Elliptic curve search results

Results (25 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	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
692.a1	692a2	692.a	692a	$2$	$2$	\( 2^{2} \cdot 173 \)	\( 2^{4} \cdot 173 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.22	2B	$1384$	$48$	$0$	$1$	$1$		$1$	$246$	$-0.320014$	$1302642688/173$	$0.88014$	$3.63330$	$[0, 1, 0, -57, 148]$	\(y^2=x^3+x^2-57x+148\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.2, 346.6.0.?, 692.24.0.?, $\ldots$	$[ ]$	$2$
2768.d1	2768c2	2768.d	2768c	$2$	$2$	\( 2^{4} \cdot 173 \)	\( 2^{4} \cdot 173 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.22	2B	$1384$	$48$	$0$	$1$	$9$	$3$	$1$	$984$	$-0.320014$	$1302642688/173$	$0.88014$	$2.99781$	$[0, -1, 0, -57, -148]$	\(y^2=x^3-x^2-57x-148\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.2, 346.6.0.?, 692.24.0.?, $\ldots$	$[ ]$	$2$
6228.c1	6228f1	6228.c	6228f	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 173 \)	\( 2^{4} \cdot 3^{6} \cdot 173 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$4152$	$48$	$0$	$1$	$1$		$1$	$1476$	$0.229292$	$1302642688/173$	$0.88014$	$3.47403$	$[0, 0, 0, -516, -4511]$	\(y^2=x^3-516x-4511\)	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.4, 346.6.0.?, 692.24.0.?, $\ldots$	$[ ]$	$1$
11072.b1	11072j1	11072.b	11072j	$2$	$2$	\( 2^{6} \cdot 173 \)	\( 2^{10} \cdot 173 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.21	2B	$1384$	$48$	$0$	$3.912786742$	$1$		$3$	$1968$	$0.026560$	$1302642688/173$	$0.88014$	$2.99813$	$[0, 1, 0, -229, -1413]$	\(y^2=x^3+x^2-229x-1413\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.3, 346.6.0.?, 692.24.0.?, $\ldots$	$[(91, 860)]$	$1$
11072.i1	11072d1	11072.i	11072d	$2$	$2$	\( 2^{6} \cdot 173 \)	\( 2^{10} \cdot 173 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.21	2B	$1384$	$48$	$0$	$1$	$1$		$1$	$1968$	$0.026560$	$1302642688/173$	$0.88014$	$2.99813$	$[0, -1, 0, -229, 1413]$	\(y^2=x^3-x^2-229x+1413\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.3, 346.6.0.?, 692.24.0.?, $\ldots$	$[ ]$	$1$
17300.a1	17300a1	17300.a	17300a	$2$	$2$	\( 2^{2} \cdot 5^{2} \cdot 173 \)	\( 2^{4} \cdot 5^{6} \cdot 173 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$6920$	$48$	$0$	$2.434326420$	$1$		$3$	$7872$	$0.484705$	$1302642688/173$	$0.88014$	$3.42440$	$[0, -1, 0, -1433, 21362]$	\(y^2=x^3-x^2-1433x+21362\)	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.2, 346.6.0.?, 692.24.0.?, $\ldots$	$[(13, 69)]$	$1$
24912.e1	24912p1	24912.e	24912p	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 173 \)	\( 2^{4} \cdot 3^{6} \cdot 173 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$4152$	$48$	$0$	$1$	$1$		$1$	$5904$	$0.229292$	$1302642688/173$	$0.88014$	$2.99828$	$[0, 0, 0, -516, 4511]$	\(y^2=x^3-516x+4511\)	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.4, 346.6.0.?, 692.24.0.?, $\ldots$	$[ ]$	$1$
33908.e1	33908f1	33908.e	33908f	$2$	$2$	\( 2^{2} \cdot 7^{2} \cdot 173 \)	\( 2^{4} \cdot 7^{6} \cdot 173 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$9688$	$48$	$0$	$1$	$1$		$1$	$22140$	$0.652941$	$1302642688/173$	$0.88014$	$3.39702$	$[0, -1, 0, -2809, -56370]$	\(y^2=x^3-x^2-2809x-56370\)	2.3.0.a.1, 4.6.0.b.1, 56.12.0-4.b.1.2, 346.6.0.?, 692.24.0.?, $\ldots$	$[ ]$	$1$
