Elliptic curve search results

Results (38 matches)

 

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
1960.e1	1960l1	1960.e	1960l	$1$	$1$	\( 2^{3} \cdot 5 \cdot 7^{2} \)	\( - 2^{10} \cdot 5 \cdot 7^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1$	$1$		$0$	$2016$	$1.013948$	$-196/5$	$0.83724$	$4.67993$	$[0, -1, 0, -800, 58780]$	\(y^2=x^3-x^2-800x+58780\)	20.2.0.a.1	$[]$
1960.i1	1960h1	1960.i	1960h	$1$	$1$	\( 2^{3} \cdot 5 \cdot 7^{2} \)	\( - 2^{10} \cdot 5 \cdot 7^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1$	$1$		$0$	$288$	$0.040994$	$-196/5$	$0.83724$	$3.13978$	$[0, 1, 0, -16, -176]$	\(y^2=x^3+x^2-16x-176\)	20.2.0.a.1	$[]$
3920.m1	3920b1	3920.m	3920b	$1$	$1$	\( 2^{4} \cdot 5 \cdot 7^{2} \)	\( - 2^{10} \cdot 5 \cdot 7^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$0.238960178$	$1$		$6$	$576$	$0.040994$	$-196/5$	$0.83724$	$2.87674$	$[0, -1, 0, -16, 176]$	\(y^2=x^3-x^2-16x+176\)	20.2.0.a.1	$[(-2, 14)]$
3920.y1	3920i1	3920.y	3920i	$1$	$1$	\( 2^{4} \cdot 5 \cdot 7^{2} \)	\( - 2^{10} \cdot 5 \cdot 7^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$5.759087921$	$1$		$2$	$4032$	$1.013948$	$-196/5$	$0.83724$	$4.28787$	$[0, 1, 0, -800, -58780]$	\(y^2=x^3+x^2-800x-58780\)	20.2.0.a.1	$[(608, 14986)]$
9800.r1	9800a1	9800.r	9800a	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{10} \cdot 5^{7} \cdot 7^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$0.667243892$	$1$		$4$	$6912$	$0.845713$	$-196/5$	$0.83724$	$3.64068$	$[0, -1, 0, -408, -21188]$	\(y^2=x^3-x^2-408x-21188\)	20.2.0.a.1	$[(82, 700)]$
9800.bc1	9800f1	9800.bc	9800f	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{10} \cdot 5^{7} \cdot 7^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1$	$1$		$0$	$48384$	$1.818668$	$-196/5$	$0.83724$	$4.91111$	$[0, 1, 0, -20008, 7307488]$	\(y^2=x^3+x^2-20008x+7307488\)	20.2.0.a.1	$[]$
15680.be1	15680ci1	15680.be	15680ci	$1$	$1$	\( 2^{6} \cdot 5 \cdot 7^{2} \)	\( - 2^{16} \cdot 5 \cdot 7^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$3.270796252$	$1$		$2$	$32256$	$1.360523$	$-196/5$	$0.83724$	$4.10305$	$[0, -1, 0, -3201, -467039]$	\(y^2=x^3-x^2-3201x-467039\)	20.2.0.a.1	$[(93, 176)]$
15680.bp1	15680bf1	15680.bp	15680bf	$1$	$1$	\( 2^{6} \cdot 5 \cdot 7^{2} \)	\( - 2^{16} \cdot 5 \cdot 7^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1$	$1$		$0$	$4608$	$0.387568$	$-196/5$	$0.83724$	$2.89443$	$[0, -1, 0, -65, -1343]$	\(y^2=x^3-x^2-65x-1343\)	20.2.0.a.1	$[]$
15680.cg1	15680i1	15680.cg	15680i	$1$	$1$	\( 2^{6} \cdot 5 \cdot 7^{2} \)	\( - 2^{16} \cdot 5 \cdot 7^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1$	$1$		$0$	$32256$	$1.360523$	$-196/5$	$0.83724$	$4.10305$	$[0, 1, 0, -3201, 467039]$	\(y^2=x^3+x^2-3201x+467039\)	20.2.0.a.1	$[]$
15680.cw1	15680cy1	15680.cw	15680cy	$1$	$1$	\( 2^{6} \cdot 5 \cdot 7^{2} \)	\( - 2^{16} \cdot 5 \cdot 7^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$0.388969722$	$1$		$4$	$4608$	$0.387568$	$-196/5$	$0.83724$	$2.89443$	$[0, 1, 0, -65, 1343]$	\(y^2=x^3+x^2-65x+1343\)	20.2.0.a.1	$[(23, 112)]$
