Elliptic curves over Q\Q of conductor 350

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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
350.a1	350c2	350.a	350c	$2$	$3$	$2 \cdot 5^{2} \cdot 7$	$- 2 \cdot 5^{2} \cdot 7^{6}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.2.0.1, 3.4.0.1	3B	$120$	$16$	$0$	$0.653095700$	$1$		$4$	$72$	$0.002135$	$-417267265/235298$	$0.94642$	$4.05406$	$[1, 1, 0, -45, -185]$	$y^2+xy=x^3+x^2-45x-185$	3.4.0.a.1, 8.2.0.a.1, 15.8.0-3.a.1.1, 24.8.0.a.1, 120.16.0.?	$[(31, 156)]$
350.a2	350c1	350.a	350c	$2$	$3$	$2 \cdot 5^{2} \cdot 7$	$- 2^{3} \cdot 5^{2} \cdot 7^{2}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.2.0.1, 3.4.0.1	3B	$120$	$16$	$0$	$0.217698566$	$1$		$6$	$24$	$-0.547172$	$397535/392$	$1.09655$	$2.75044$	$[1, 1, 0, 5, 5]$	$y^2+xy=x^3+x^2+5x+5$	3.4.0.a.1, 8.2.0.a.1, 15.8.0-3.a.1.2, 24.8.0.a.1, 120.16.0.?	$[(1, 3)]$
350.b1	350a3	350.b	350a	$4$	$4$	$2 \cdot 5^{2} \cdot 7$	$2 \cdot 5^{8} \cdot 7^{4}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$280$	$48$	$0$	$1$	$1$		$0$	$384$	$0.843707$	$2121328796049/120050$	$1.01959$	$6.49371$	$[1, -1, 0, -6692, -209034]$	$y^2+xy=x^3-x^2-6692x-209034$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 20.12.0-4.c.1.1, 40.24.0-8.k.1.1, $\ldots$	$[]$
350.b2	350a4	350.b	350a	$4$	$4$	$2 \cdot 5^{2} \cdot 7$	$2 \cdot 5^{14} \cdot 7$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$280$	$48$	$0$	$1$	$1$		$0$	$384$	$0.843707$	$74565301329/5468750$	$0.99962$	$5.92215$	$[1, -1, 0, -2192, 37466]$	$y^2+xy=x^3-x^2-2192x+37466$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 40.24.0-8.p.1.4, 56.24.0.bp.1, $\ldots$	$[]$
350.b3	350a2	350.b	350a	$4$	$4$	$2 \cdot 5^{2} \cdot 7$	$2^{2} \cdot 5^{10} \cdot 7^{2}$	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.3	2Cs	$280$	$48$	$0$	$1$	$1$		$2$	$192$	$0.497133$	$611960049/122500$	$1.02632$	$5.10228$	$[1, -1, 0, -442, -2784]$	$y^2+xy=x^3-x^2-442x-2784$	2.6.0.a.1, 8.12.0.a.1, 20.12.0-2.a.1.1, 28.12.0.b.1, 40.24.0-8.a.1.2, $\ldots$	$[]$
350.b4	350a1	350.b	350a	$4$	$4$	$2 \cdot 5^{2} \cdot 7$	$- 2^{4} \cdot 5^{8} \cdot 7$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$280$	$48$	$0$	$1$	$1$		$1$	$96$	$0.150559$	$1367631/2800$	$1.00023$	$4.21932$	$[1, -1, 0, 58, -284]$	$y^2+xy=x^3-x^2+58x-284$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 14.6.0.b.1, 20.12.0-4.c.1.2, $\ldots$	$[]$
350.c1	350e1	350.c	350e	$1$	$1$	$2 \cdot 5^{2} \cdot 7$	$- 2^{11} \cdot 5^{10} \cdot 7^{2}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.1		$8$	$2$	$0$	$1$	$1$		$0$	$1320$	$1.041822$	$-1026590625/100352$	$1.12597$	$6.31622$	$[1, -1, 0, -4492, 126416]$	$y^2+xy=x^3-x^2-4492x+126416$	8.2.0.a.1	$[]$
350.d1	350f1	350.d	350f	$1$	$1$	$2 \cdot 5^{2} \cdot 7$	$- 2^{11} \cdot 5^{4} \cdot 7^{2}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.1		$8$	$2$	$0$	$0.012846808$	$1$		$24$	$264$	$0.237103$	$-1026590625/100352$	$1.12597$	$4.66774$	$[1, -1, 1, -180, 1047]$	$y^2+xy+y=x^3-x^2-180x+1047$	8.2.0.a.1	$[(-1, 35)]$
