Elliptic curves over $\Q$ of conductor 5010

Results (17 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
5010.a1	5010a2	5010.a	5010a	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 167 \)	\( 2^{7} \cdot 3^{6} \cdot 5^{10} \cdot 167 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$20040$	$12$	$0$	$1$	$1$		$0$	$30240$	$1.642057$	$156406207396688718841/152178750000000$	$0.98374$	$5.45815$	$[1, 1, 0, -112247, -14509419]$	\(y^2+xy=x^3+x^2-112247x-14509419\)	2.3.0.a.1, 60.6.0.c.1, 1336.6.0.?, 20040.12.0.?	$[]$
5010.a2	5010a1	5010.a	5010a	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 167 \)	\( - 2^{14} \cdot 3^{3} \cdot 5^{5} \cdot 167^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$20040$	$12$	$0$	$1$	$1$		$1$	$15120$	$1.295485$	$-17101922279625721/38553753600000$	$0.96304$	$4.57394$	$[1, 1, 0, -5367, -337131]$	\(y^2+xy=x^3+x^2-5367x-337131\)	2.3.0.a.1, 30.6.0.a.1, 1336.6.0.?, 20040.12.0.?	$[]$
5010.b1	5010b1	5010.b	5010b	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 167 \)	\( - 2 \cdot 3^{3} \cdot 5 \cdot 167 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$20040$	$2$	$0$	$1$	$1$		$0$	$864$	$-0.426844$	$1685159/45090$	$0.81219$	$2.13040$	$[1, 1, 0, 3, -9]$	\(y^2+xy=x^3+x^2+3x-9\)	20040.2.0.?	$[]$
5010.c1	5010d2	5010.c	5010d	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 167 \)	\( 2 \cdot 3^{7} \cdot 5^{8} \cdot 167^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$4008$	$12$	$0$	$0.651187226$	$1$		$6$	$21504$	$1.386526$	$1046819248735488409/47650971093750$	$0.96370$	$4.87045$	$[1, 0, 1, -21154, 1134902]$	\(y^2+xy+y=x^3-21154x+1134902\)	2.3.0.a.1, 24.6.0.a.1, 668.6.0.?, 4008.12.0.?	$[(28, 737)]$
5010.c2	5010d1	5010.c	5010d	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 167 \)	\( - 2^{2} \cdot 3^{14} \cdot 5^{4} \cdot 167 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$4008$	$12$	$0$	$0.325593613$	$1$		$11$	$10752$	$1.039953$	$40675641638471/1996889557500$	$1.14741$	$4.19822$	$[1, 0, 1, 716, 67646]$	\(y^2+xy+y=x^3+716x+67646\)	2.3.0.a.1, 24.6.0.d.1, 334.6.0.?, 4008.12.0.?	$[(-17, 233)]$
5010.d1	5010c1	5010.d	5010c	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 167 \)	\( - 2^{8} \cdot 3^{2} \cdot 5 \cdot 167 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1670$	$2$	$0$	$0.321007274$	$1$		$4$	$1920$	$0.143117$	$-2796665386969/1923840$	$0.88451$	$3.36424$	$[1, 0, 1, -294, 1912]$	\(y^2+xy+y=x^3-294x+1912\)	1670.2.0.?	$[(5, 21)]$
5010.e1	5010e3	5010.e	5010e	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 167 \)	\( 2 \cdot 3^{12} \cdot 5^{4} \cdot 167 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.8	2B	$20040$	$48$	$0$	$1$	$1$		$0$	$7296$	$0.855887$	$1116093485689489/110938308750$	$0.92895$	$4.06712$	$[1, 1, 1, -2161, 34289]$	\(y^2+xy+y=x^3+x^2-2161x+34289\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 120.24.0.?, 668.12.0.?, $\ldots$	$[]$
5010.e2	5010e2	5010.e	5010e	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 167 \)	\( 2^{2} \cdot 3^{6} \cdot 5^{2} \cdot 167^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.1	2Cs	$20040$	$48$	$0$	$1$	$1$		$2$	$3648$	$0.509314$	$13092526729009/2033108100$	$0.95621$	$3.54530$	$[1, 1, 1, -491, -3787]$	\(y^2+xy+y=x^3+x^2-491x-3787\)	2.6.0.a.1, 8.12.0-2.a.1.1, 60.12.0-2.a.1.1, 120.24.0.?, 668.12.0.?, $\ldots$	$[]$
5010.e3	5010e1	5010.e	5010e	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 167 \)	\( 2^{4} \cdot 3^{3} \cdot 5 \cdot 167 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.12	2B	$20040$	$48$	$0$	$1$	$1$		$1$	$1824$	$0.162740$	$11556972012529/360720$	$0.89560$	$3.53065$	$[1, 1, 1, -471, -4131]$	\(y^2+xy+y=x^3+x^2-471x-4131\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 60.12.0-4.c.1.2, 120.24.0.?, $\ldots$	$[]$