69200.a1	69200k1	69200.a	69200k	$2$	$2$	\( 2^{4} \cdot 5^{2} \cdot 173 \)	\( 2^{4} \cdot 5^{6} \cdot 173 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$6920$	$48$	$0$	$6.742224279$	$1$		$1$	$31488$	$0.484705$	$1302642688/173$	$0.88014$	$2.99844$	$[0, 1, 0, -1433, -21362]$	\(y^2=x^3+x^2-1433x-21362\)	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.2, 346.6.0.?, 692.24.0.?, $\ldots$	$[(2817/8, 26975/8)]$	$1$
83732.a1	83732e1	83732.a	83732e	$2$	$2$	\( 2^{2} \cdot 11^{2} \cdot 173 \)	\( 2^{4} \cdot 11^{6} \cdot 173 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$15224$	$48$	$0$	$1$	$1$		$1$	$86100$	$0.878934$	$1302642688/173$	$0.88014$	$3.36536$	$[0, 1, 0, -6937, -224688]$	\(y^2=x^3+x^2-6937x-224688\)	2.3.0.a.1, 4.6.0.b.1, 88.12.0.?, 346.6.0.?, 692.24.0.?, $\ldots$	$[ ]$	$1$
99648.be1	99648j1	99648.be	99648j	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 173 \)	\( 2^{10} \cdot 3^{6} \cdot 173 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$4152$	$48$	$0$	$1$	$1$		$1$	$47232$	$0.575866$	$1302642688/173$	$0.88014$	$2.99849$	$[0, 0, 0, -2064, -36088]$	\(y^2=x^3-2064x-36088\)	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.1, 346.6.0.?, 692.24.0.?, $\ldots$	$[ ]$	$1$
99648.bh1	99648bb1	99648.bh	99648bb	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 173 \)	\( 2^{10} \cdot 3^{6} \cdot 173 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$4152$	$48$	$0$	$4.634330799$	$1$		$1$	$47232$	$0.575866$	$1302642688/173$	$0.88014$	$2.99849$	$[0, 0, 0, -2064, 36088]$	\(y^2=x^3-2064x+36088\)	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.1, 346.6.0.?, 692.24.0.?, $\ldots$	$[(334/3, 2780/3)]$	$1$
116948.a1	116948c1	116948.a	116948c	$2$	$2$	\( 2^{2} \cdot 13^{2} \cdot 173 \)	\( 2^{4} \cdot 13^{6} \cdot 173 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$17992$	$48$	$0$	$2.294310984$	$1$		$13$	$118080$	$0.962461$	$1302642688/173$	$0.88014$	$3.35490$	$[0, 1, 0, -9689, 363832]$	\(y^2=x^3+x^2-9689x+363832\)	2.3.0.a.1, 4.6.0.b.1, 104.12.0.?, 346.6.0.?, 692.24.0.?, $\ldots$	$[(69, 169), (-8, 664)]$	$1$
119716.a1	119716a1	119716.a	119716a	$2$	$2$	\( 2^{2} \cdot 173^{2} \)	\( 2^{4} \cdot 173^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.24	2B	$1384$	$48$	$0$	$1$	$9$	$3$	$1$	$1840572$	$2.256630$	$1302642688/173$	$0.88014$	$4.67635$	$[0, -1, 0, -1715929, 865634250]$	\(y^2=x^3-x^2-1715929x+865634250\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.4, 346.6.0.?, 692.24.0.?, $\ldots$	$[ ]$	$1$
135632.c1	135632b1	135632.c	135632b	$2$	$2$	\( 2^{4} \cdot 7^{2} \cdot 173 \)	\( 2^{4} \cdot 7^{6} \cdot 173 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$9688$	$48$	$0$	$1$	$1$		$1$	$88560$	$0.652941$	$1302642688/173$	$0.88014$	$2.99853$	$[0, 1, 0, -2809, 56370]$	\(y^2=x^3+x^2-2809x+56370\)	2.3.0.a.1, 4.6.0.b.1, 56.12.0-4.b.1.2, 346.6.0.?, 692.24.0.?, $\ldots$	$[ ]$	$1$
155700.p1	155700i1	155700.p	155700i	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 173 \)	\( 2^{4} \cdot 3^{6} \cdot 5^{6} \cdot 173 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$20760$	$48$	$0$	$17.05553471$	$1$		$1$	$188928$	$1.034012$	$1302642688/173$	$0.88014$	$3.34640$	$[0, 0, 0, -12900, -563875]$	\(y^2=x^3-12900x-563875\)	2.3.0.a.1, 4.6.0.b.1, 120.12.0.?, 346.6.0.?, 692.24.0.?, $\ldots$	$[(90983465/748, 535706341675/748)]$	$1$
199988.f1	199988f1	199988.f	199988f	$2$	$2$	\( 2^{2} \cdot 17^{2} \cdot 173 \)	\( 2^{4} \cdot 17^{6} \cdot 173 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$23528$	$48$	$0$	$23.03121130$	$1$		$1$	$314880$	$1.096592$	$1302642688/173$	$0.88014$	$3.33930$	$[0, -1, 0, -16569, 826358]$	\(y^2=x^3-x^2-16569x+826358\)	2.3.0.a.1, 4.6.0.b.1, 136.12.0.?, 346.6.0.?, 692.24.0.?, $\ldots$	$[(-6570988438/6773, 152264474568396/6773)]$	$1$