350.e1	350b2	350.e	350b	$2$	$3$	$2 \cdot 5^{2} \cdot 7$	$- 2 \cdot 5^{8} \cdot 7^{6}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.2.0.1, 3.8.0.2	3B.1.2	$24$	$16$	$0$	$1$	$1$		$0$	$360$	$0.806853$	$-417267265/235298$	$0.94642$	$5.70253$	$[1, 0, 0, -1138, -20858]$	$y^2+xy=x^3-1138x-20858$	3.8.0-3.a.1.1, 8.2.0.a.1, 24.16.0-24.a.1.6	$[]$
350.e2	350b1	350.e	350b	$2$	$3$	$2 \cdot 5^{2} \cdot 7$	$- 2^{3} \cdot 5^{8} \cdot 7^{2}$	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.2.0.1, 3.8.0.1	3B.1.1	$24$	$16$	$0$	$1$	$1$		$2$	$120$	$0.257547$	$397535/392$	$1.09655$	$4.39891$	$[1, 0, 0, 112, 392]$	$y^2+xy=x^3+112x+392$	3.8.0-3.a.1.2, 8.2.0.a.1, 24.16.0-24.a.1.8	$[]$
350.f1	350d6	350.f	350d	$6$	$18$	$2 \cdot 5^{2} \cdot 7$	$2^{9} \cdot 5^{6} \cdot 7^{2}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 9.12.0.1	2B, 3B	$2520$	$864$	$21$	$1$	$1$		$0$	$864$	$1.217819$	$2251439055699625/25088$	$1.06489$	$7.68308$	$[1, 1, 1, -68263, -6893219]$	$y^2+xy+y=x^3+x^2-68263x-6893219$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 9.12.0.a.1, $\ldots$	$[]$
350.f2	350d5	350.f	350d	$6$	$18$	$2 \cdot 5^{2} \cdot 7$	$- 2^{18} \cdot 5^{6} \cdot 7$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 9.12.0.1	2B, 3B	$2520$	$864$	$21$	$1$	$1$		$1$	$432$	$0.871246$	$-548347731625/1835008$	$1.02933$	$6.26374$	$[1, 1, 1, -4263, -109219]$	$y^2+xy+y=x^3+x^2-4263x-109219$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 9.12.0.a.1, $\ldots$	$[]$
350.f3	350d4	350.f	350d	$6$	$18$	$2 \cdot 5^{2} \cdot 7$	$2^{3} \cdot 5^{6} \cdot 7^{6}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 3.12.0.1	2B, 3Cs	$2520$	$864$	$21$	$1$	$1$		$0$	$288$	$0.668514$	$4956477625/941192$	$1.00821$	$5.45936$	$[1, 1, 1, -888, -8719]$	$y^2+xy+y=x^3+x^2-888x-8719$	2.3.0.a.1, 3.12.0.a.1, 6.36.0.a.1, 8.6.0.b.1, 15.24.0-3.a.1.1, $\ldots$	$[]$
350.f4	350d2	350.f	350d	$6$	$18$	$2 \cdot 5^{2} \cdot 7$	$2 \cdot 5^{6} \cdot 7^{2}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 9.12.0.1	2B, 3B	$2520$	$864$	$21$	$1$	$1$		$0$	$96$	$0.119208$	$128787625/98$	$0.96763$	$4.83623$	$[1, 1, 1, -263, 1531]$	$y^2+xy+y=x^3+x^2-263x+1531$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 9.12.0.a.1, $\ldots$	$[]$
350.f5	350d1	350.f	350d	$6$	$18$	$2 \cdot 5^{2} \cdot 7$	$- 2^{2} \cdot 5^{6} \cdot 7$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 9.12.0.1	2B, 3B	$2520$	$864$	$21$	$1$	$1$		$1$	$48$	$-0.227366$	$-15625/28$	$1.01712$	$3.53767$	$[1, 1, 1, -13, 31]$	$y^2+xy+y=x^3+x^2-13x+31$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 9.12.0.a.1, $\ldots$	$[]$
350.f6	350d3	350.f	350d	$6$	$18$	$2 \cdot 5^{2} \cdot 7$	$- 2^{6} \cdot 5^{6} \cdot 7^{3}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 3.12.0.1	2B, 3Cs	$2520$	$864$	$21$	$1$	$1$		$1$	$144$	$0.321940$	$9938375/21952$	$0.98695$	$4.57570$	$[1, 1, 1, 112, -719]$	$y^2+xy+y=x^3+x^2+112x-719$	2.3.0.a.1, 3.12.0.a.1, 6.36.0.a.1, 8.6.0.c.1, 14.6.0.b.1, $\ldots$	$[]$

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