$4.28345$	$[1, -1, 0, -146, -638]$	\(y^2+xy=x^3-x^2-146x-638\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 52.12.0-4.c.1.1, 104.24.0.?, $\ldots$	$[]$
494.b3	494b2	494.b	494b	$4$	$4$	\( 2 \cdot 13 \cdot 19 \)	\( 2^{2} \cdot 13^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.1	2Cs	$1976$	$48$	$0$	$1$	$1$		$2$	$68$	$-0.274344$	$469097433/244036$	$0.96358$	$3.21906$	$[1, -1, 0, -16, 12]$	\(y^2+xy=x^3-x^2-16x+12\)	2.6.0.a.1, 8.12.0-2.a.1.1, 52.12.0-2.a.1.1, 76.12.0.?, 104.24.0.?, $\ldots$	$[]$
494.b4	494b1	494.b	494b	$4$	$4$	\( 2 \cdot 13 \cdot 19 \)	\( - 2^{4} \cdot 13 \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.12	2B	$1976$	$48$	$0$	$1$	$1$		$1$	$34$	$-0.620917$	$6128487/3952$	$0.83799$	$2.51969$	$[1, -1, 0, 4, 0]$	\(y^2+xy=x^3-x^2+4x\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 52.12.0-4.c.1.2, 76.12.0.?, $\ldots$	$[]$
494.c1	494c1	494.c	494c	$1$	$1$	\( 2 \cdot 13 \cdot 19 \)	\( - 2 \cdot 13 \cdot 19^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$104$	$2$	$0$	$1$	$1$		$0$	$152$	$-0.270239$	$-25334470953/9386$	$0.90338$	$3.86230$	$[1, -1, 0, -61, -169]$	\(y^2+xy=x^3-x^2-61x-169\)	104.2.0.?	$[]$
494.d1	494d1	494.d	494d	$1$	$1$	\( 2 \cdot 13 \cdot 19 \)	\( - 2^{13} \cdot 13^{3} \cdot 19^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$104$	$2$	$0$	$0.020984121$	$1$		$18$	$312$	$0.638902$	$-110931033861649/6497214464$	$0.94569$	$5.22953$	$[1, 1, 1, -1001, 12375]$	\(y^2+xy+y=x^3+x^2-1001x+12375\)	104.2.0.?	$[(45, 224)]$

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