Elliptic curve search results

Results (15 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
6630.v1	6630w7	6630.v	6630w	$8$	$12$	\( 2 \cdot 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 2^{2} \cdot 3^{2} \cdot 5^{6} \cdot 13^{3} \cdot 17^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	4.12.0.8, 3.8.0.2	2B, 3B.1.2	$5304$	$384$	$5$	$15.20405663$	$1$		$0$	$3317760$	$3.774197$	$31664865542564944883878115208137569/103216295812500$	$1.05921$	$9.02799$	$2$	$[1, 0, 0, -6591000006, -205956849489264]$	\(y^2+xy=x^3-6591000006x-205956849489264\)	2.3.0.a.1, 3.8.0-3.a.1.1, 4.12.0-4.c.1.2, 6.24.0-6.a.1.2, 12.96.0-12.c.4.6, $\ldots$	$[(79462424/19, 650248165832/19)]$	$1$
19890.n1	19890r7	19890.n	19890r	$8$	$12$	\( 2 \cdot 3^{2} \cdot 5 \cdot 13 \cdot 17 \)	\( 2^{2} \cdot 3^{8} \cdot 5^{6} \cdot 13^{3} \cdot 17^{4} \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.6.0.1, 3.8.0.1	2B, 3B.1.1	$5304$	$384$	$5$	$1$	$1$		$4$	$26542080$	$4.323502$	$31664865542564944883878115208137569/103216295812500$	$1.05921$	$8.69190$	$2$	$[1, -1, 0, -59319000054, 5560834936210128]$	\(y^2+xy=x^3-x^2-59319000054x+5560834936210128\)	2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.c.1, 6.24.0-6.a.1.4, 12.96.0-12.c.4.5, $\ldots$	$[ ]$	$1$
33150.l1	33150b8	33150.l	33150b	$8$	$12$	\( 2 \cdot 3 \cdot 5^{2} \cdot 13 \cdot 17 \)	\( 2^{2} \cdot 3^{2} \cdot 5^{12} \cdot 13^{3} \cdot 17^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.6.0.1, 3.4.0.1	2B, 3B	$26520$	$384$	$5$	$131.7002867$	$1$		$0$	$79626240$	$4.578918$	$31664865542564944883878115208137569/103216295812500$	$1.05921$	$8.55979$	$2$	$[1, 1, 0, -164775000150, -25744606186158000]$	\(y^2+xy=x^3+x^2-164775000150x-25744606186158000\)	2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.48.0.c.4, $\ldots$	$[(105983730270605665109991911242150074348244356917885700345005/343885001081919872460278813, 30042914455247178716596755185056271765363144600483983123434560483510268537785511079681455/343885001081919872460278813)]$	$1$
53040.s1	53040bp8	53040.s	53040bp	$8$	$12$	\( 2^{4} \cdot 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 2^{14} \cdot 3^{2} \cdot 5^{6} \cdot 13^{3} \cdot 17^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.12.0.7, 3.4.0.1	2B, 3B	$5304$	$384$	$5$	$1$	$4$	$2$	$3$	$79626240$	$4.467346$	$31664865542564944883878115208137569/103216295812500$	$1.05921$	$8.06691$	$1$	$[0, -1, 0, -105456000096, 13181238367312896]$	\(y^2=x^3-x^2-105456000096x+13181238367312896\)	2.3.0.a.1, 3.4.0.a.1, 4.12.0-4.c.1.1, 6.12.0.a.1, 12.96.0-12.c.4.8, $\ldots$	$[ ]$	$1$
86190.bm1	86190bm8	86190.bm	86190bm	$8$	$12$	\( 2 \cdot 3 \cdot 5 \cdot 13^{2} \cdot 17 \)	\( 2^{2} \cdot 3^{2} \cdot 5^{6} \cdot 13^{9} \cdot 17^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.12.0.8, 3.4.0.1	2B, 3B	$5304$	$384$	$5$	$1$	$9$	$3$	$0$	$557383680$	$5.056671$	$31664865542564944883878115208137569/103216295812500$	$1.05921$	$8.34456$	$2$	$[1, 0, 1, -1113879001018, -452486084448911992]$	\(y^2+xy+y=x^3-1113879001018x-452486084448911992\)	2.3.0.a.1, 3.4.0.a.1, 4.12.0-4.c.1.2, 6.24.0-6.a.1.3, 12.96.0-12.c.4.3, $\ldots$	$[ ]$	$1$