17640.m1	17640q1	17640.m	17640q	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{2} \)	\( - 2^{10} \cdot 3^{6} \cdot 5 \cdot 7^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$10.65655807$	$1$		$0$	$60480$	$1.563255$	$-196/5$	$0.83724$	$4.30243$	$[0, 0, 0, -7203, -1579858]$	\(y^2=x^3-7203x-1579858\)	20.2.0.a.1	$[(75527/23, 6686980/23)]$
17640.bw1	17640z1	17640.bw	17640z	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{2} \)	\( - 2^{10} \cdot 3^{6} \cdot 5 \cdot 7^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$2.331670055$	$1$		$2$	$8640$	$0.590301$	$-196/5$	$0.83724$	$3.10837$	$[0, 0, 0, -147, 4606]$	\(y^2=x^3-147x+4606\)	20.2.0.a.1	$[(15, 76)]$
19600.bh1	19600p1	19600.bh	19600p	$1$	$1$	\( 2^{4} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{10} \cdot 5^{7} \cdot 7^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1$	$1$		$0$	$96768$	$1.818668$	$-196/5$	$0.83724$	$4.56668$	$[0, -1, 0, -20008, -7307488]$	\(y^2=x^3-x^2-20008x-7307488\)	20.2.0.a.1	$[]$
19600.cq1	19600a1	19600.cq	19600a	$1$	$1$	\( 2^{4} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{10} \cdot 5^{7} \cdot 7^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1.656784707$	$1$		$4$	$13824$	$0.845713$	$-196/5$	$0.83724$	$3.38535$	$[0, 1, 0, -408, 21188]$	\(y^2=x^3+x^2-408x+21188\)	20.2.0.a.1	$[(-32, 50)]$
35280.cd1	35280bg1	35280.cd	35280bg	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \)	\( - 2^{10} \cdot 3^{6} \cdot 5 \cdot 7^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$6.720077896$	$1$		$0$	$120960$	$1.563255$	$-196/5$	$0.83724$	$4.01762$	$[0, 0, 0, -7203, 1579858]$	\(y^2=x^3-7203x+1579858\)	20.2.0.a.1	$[(499/3, 31382/3)]$
35280.ex1	35280bx1	35280.ex	35280bx	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \)	\( - 2^{10} \cdot 3^{6} \cdot 5 \cdot 7^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1.853154309$	$1$		$2$	$17280$	$0.590301$	$-196/5$	$0.83724$	$2.90260$	$[0, 0, 0, -147, -4606]$	\(y^2=x^3-147x-4606\)	20.2.0.a.1	$[(35, 182)]$
78400.dl1	78400bn1	78400.dl	78400bn	$1$	$1$	\( 2^{6} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{16} \cdot 5^{7} \cdot 7^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1$	$1$		$0$	$774144$	$2.165241$	$-196/5$	$0.83724$	$4.37396$	$[0, -1, 0, -80033, 58539937]$	\(y^2=x^3-x^2-80033x+58539937\)	20.2.0.a.1	$[]$
78400.dy1	78400gc1	78400.dy	78400gc	$1$	$1$	\( 2^{6} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{16} \cdot 5^{7} \cdot 7^{4} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$0.970201139$	$1$		$16$	$110592$	$1.192287$	$-196/5$	$0.83724$	$3.33794$	$[0, -1, 0, -1633, 171137]$	\(y^2=x^3-x^2-1633x+171137\)	20.2.0.a.1	$[(-43, 400), (37, 400)]$
78400.ho1	78400b1	78400.ho	78400b	$1$	$1$	\( 2^{6} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{16} \cdot 5^{7} \cdot 7^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$0.886349073$	$1$		$2$	$110592$	$1.192287$	$-196/5$	$0.83724$	$3.33794$	$[0, 1, 0, -1633, -171137]$	\(y^2=x^3+x^2-1633x-171137\)	20.2.0.a.1	$[(93, 700)]$
78400.if1	78400hg1	78400.if	78400hg	$1$	$1$	\( 2^{6} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{16} \cdot 5^{7} \cdot 7^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$8.582159989$	$1$		$0$	$774144$	$2.165241$	$-196/5$	$0.83724$	$4.37396$	$[0, 1, 0, -80033, -58539937]$	\(y^2=x^3+x^2-80033x-58539937\)	20.2.0.a.1	$[(23399/5, 3277168/5)]$