5010.e4	5010e4	5010.e	5010e	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 167 \)	\( - 2 \cdot 3^{3} \cdot 5 \cdot 167^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.7	2B	$20040$	$48$	$0$	$1$	$4$	$2$	$0$	$7296$	$0.855887$	$70092508729391/210005006670$	$0.93642$	$3.91005$	$[1, 1, 1, 859, -19447]$	\(y^2+xy+y=x^3+x^2+859x-19447\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 60.12.0-4.c.1.1, 120.24.0.?, $\ldots$	$[]$
5010.f1	5010f1	5010.f	5010f	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 167 \)	\( - 2^{4} \cdot 3^{6} \cdot 5 \cdot 167 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1670$	$2$	$0$	$0.350671163$	$1$		$4$	$1344$	$0.022768$	$1524845951/9739440$	$0.86272$	$2.75278$	$[1, 1, 1, 24, 153]$	\(y^2+xy+y=x^3+x^2+24x+153\)	1670.2.0.?	$[(7, 23)]$
5010.g1	5010g4	5010.g	5010g	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 167 \)	\( 2^{2} \cdot 3 \cdot 5^{8} \cdot 167 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$4008$	$48$	$0$	$4.257602131$	$1$		$0$	$6144$	$0.896970$	$135518735544698449/782812500$	$1.00003$	$4.63047$	$[1, 0, 0, -10701, 425181]$	\(y^2+xy=x^3-10701x+425181\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.1, 24.24.0-24.ba.1.12, $\ldots$	$[(550/3, -293/3)]$
5010.g2	5010g3	5010.g	5010g	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 167 \)	\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 167^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$4008$	$48$	$0$	$4.257602131$	$1$		$2$	$6144$	$0.896970$	$1147369112034769/233338896300$	$0.93217$	$4.07037$	$[1, 0, 0, -2181, -31755]$	\(y^2+xy=x^3-2181x-31755\)	2.3.0.a.1, 4.12.0-4.c.1.2, 12.24.0-12.h.1.1, 1336.24.0.?, 4008.48.0.?	$[(74, 425)]$
5010.g3	5010g2	5010.g	5010g	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 167 \)	\( 2^{4} \cdot 3^{2} \cdot 5^{4} \cdot 167^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$2004$	$48$	$0$	$2.128801065$	$1$		$6$	$3072$	$0.550396$	$34930508298769/2510010000$	$0.90547$	$3.66049$	$[1, 0, 0, -681, 6345]$	\(y^2+xy=x^3-681x+6345\)	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.2, 668.24.0.?, 2004.48.0.?	$[(24, 51)]$
5010.g4	5010g1	5010.g	5010g	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 167 \)	\( - 2^{8} \cdot 3^{4} \cdot 5^{2} \cdot 167 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$4008$	$48$	$0$	$1.064400532$	$1$		$11$	$1536$	$0.203822$	$6549699311/86572800$	$0.89046$	$3.01513$	$[1, 0, 0, 39, 441]$	\(y^2+xy=x^3+39x+441\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.ba.1.8, 334.6.0.?, 668.24.0.?, $\ldots$	$[(0, 21)]$
5010.h1	5010h2	5010.h	5010h	$2$	$7$	\( 2 \cdot 3 \cdot 5 \cdot 167 \)	\( - 2 \cdot 3 \cdot 5 \cdot 167^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.5	7B.1.3	$140280$	$96$	$2$	$1$	$49$	$7$	$0$	$65856$	$2.065693$	$-6093832136609347161121/108676727597808690$	$0.99714$	$5.89163$	$[1, 0, 0, -380530, -91764010]$	\(y^2+xy=x^3-380530x-91764010\)	7.48.0-7.a.2.2, 20040.2.0.?, 140280.96.2.?	$[]$
5010.h2	5010h1	5010.h	5010h	$2$	$7$	\( 2 \cdot 3 \cdot 5 \cdot 167 \)	\( - 2^{7} \cdot 3^{7} \cdot 5^{7} \cdot 167 \)	$0$	$\Z/7\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.1	7B.1.1	$140280$	$96$	$2$	$1$	$1$		$6$	$9408$	$1.092737$	$-358531401121921/3652290000000$	$0.96117$	$4.27697$	$[1, 0, 0, -1480, 94400]$	\(y^2+xy=x^3-1480x+94400\)	7.48.0-7.a.1.2, 20040.2.0.?, 140280.96.2.?	$[]$