99450.dq1	99450cr8	99450.dq	99450cr	$8$	$12$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 \cdot 17 \)	\( 2^{2} \cdot 3^{8} \cdot 5^{12} \cdot 13^{3} \cdot 17^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.6.0.1, 3.4.0.1	2B, 3B	$26520$	$384$	$5$	$1$	$9$	$3$	$0$	$637009920$	$5.128220$	$31664865542564944883878115208137569/103216295812500$	$1.05921$	$8.31541$	$2$	$[1, -1, 1, -1482975001355, 695102884051264647]$	\(y^2+xy+y=x^3-x^2-1482975001355x+695102884051264647\)	2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.48.0.c.4, $\ldots$	$[ ]$	$1$
112710.cj1	112710cj8	112710.cj	112710cj	$8$	$12$	\( 2 \cdot 3 \cdot 5 \cdot 13 \cdot 17^{2} \)	\( 2^{2} \cdot 3^{2} \cdot 5^{6} \cdot 13^{3} \cdot 17^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.12.0.6, 3.4.0.1	2B, 3B	$5304$	$384$	$5$	$1$	$16$	$2$	$0$	$955514880$	$5.190804$	$31664865542564944883878115208137569/103216295812500$	$1.05921$	$8.29050$	$2$	$[1, 1, 1, -1904799001740, -1011864096741752295]$	\(y^2+xy+y=x^3+x^2-1904799001740x-1011864096741752295\)	2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 8.12.0-4.c.1.5, $\ldots$	$[ ]$	$1$
159120.ek1	159120z8	159120.ek	159120z	$8$	$12$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 13 \cdot 17 \)	\( 2^{14} \cdot 3^{8} \cdot 5^{6} \cdot 13^{3} \cdot 17^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.6.0.1, 3.4.0.1	2B, 3B	$5304$	$384$	$5$	$14.81749754$	$1$		$1$	$637009920$	$5.016647$	$31664865542564944883878115208137569/103216295812500$	$1.05921$	$7.87732$	$2$	$[0, 0, 0, -949104000867, -355892486813447326]$	\(y^2=x^3-949104000867x-355892486813447326\)	2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.96.0-12.c.4.7, $\ldots$	$[(12659438503/29, 1421305513705350/29)]$	$1$
212160.cc1	212160gf8	212160.cc	212160gf	$8$	$12$	\( 2^{6} \cdot 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 2^{20} \cdot 3^{2} \cdot 5^{6} \cdot 13^{3} \cdot 17^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.12.0.7, 3.4.0.1	2B, 3B	$5304$	$384$	$5$	$35.16816281$	$1$		$1$	$637009920$	$4.813919$	$31664865542564944883878115208137569/103216295812500$	$1.05921$	$7.49421$	$2$	$[0, -1, 0, -421824000385, -105449485114502783]$	\(y^2=x^3-x^2-421824000385x-105449485114502783\)	2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 8.12.0-4.c.1.3, $\ldots$	$[(56035845267671163/143891, 12840739624140815013331180/143891)]$	$1$
212160.hq1	212160z7	212160.hq	212160z	$8$	$12$	\( 2^{6} \cdot 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 2^{20} \cdot 3^{2} \cdot 5^{6} \cdot 13^{3} \cdot 17^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.12.0.8, 3.4.0.1	2B, 3B	$5304$	$384$	$5$	$11.89126990$	$1$		$1$	$637009920$	$4.813919$	$31664865542564944883878115208137569/103216295812500$	$1.05921$	$7.49421$	$2$	$[0, 1, 0, -421824000385, 105449485114502783]$	\(y^2=x^3+x^2-421824000385x+105449485114502783\)	2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 8.12.0-4.c.1.4, $\ldots$	$[(5310224021/119, 22053784500/119)]$	$1$
