Elliptic curve search results

Results (21 matches)

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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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
563.a1	563a1	563.a	563a	$1$	$1$	\( 563 \)	\( -563 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1126$	$2$	$0$	$0.219229003$	$1$		$14$	$52$	$-0.571680$	$-374805361/563$	$0.80334$	$3.11758$	$1$	$[1, 1, 1, -15, 16]$	\(y^2+xy+y=x^3+x^2-15x+16\)	1126.2.0.?	$[(2, -2), (4, 4)]$	$1$
5067.c1	5067c1	5067.c	5067c	$1$	$1$	\( 3^{2} \cdot 563 \)	\( - 3^{6} \cdot 563 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1126$	$2$	$0$	$1$	$4$	$2$	$0$	$1560$	$-0.022374$	$-374805361/563$	$0.80334$	$3.08730$	$1$	$[1, -1, 0, -135, -572]$	\(y^2+xy=x^3-x^2-135x-572\)	1126.2.0.?	$[ ]$	$1$
9008.b1	9008d1	9008.b	9008d	$1$	$1$	\( 2^{4} \cdot 563 \)	\( - 2^{12} \cdot 563 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1126$	$2$	$0$	$1$	$1$		$0$	$3328$	$0.121467$	$-374805361/563$	$0.80334$	$3.08178$	$1$	$[0, 1, 0, -240, -1516]$	\(y^2=x^3+x^2-240x-1516\)	1126.2.0.?	$[ ]$	$1$
14075.f1	14075b1	14075.f	14075b	$1$	$1$	\( 5^{2} \cdot 563 \)	\( - 5^{6} \cdot 563 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1126$	$2$	$0$	$1.553684722$	$1$		$2$	$4160$	$0.233039$	$-374805361/563$	$0.80334$	$3.07796$	$1$	$[1, 0, 1, -376, 2773]$	\(y^2+xy+y=x^3-376x+2773\)	1126.2.0.?	$[(11, -4)]$	$1$
27587.b1	27587b1	27587.b	27587b	$1$	$1$	\( 7^{2} \cdot 563 \)	\( - 7^{6} \cdot 563 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1126$	$2$	$0$	$1$	$4$	$2$	$0$	$12168$	$0.401275$	$-374805361/563$	$0.80334$	$3.07283$	$1$	$[1, 0, 0, -736, -7757]$	\(y^2+xy=x^3-736x-7757\)	1126.2.0.?	$[ ]$	$1$
36032.e1	36032i1	36032.e	36032i	$1$	$1$	\( 2^{6} \cdot 563 \)	\( - 2^{18} \cdot 563 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1126$	$2$	$0$	$8.079944765$	$1$		$0$	$26624$	$0.468041$	$-374805361/563$	$0.80334$	$3.07097$	$1$	$[0, -1, 0, -961, -11167]$	\(y^2=x^3-x^2-961x-11167\)	1126.2.0.?	$[(2368/7, 78905/7)]$	$1$
36032.g1	36032b1	36032.g	36032b	$1$	$1$	\( 2^{6} \cdot 563 \)	\( - 2^{18} \cdot 563 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1126$	$2$	$0$	$2.062228479$	$1$		$2$	$26624$	$0.468041$	$-374805361/563$	$0.80334$	$3.07097$	$1$	$[0, 1, 0, -961, 11167]$	\(y^2=x^3+x^2-961x+11167\)	1126.2.0.?	$[(18, 5)]$	$1$
68123.d1	68123a1	68123.d	68123a	$1$	$1$	\( 11^{2} \cdot 563 \)	\( - 11^{6} \cdot 563 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1126$	$2$	$0$	$1$	$1$		$0$	$66560$	$0.627268$	$-374805361/563$	$0.80334$	$3.06691$	$1$	$[1, 1, 0, -1817, -30620]$	\(y^2+xy=x^3+x^2-1817x-30620\)	1126.2.0.?	$[ ]$	$1$
81072.s1	81072s1	81072.s	81072s	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 563 \)	\( - 2^{12} \cdot 3^{6} \cdot 563 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1126$	$2$	$0$	$1$	$1$		$0$	$99840$	$0.670774$	$-374805361/563$	$0.80334$	$3.06588$	$1$	$[0, 0, 0, -2163, 38770]$	\(y^2=x^3-2163x+38770\)	1126.2.0.?	$[ ]$	$1$
95147.a1	95147a1	95147.a	95147a	$1$	$1$	\( 13^{2} \cdot 563 \)	\( - 13^{6} \cdot 563 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1126$	$2$	$0$	$1$	$1$		$0$	$119808$	$0.710794$	$-374805361/563$	$0.80334$	$3.06496$	$1$	$[1, 1, 0, -2538, 48235]$	\(y^2+xy=x^3+x^2-2538x+48235\)	1126.2.0.?	$[ ]$	$1$
126675.h1	126675l1	126675.h	126675l	$1$	$1$	\( 3^{2} \cdot 5^{2} \cdot 563 \)	\( - 3^{6} \cdot 5^{6} \cdot 563 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1126$	$2$	$0$	$9.079004094$	$1$		$0$	$124800$	$0.782345$	$-374805361/563$	$0.80334$	$3.06338$	$1$	$[1, -1, 1, -3380, -74878]$	\(y^2+xy+y=x^3-x^2-3380x-74878\)	1126.2.0.?	$[(6070/9, 189179/9)]$	$1$
