Elliptic curves over $\Q$ of conductor 890

Results (16 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
890.a1	890b2	890.a	890b	$2$	$2$	\( 2 \cdot 5 \cdot 89 \)	\( 2^{2} \cdot 5 \cdot 89^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$1780$	$12$	$0$	$0.851103202$	$1$		$6$	$192$	$-0.088189$	$141339344329/158420$	$0.87673$	$3.78053$	$[1, 0, 1, -109, -444]$	\(y^2+xy+y=x^3-109x-444\)	2.3.0.a.1, 10.6.0.a.1, 356.6.0.?, 1780.12.0.?	$[(-6, 3)]$
890.a2	890b1	890.a	890b	$2$	$2$	\( 2 \cdot 5 \cdot 89 \)	\( 2^{4} \cdot 5^{2} \cdot 89 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$1780$	$12$	$0$	$0.425551601$	$1$		$9$	$96$	$-0.434763$	$68417929/35600$	$0.82844$	$2.65654$	$[1, 0, 1, -9, -4]$	\(y^2+xy+y=x^3-9x-4\)	2.3.0.a.1, 20.6.0.c.1, 178.6.0.?, 1780.12.0.?	$[(-2, 3)]$
890.b1	890e1	890.b	890e	$2$	$2$	\( 2 \cdot 5 \cdot 89 \)	\( 2^{12} \cdot 5^{4} \cdot 89 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.21	2B	$712$	$48$	$0$	$0.880929457$	$1$		$7$	$576$	$0.507392$	$162780279643801/227840000$	$0.93075$	$4.81849$	$[1, 0, 1, -1138, -14844]$	\(y^2+xy+y=x^3-1138x-14844\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.3, 178.6.0.?, 356.24.0.?, $\ldots$	$[(-20, 7)]$
890.b2	890e2	890.b	890e	$2$	$2$	\( 2 \cdot 5 \cdot 89 \)	\( - 2^{6} \cdot 5^{8} \cdot 89^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.12	2B	$712$	$48$	$0$	$0.440464728$	$1$		$12$	$1152$	$0.853965$	$-60425492474521/198025000000$	$0.95315$	$4.95183$	$[1, 0, 1, -818, -23292]$	\(y^2+xy+y=x^3-818x-23292\)	2.3.0.a.1, 4.12.0-4.a.1.1, 356.24.0.?, 712.48.0.?	$[(69, 465)]$
890.c1	890a2	890.c	890a	$2$	$2$	\( 2 \cdot 5 \cdot 89 \)	\( 2 \cdot 5 \cdot 89^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$3560$	$12$	$0$	$1.025400975$	$1$		$4$	$128$	$-0.206056$	$18588565449/79210$	$0.96908$	$3.48182$	$[1, -1, 0, -55, 171]$	\(y^2+xy=x^3-x^2-55x+171\)	2.3.0.a.1, 40.6.0.b.1, 356.6.0.?, 3560.12.0.?	$[(5, -1)]$
890.c2	890a1	890.c	890a	$2$	$2$	\( 2 \cdot 5 \cdot 89 \)	\( 2^{2} \cdot 5^{2} \cdot 89 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$3560$	$12$	$0$	$0.512700487$	$1$		$7$	$64$	$-0.552629$	$15438249/8900$	$1.07701$	$2.43732$	$[1, -1, 0, -5, 1]$	\(y^2+xy=x^3-x^2-5x+1\)	2.3.0.a.1, 40.6.0.c.1, 178.6.0.?, 3560.12.0.?	$[(0, 1)]$
890.d1	890d1	890.d	890d	$1$	$1$	\( 2 \cdot 5 \cdot 89 \)	\( - 2^{3} \cdot 5 \cdot 89 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$3560$	$2$	$0$	$0.449162415$	$1$		$4$	$72$	$-0.518641$	$-217081801/3560$	$0.80433$	$2.83067$	$[1, 0, 1, -13, 16]$	\(y^2+xy+y=x^3-13x+16\)	3560.2.0.?	$[(2, -1)]$
890.e1	890c2	890.e	890c	$2$	$2$	\( 2 \cdot 5 \cdot 89 \)	\( 2 \cdot 5^{4} \cdot 89^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.6	2B	$712$	$12$	$0$	$1$	$1$		$0$	$896$	$0.706430$	$32795348404864969/9901250$	$0.96080$	$5.59974$	$[1, 1, 0, -6668, 206822]$	\(y^2+xy=x^3+x^2-6668x+206822\)	2.3.0.a.1, 8.6.0.b.1, 356.6.0.?, 712.12.0.?	$[]$