249812.f1	249812f1	249812.f	249812f	$2$	$2$	\( 2^{2} \cdot 19^{2} \cdot 173 \)	\( 2^{4} \cdot 19^{6} \cdot 173 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$26296$	$48$	$0$	$1$	$1$		$1$	$438372$	$1.152206$	$1302642688/173$	$0.88014$	$3.33323$	$[0, -1, 0, -20697, -1139062]$	\(y^2=x^3-x^2-20697x-1139062\)	2.3.0.a.1, 4.6.0.b.1, 152.12.0.?, 346.6.0.?, 692.24.0.?, $\ldots$	$[ ]$	$1$
276800.i1	276800i1	276800.i	276800i	$2$	$2$	\( 2^{6} \cdot 5^{2} \cdot 173 \)	\( 2^{10} \cdot 5^{6} \cdot 173 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$6920$	$48$	$0$	$4.996409339$	$1$		$1$	$251904$	$0.831279$	$1302642688/173$	$0.88014$	$2.99861$	$[0, 1, 0, -5733, 165163]$	\(y^2=x^3+x^2-5733x+165163\)	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.3, 346.6.0.?, 692.24.0.?, $\ldots$	$[(797/2, 21125/2)]$	$1$
276800.bt1	276800bt1	276800.bt	276800bt	$2$	$2$	\( 2^{6} \cdot 5^{2} \cdot 173 \)	\( 2^{10} \cdot 5^{6} \cdot 173 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$6920$	$48$	$0$	$1$	$4$	$2$	$1$	$251904$	$0.831279$	$1302642688/173$	$0.88014$	$2.99861$	$[0, -1, 0, -5733, -165163]$	\(y^2=x^3-x^2-5733x-165163\)	2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.3, 346.6.0.?, 692.24.0.?, $\ldots$	$[ ]$	$1$
305172.be1	305172be1	305172.be	305172be	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 173 \)	\( 2^{4} \cdot 3^{6} \cdot 7^{6} \cdot 173 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$29064$	$48$	$0$	$1$	$1$		$1$	$531360$	$1.202248$	$1302642688/173$	$0.88014$	$3.32794$	$[0, 0, 0, -25284, 1547273]$	\(y^2=x^3-25284x+1547273\)	2.3.0.a.1, 4.6.0.b.1, 168.12.0.?, 346.6.0.?, 692.24.0.?, $\ldots$	$[ ]$	$1$
334928.ba1	334928ba1	334928.ba	334928ba	$2$	$2$	\( 2^{4} \cdot 11^{2} \cdot 173 \)	\( 2^{4} \cdot 11^{6} \cdot 173 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$15224$	$48$	$0$	$1$	$1$		$1$	$344400$	$0.878934$	$1302642688/173$	$0.88014$	$2.99863$	$[0, -1, 0, -6937, 224688]$	\(y^2=x^3-x^2-6937x+224688\)	2.3.0.a.1, 4.6.0.b.1, 88.12.0.?, 346.6.0.?, 692.24.0.?, $\ldots$	$[ ]$	$1$
366068.a1	366068a1	366068.a	366068a	$2$	$2$	\( 2^{2} \cdot 23^{2} \cdot 173 \)	\( 2^{4} \cdot 23^{6} \cdot 173 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$31832$	$48$	$0$	$16.43075148$	$1$		$1$	$757680$	$1.247732$	$1302642688/173$	$0.88014$	$3.32329$	$[0, 1, 0, -30329, -2042900]$	\(y^2=x^3+x^2-30329x-2042900\)	2.3.0.a.1, 4.6.0.b.1, 184.12.0.?, 346.6.0.?, 692.24.0.?, $\ldots$	$[(209673772/1019, 346374656732/1019)]$	$1$
467792.w1	467792w1	467792.w	467792w	$2$	$2$	\( 2^{4} \cdot 13^{2} \cdot 173 \)	\( 2^{4} \cdot 13^{6} \cdot 173 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$17992$	$48$	$0$	$1$	$4$	$2$	$1$	$472320$	$0.962461$	$1302642688/173$	$0.88014$	$2.99867$	$[0, -1, 0, -9689, -363832]$	\(y^2=x^3-x^2-9689x-363832\)	2.3.0.a.1, 4.6.0.b.1, 104.12.0.?, 346.6.0.?, 692.24.0.?, $\ldots$	$[ ]$	$1$
478864.a1	478864a1	478864.a	478864a	$2$	$2$	\( 2^{4} \cdot 173^{2} \)	\( 2^{4} \cdot 173^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.24	2B	$1384$	$48$	$0$	$1$	$1$		$1$	$7362288$	$2.256630$	$1302642688/173$	$0.88014$	$4.18069$	$[0, 1, 0, -1715929, -865634250]$	\(y^2=x^3+x^2-1715929x-865634250\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.4, 346.6.0.?, 692.24.0.?, $\ldots$	$[ ]$	$1$

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