88200.cp1	88200gk1	88200.cp	88200gk	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{10} \cdot 3^{6} \cdot 5^{7} \cdot 7^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1$	$1$		$0$	$1451520$	$2.367973$	$-196/5$	$0.83724$	$4.54236$	$[0, 0, 0, -180075, -197482250]$	\(y^2=x^3-180075x-197482250\)	20.2.0.a.1	$[]$
88200.cq1	88200fq1	88200.cq	88200fq	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{10} \cdot 3^{6} \cdot 5^{7} \cdot 7^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$0.525139847$	$1$		$4$	$207360$	$1.395020$	$-196/5$	$0.83724$	$3.51706$	$[0, 0, 0, -3675, 575750]$	\(y^2=x^3-3675x+575750\)	20.2.0.a.1	$[(35, 700)]$
141120.cp1	141120ff1	141120.cp	141120ff	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7^{2} \)	\( - 2^{16} \cdot 3^{6} \cdot 5 \cdot 7^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1.160207045$	$1$		$4$	$138240$	$0.936873$	$-196/5$	$0.83724$	$2.91399$	$[0, 0, 0, -588, -36848]$	\(y^2=x^3-588x-36848\)	20.2.0.a.1	$[(42, 112)]$
141120.fl1	141120nm1	141120.fl	141120nm	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7^{2} \)	\( - 2^{16} \cdot 3^{6} \cdot 5 \cdot 7^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1$	$1$		$0$	$138240$	$0.936873$	$-196/5$	$0.83724$	$2.91399$	$[0, 0, 0, -588, 36848]$	\(y^2=x^3-588x+36848\)	20.2.0.a.1	$[]$
141120.ko1	141120r1	141120.ko	141120r	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7^{2} \)	\( - 2^{16} \cdot 3^{6} \cdot 5 \cdot 7^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$7.327587163$	$1$		$2$	$967680$	$1.909828$	$-196/5$	$0.83724$	$3.89865$	$[0, 0, 0, -28812, 12638864]$	\(y^2=x^3-28812x+12638864\)	20.2.0.a.1	$[(8474, 779920)]$
141120.nr1	141120jp1	141120.nr	141120jp	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7^{2} \)	\( - 2^{16} \cdot 3^{6} \cdot 5 \cdot 7^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1$	$9$	$3$	$0$	$967680$	$1.909828$	$-196/5$	$0.83724$	$3.89865$	$[0, 0, 0, -28812, -12638864]$	\(y^2=x^3-28812x-12638864\)	20.2.0.a.1	$[]$
176400.om1	176400pt1	176400.om	176400pt	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{10} \cdot 3^{6} \cdot 5^{7} \cdot 7^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$9.327373002$	$1$		$0$	$2903040$	$2.367973$	$-196/5$	$0.83724$	$4.28173$	$[0, 0, 0, -180075, 197482250]$	\(y^2=x^3-180075x+197482250\)	20.2.0.a.1	$[(-4765/11, 19034350/11)]$
176400.on1	176400ri1	176400.on	176400ri	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{10} \cdot 3^{6} \cdot 5^{7} \cdot 7^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1$	$1$		$0$	$414720$	$1.395020$	$-196/5$	$0.83724$	$3.31526$	$[0, 0, 0, -3675, -575750]$	\(y^2=x^3-3675x-575750\)	20.2.0.a.1	$[]$
237160.x1	237160x1	237160.x	237160x	$1$	$1$	\( 2^{3} \cdot 5 \cdot 7^{2} \cdot 11^{2} \)	\( - 2^{10} \cdot 5 \cdot 7^{10} \cdot 11^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1$	$4$	$2$	$0$	$2822400$	$2.212898$	$-196/5$	$0.83724$	$4.02897$	$[0, -1, 0, -96840, -77848868]$	\(y^2=x^3-x^2-96840x-77848868\)	20.2.0.a.1	$[]$