890.e2	890c1	890.e	890c	$2$	$2$	\( 2 \cdot 5 \cdot 89 \)	\( 2^{2} \cdot 5^{8} \cdot 89 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.1	2B	$712$	$12$	$0$	$1$	$1$		$1$	$448$	$0.359857$	$8107275964969/139062500$	$0.91053$	$4.37679$	$[1, 1, 0, -418, 3072]$	\(y^2+xy=x^3+x^2-418x+3072\)	2.3.0.a.1, 8.6.0.c.1, 178.6.0.?, 712.12.0.?	$[]$
890.f1	890f1	890.f	890f	$1$	$1$	\( 2 \cdot 5 \cdot 89 \)	\( - 2^{13} \cdot 5 \cdot 89 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$3560$	$2$	$0$	$0.090346383$	$1$		$10$	$312$	$-0.060440$	$206425071/3645440$	$1.00372$	$3.31758$	$[1, -1, 1, 12, 87]$	\(y^2+xy+y=x^3-x^2+12x+87\)	3560.2.0.?	$[(5, 13)]$
890.g1	890g2	890.g	890g	$2$	$5$	\( 2 \cdot 5 \cdot 89 \)	\( - 2 \cdot 5 \cdot 89^{5} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$5$	5.24.0.3	5B.1.2	$3560$	$48$	$1$	$7.965230967$	$1$		$0$	$1000$	$0.817688$	$-938917686360961/55840594490$	$0.94287$	$5.09092$	$[1, 1, 1, -2040, -38093]$	\(y^2+xy+y=x^3+x^2-2040x-38093\)	5.24.0-5.a.2.2, 3560.48.1.?	$[(1915/6, 12823/6)]$
890.g2	890g1	890.g	890g	$2$	$5$	\( 2 \cdot 5 \cdot 89 \)	\( - 2^{5} \cdot 5^{5} \cdot 89 \)	$1$	$\Z/5\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$5$	5.24.0.1	5B.1.1	$3560$	$48$	$1$	$1.593046193$	$1$		$12$	$200$	$0.012969$	$109902239/8900000$	$0.90965$	$3.45286$	$[1, 1, 1, 10, 147]$	\(y^2+xy+y=x^3+x^2+10x+147\)	5.24.0-5.a.1.2, 3560.48.1.?	$[(-5, 3)]$
890.h1	890h3	890.h	890h	$4$	$4$	\( 2 \cdot 5 \cdot 89 \)	\( 2^{2} \cdot 5^{8} \cdot 89 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.57	2B	$7120$	$192$	$3$	$1$	$1$		$0$	$640$	$0.566391$	$772635063744081/139062500$	$1.00068$	$5.04781$	$[1, -1, 1, -1912, -31689]$	\(y^2+xy+y=x^3-x^2-1912x-31689\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.o.1.3, 80.48.0.?, 178.6.0.?, $\ldots$	$[]$
890.h2	890h2	890.h	890h	$4$	$4$	\( 2 \cdot 5 \cdot 89 \)	\( 2^{4} \cdot 5^{4} \cdot 89^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.24.0.7	2Cs	$3560$	$192$	$3$	$1$	$1$		$2$	$320$	$0.219818$	$252555814161/79210000$	$1.04647$	$3.86601$	$[1, -1, 1, -132, -361]$	\(y^2+xy+y=x^3-x^2-132x-361\)	2.6.0.a.1, 4.24.0-4.a.1.1, 40.48.0-40.k.1.2, 356.48.0.?, 712.96.0.?, $\ldots$	$[]$
890.h3	890h1	890.h	890h	$4$	$4$	\( 2 \cdot 5 \cdot 89 \)	\( 2^{8} \cdot 5^{2} \cdot 89 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.47	2B	$7120$	$192$	$3$	$1$	$1$		$3$	$160$	$-0.126756$	$15271450641/569600$	$0.87612$	$3.45288$	$[1, -1, 1, -52, 151]$	\(y^2+xy+y=x^3-x^2-52x+151\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.o.1.1, 80.48.0.?, 178.6.0.?, $\ldots$	$[]$
890.h4	890h4	890.h	890h	$4$	$4$	\( 2 \cdot 5 \cdot 89 \)	\( - 2^{2} \cdot 5^{2} \cdot 89^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.24.0.11	2B	$7120$	$192$	$3$	$1$	$4$	$2$	$2$	$640$	$0.566391$	$5525519137839/6274224100$	$0.95675$	$4.32034$	$[1, -1, 1, 368, -2761]$	\(y^2+xy+y=x^3-x^2+368x-2761\)	2.3.0.a.1, 4.24.0-4.d.1.1, 20.48.0-20.d.1.2, 712.48.0.?, 1424.96.0.?, $\ldots$	$[]$