162707.a1	162707a1	162707.a	162707a	$1$	$1$	\( 17^{2} \cdot 563 \)	\( - 17^{6} \cdot 563 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1126$	$2$	$0$	$1$	$4$	$2$	$0$	$262080$	$0.844927$	$-374805361/563$	$0.80334$	$3.06206$	$1$	$[1, 0, 0, -4341, 109868]$	\(y^2+xy=x^3-4341x+109868\)	1126.2.0.?	$[ ]$	$1$
203243.c1	203243c1	203243.c	203243c	$1$	$1$	\( 19^{2} \cdot 563 \)	\( - 19^{6} \cdot 563 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1126$	$2$	$0$	$29.84211994$	$1$		$2$	$365976$	$0.900539$	$-374805361/563$	$0.80334$	$3.06093$	$1$	$[1, 0, 1, -5423, -154343]$	\(y^2+xy+y=x^3-5423x-154343\)	1126.2.0.?	$[(85, -69), (391/2, 3621/2)]$	$1$
225200.c1	225200c1	225200.c	225200c	$1$	$1$	\( 2^{4} \cdot 5^{2} \cdot 563 \)	\( - 2^{12} \cdot 5^{6} \cdot 563 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1126$	$2$	$0$	$1.920093436$	$1$		$4$	$266240$	$0.926187$	$-374805361/563$	$0.80334$	$3.06042$	$1$	$[0, -1, 0, -6008, -177488]$	\(y^2=x^3-x^2-6008x-177488\)	1126.2.0.?	$[(92, 200)]$	$1$
248283.i1	248283i1	248283.i	248283i	$1$	$1$	\( 3^{2} \cdot 7^{2} \cdot 563 \)	\( - 3^{6} \cdot 7^{6} \cdot 563 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1126$	$2$	$0$	$11.73814407$	$1$		$4$	$365040$	$0.950582$	$-374805361/563$	$0.80334$	$3.05995$	$1$	$[1, -1, 0, -6624, 209439]$	\(y^2+xy=x^3-x^2-6624x+209439\)	1126.2.0.?	$[(46, -1), (199/2, 75/2)]$	$1$
297827.a1	297827a1	297827.a	297827a	$1$	$1$	\( 23^{2} \cdot 563 \)	\( - 23^{6} \cdot 563 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1126$	$2$	$0$	$1$	$16$	$2$	$0$	$648648$	$0.996067$	$-374805361/563$	$0.80334$	$3.05908$	$1$	$[1, 1, 1, -7946, -276294]$	\(y^2+xy+y=x^3+x^2-7946x-276294\)	1126.2.0.?	$[ ]$	$1$
316969.a1	316969a1	316969.a	316969a	$1$	$1$	\( 563^{2} \)	\( - 563^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1126$	$2$	$0$	$1$	$16$	$2$	$0$	$16482336$	$2.594959$	$-374805361/563$	$0.80334$	$4.55879$	$1$	$[1, 1, 0, -4761138, -4005828725]$	\(y^2+xy=x^3+x^2-4761138x-4005828725\)	1126.2.0.?	$[ ]$	$1$
324288.a1	324288a1	324288.a	324288a	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 563 \)	\( - 2^{18} \cdot 3^{6} \cdot 563 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1126$	$2$	$0$	$7.300111193$	$1$		$0$	$798720$	$1.017347$	$-374805361/563$	$0.80334$	$3.05868$	$1$	$[0, 0, 0, -8652, -310160]$	\(y^2=x^3-8652x-310160\)	1126.2.0.?	$[(997/3, 8137/3)]$	$1$
324288.d1	324288d1	324288.d	324288d	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 563 \)	\( - 2^{18} \cdot 3^{6} \cdot 563 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1126$	$2$	$0$	$4.005063140$	$1$		$2$	$798720$	$1.017347$	$-374805361/563$	$0.80334$	$3.05868$	$1$	$[0, 0, 0, -8652, 310160]$	\(y^2=x^3-8652x+310160\)	1126.2.0.?	$[(77, 317)]$	$1$
441392.m1	441392m1	441392.m	441392m	$1$	$1$	\( 2^{4} \cdot 7^{2} \cdot 563 \)	\( - 2^{12} \cdot 7^{6} \cdot 563 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1126$	$2$	$0$	$1$	$1$		$0$	$778752$	$1.094423$	$-374805361/563$	$0.80334$	$3.05729$	$1$	$[0, -1, 0, -11776, 496448]$	\(y^2=x^3-x^2-11776x+496448\)	1126.2.0.?	$[ ]$	$1$
473483.c1	473483c1	473483.c	473483c	$1$	$1$	\( 29^{2} \cdot 563 \)	\( - 29^{6} \cdot 563 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1126$	$2$	$0$	$3.626133807$	$1$		$2$	$1304576$	$1.111967$	$-374805361/563$	$0.80334$	$3.05698$	$1$	$[1, 0, 1, -12633, 546147]$	\(y^2+xy+y=x^3-12633x+546147\)	1126.2.0.?	$[(57, 81)]$	$1$

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