237160.bu1	237160bu1	237160.bu	237160bu	$1$	$1$	\( 2^{3} \cdot 5 \cdot 7^{2} \cdot 11^{2} \)	\( - 2^{10} \cdot 5 \cdot 7^{4} \cdot 11^{6} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$2.276771598$	$1$		$8$	$403200$	$1.239943$	$-196/5$	$0.83724$	$3.08561$	$[0, 1, 0, -1976, 226400]$	\(y^2=x^3+x^2-1976x+226400\)	20.2.0.a.1	$[(-4, 484), (44, 476)]$
331240.u1	331240u1	331240.u	331240u	$1$	$1$	\( 2^{3} \cdot 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{10} \cdot 5 \cdot 7^{10} \cdot 13^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1$	$1$		$0$	$4741632$	$2.296425$	$-196/5$	$0.83724$	$4.00192$	$[0, -1, 0, -135256, 128598716]$	\(y^2=x^3-x^2-135256x+128598716\)	20.2.0.a.1	$[]$
331240.cc1	331240cc1	331240.cc	331240cc	$1$	$1$	\( 2^{3} \cdot 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{10} \cdot 5 \cdot 7^{4} \cdot 13^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1$	$1$		$0$	$677376$	$1.323469$	$-196/5$	$0.83724$	$3.08336$	$[0, 1, 0, -2760, -375712]$	\(y^2=x^3+x^2-2760x-375712\)	20.2.0.a.1	$[]$
474320.cn1	474320cn1	474320.cn	474320cn	$1$	$1$	\( 2^{4} \cdot 5 \cdot 7^{2} \cdot 11^{2} \)	\( - 2^{10} \cdot 5 \cdot 7^{4} \cdot 11^{6} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$9.681338129$	$1$		$6$	$806400$	$1.239943$	$-196/5$	$0.83724$	$2.92197$	$[0, -1, 0, -1976, -226400]$	\(y^2=x^3-x^2-1976x-226400\)	20.2.0.a.1	$[(125, 1210), (86, 482)]$
474320.hp1	474320hp1	474320.hp	474320hp	$1$	$1$	\( 2^{4} \cdot 5 \cdot 7^{2} \cdot 11^{2} \)	\( - 2^{10} \cdot 5 \cdot 7^{10} \cdot 11^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1$	$4$	$2$	$0$	$5644800$	$2.212898$	$-196/5$	$0.83724$	$3.81530$	$[0, 1, 0, -96840, 77848868]$	\(y^2=x^3+x^2-96840x+77848868\)	20.2.0.a.1	$[]$
705600.pi1	-	705600.pi	-	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{16} \cdot 3^{6} \cdot 5^{7} \cdot 7^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1$	$1$		$0$	$23224320$	$2.714546$	$-196/5$	$0.83724$	$4.14979$	$[0, 0, 0, -720300, 1579858000]$	\(y^2=x^3-720300x+1579858000\)	20.2.0.a.1	$[]$
705600.pt1	-	705600.pt	-	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{16} \cdot 3^{6} \cdot 5^{7} \cdot 7^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$6.260039110$	$1$		$2$	$3317760$	$1.741592$	$-196/5$	$0.83724$	$3.28280$	$[0, 0, 0, -14700, -4606000]$	\(y^2=x^3-14700x-4606000\)	20.2.0.a.1	$[(14690, 1780400)]$
705600.bna1	-	705600.bna	-	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{16} \cdot 3^{6} \cdot 5^{7} \cdot 7^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$18.42599659$	$1$		$0$	$23224320$	$2.714546$	$-196/5$	$0.83724$	$4.14979$	$[0, 0, 0, -720300, -1579858000]$	\(y^2=x^3-720300x-1579858000\)	20.2.0.a.1	$[(946181140/813, 9649968187600/813)]$
705600.bnj1	-	705600.bnj	-	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{16} \cdot 3^{6} \cdot 5^{7} \cdot 7^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$20$	$2$	$0$	$1$	$1$		$0$	$3317760$	$1.741592$	$-196/5$	$0.83724$	$3.28280$	$[0, 0, 0, -14700, 4606000]$	\(y^2=x^3-14700x+4606000\)	20.2.0.a.1	$[]$