258570.ef1	258570ef7	258570.ef	258570ef	$8$	$12$	\( 2 \cdot 3^{2} \cdot 5 \cdot 13^{2} \cdot 17 \)	\( 2^{2} \cdot 3^{8} \cdot 5^{6} \cdot 13^{9} \cdot 17^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.6.0.1, 3.4.0.1	2B, 3B	$5304$	$384$	$5$	$22.46181176$	$1$		$0$	$4459069440$	$5.605980$	$31664865542564944883878115208137569/103216295812500$	$1.05921$	$8.13789$	$2$	$[1, -1, 1, -10024911009158, 12217124280120623777]$	\(y^2+xy+y=x^3-x^2-10024911009158x+12217124280120623777\)	2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.24.0-6.a.1.1, 12.96.0-12.c.4.4, $\ldots$	$[(-15804073218099/4841, 490255287992404069949/4841)]$	$1$
265200.dz1	265200dz7	265200.dz	265200dz	$8$	$12$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13 \cdot 17 \)	\( 2^{14} \cdot 3^{2} \cdot 5^{12} \cdot 13^{3} \cdot 17^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.6.0.1, 3.4.0.1	2B, 3B	$26520$	$384$	$5$	$36.15811878$	$1$		$1$	$1911029760$	$5.272064$	$31664865542564944883878115208137569/103216295812500$	$1.05921$	$7.80053$	$2$	$[0, 1, 0, -2636400002408, 1647649523114107188]$	\(y^2=x^3+x^2-2636400002408x+1647649523114107188\)	2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.48.0.c.4, $\ldots$	$[(414072431860180444/391181, 226576240615305000830213154/391181)]$	$1$
324870.el1	324870el7	324870.el	324870el	$8$	$12$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 2^{2} \cdot 3^{2} \cdot 5^{6} \cdot 7^{6} \cdot 13^{3} \cdot 17^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.6.0.1, 3.4.0.1	2B, 3B	$37128$	$384$	$5$	$1$	$4$	$2$	$0$	$955514880$	$4.747154$	$31664865542564944883878115208137569/103216295812500$	$1.05921$	$7.17947$	$2$	$[1, 1, 1, -322959000295, 70642876415817257]$	\(y^2+xy+y=x^3+x^2-322959000295x+70642876415817257\)	2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.48.0.c.4, $\ldots$	$[ ]$	$1$
338130.y1	338130y7	338130.y	338130y	$8$	$12$	\( 2 \cdot 3^{2} \cdot 5 \cdot 13 \cdot 17^{2} \)	\( 2^{2} \cdot 3^{8} \cdot 5^{6} \cdot 13^{3} \cdot 17^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.6.0.1, 3.4.0.1	2B, 3B	$5304$	$384$	$5$	$8.414395627$	$1$		$0$	$7644119040$	$5.740112$	$31664865542564944883878115208137569/103216295812500$	$1.05921$	$8.09284$	$2$	$[1, -1, 0, -17143191015660, 27320313468836296300]$	\(y^2+xy=x^3-x^2-17143191015660x+27320313468836296300\)	2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.48.0.c.4, $\ldots$	$[(862649276/19, 7794458570/19)]$	$1$
430950.ep1	430950ep8	430950.ep	430950ep	$8$	$12$	\( 2 \cdot 3 \cdot 5^{2} \cdot 13^{2} \cdot 17 \)	\( 2^{2} \cdot 3^{2} \cdot 5^{12} \cdot 13^{9} \cdot 17^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.6.0.1, 3.4.0.1	2B, 3B	$26520$	$384$	$5$	$1$	$144$	$2, 3$	$0$	$13377208320$	$5.861389$	$31664865542564944883878115208137569/103216295812500$	$1.05921$	$8.05371$	$2$	$[1, 1, 1, -27846975025438, -56560760556113998969]$	\(y^2+xy+y=x^3+x^2-27846975025438x-56560760556113998969\)	2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 12.48.0.c.4, $\ldots$	$[ ]$	$1$

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