Elliptic curve search results

Results (32 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	Weierstrass coefficients	Weierstrass equation	mod-$m$ images
930.j1	930j2	930.j	930j	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 31 \)	\( 2^{13} \cdot 3^{4} \cdot 5 \cdot 31^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$1240$	$12$	$0$	$1$	$1$		$0$	$4160$	$1.481724$	$1152829477932246539641/3188367360$	$[1, 0, 1, -218448, 39279646]$	\(y^2+xy+y=x^3-218448x+39279646\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
2790.v1	2790x2	2790.v	2790x	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 31 \)	\( 2^{13} \cdot 3^{10} \cdot 5 \cdot 31^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$1$	$1$		$0$	$33280$	$2.031029$	$1152829477932246539641/3188367360$	$[1, -1, 1, -1966028, -1060550449]$	\(y^2+xy+y=x^3-x^2-1966028x-1060550449\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
4650.x1	4650bd2	4650.x	4650bd	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 31 \)	\( 2^{13} \cdot 3^{4} \cdot 5^{7} \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$0.396124127$	$1$		$10$	$99840$	$2.286442$	$1152829477932246539641/3188367360$	$[1, 1, 1, -5461188, 4909955781]$	\(y^2+xy+y=x^3+x^2-5461188x+4909955781\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
7440.g1	7440n2	7440.g	7440n	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5 \cdot 31 \)	\( 2^{25} \cdot 3^{4} \cdot 5 \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$14.65163944$	$1$		$1$	$99840$	$2.174870$	$1152829477932246539641/3188367360$	$[0, -1, 0, -3495160, -2513897360]$	\(y^2=x^3-x^2-3495160x-2513897360\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
13950.b1	13950bd2	13950.b	13950bd	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 31 \)	\( 2^{13} \cdot 3^{10} \cdot 5^{7} \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$5.594771259$	$1$		$2$	$798720$	$2.835747$	$1152829477932246539641/3188367360$	$[1, -1, 0, -49150692, -132617956784]$	\(y^2+xy=x^3-x^2-49150692x-132617956784\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
22320.c1	22320bl2	22320.c	22320bl	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 31 \)	\( 2^{25} \cdot 3^{10} \cdot 5 \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$1.884036682$	$1$		$3$	$798720$	$2.724178$	$1152829477932246539641/3188367360$	$[0, 0, 0, -31456443, 67906685162]$	\(y^2=x^3-31456443x+67906685162\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
28830.k1	28830k2	28830.k	28830k	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 31^{2} \)	\( 2^{13} \cdot 3^{4} \cdot 5 \cdot 31^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$53.13606190$	$1$		$0$	$3993600$	$3.198715$	$1152829477932246539641/3188367360$	$[1, 1, 0, -209928067, -1170809725619]$	\(y^2+xy=x^3+x^2-209928067x-1170809725619\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
29760.w1	29760l2	29760.w	29760l	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5 \cdot 31 \)	\( 2^{31} \cdot 3^{4} \cdot 5 \cdot 31^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$1$	$1$		$1$	$798720$	$2.521442$	$1152829477932246539641/3188367360$	$[0, -1, 0, -13980641, 20125159521]$	\(y^2=x^3-x^2-13980641x+20125159521\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
29760.bn1	29760ch2	29760.bn	29760ch	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5 \cdot 31 \)	\( 2^{31} \cdot 3^{4} \cdot 5 \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$8.402275262$	$1$		$3$	$798720$	$2.521442$	$1152829477932246539641/3188367360$	$[0, 1, 0, -13980641, -20125159521]$	\(y^2=x^3+x^2-13980641x-20125159521\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
37200.dy1	37200cx2	37200.dy	37200cx	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 31 \)	\( 2^{25} \cdot 3^{4} \cdot 5^{7} \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$9.994002118$	$1$		$1$	$2396160$	$2.979591$	$1152829477932246539641/3188367360$	$[0, 1, 0, -87379008, -314411928012]$	\(y^2=x^3+x^2-87379008x-314411928012\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
45570.e1	45570d2	45570.e	45570d	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 31 \)	\( 2^{13} \cdot 3^{4} \cdot 5 \cdot 7^{6} \cdot 31^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$1$	$4$	$2$	$0$	$1198080$	$2.454678$	$1152829477932246539641/3188367360$	$[1, 1, 0, -10703928, -13483622592]$	\(y^2+xy=x^3+x^2-10703928x-13483622592\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
86490.cg1	86490ch2	86490.cg	86490ch	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 31^{2} \)	\( 2^{13} \cdot 3^{10} \cdot 5 \cdot 31^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$1$	$1$		$0$	$31948800$	$3.748024$	$1152829477932246539641/3188367360$	$[1, -1, 1, -1889352608, 31609973239107]$	\(y^2+xy+y=x^3-x^2-1889352608x+31609973239107\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
89280.db1	89280fk2	89280.db	89280fk	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 31 \)	\( 2^{31} \cdot 3^{10} \cdot 5 \cdot 31^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$1$	$1$		$1$	$6389760$	$3.070751$	$1152829477932246539641/3188367360$	$[0, 0, 0, -125825772, 543253481296]$	\(y^2=x^3-125825772x+543253481296\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
89280.fx1	89280cy2	89280.fx	89280cy	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 31 \)	\( 2^{31} \cdot 3^{10} \cdot 5 \cdot 31^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$1$	$25$	$5$	$1$	$6389760$	$3.070751$	$1152829477932246539641/3188367360$	$[0, 0, 0, -125825772, -543253481296]$	\(y^2=x^3-125825772x-543253481296\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
111600.gn1	111600eh2	111600.gn	111600eh	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 31 \)	\( 2^{25} \cdot 3^{10} \cdot 5^{7} \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$4.733369564$	$1$		$3$	$19169280$	$3.528896$	$1152829477932246539641/3188367360$	$[0, 0, 0, -786411075, 8488335645250]$	\(y^2=x^3-786411075x+8488335645250\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
112530.cy1	112530dg2	112530.cy	112530dg	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 11^{2} \cdot 31 \)	\( 2^{13} \cdot 3^{4} \cdot 5 \cdot 11^{6} \cdot 31^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$1$	$1$		$0$	$5824000$	$2.680672$	$1152829477932246539641/3188367360$	$[1, 0, 0, -26432150, -52307641308]$	\(y^2+xy=x^3-26432150x-52307641308\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
136710.fr1	136710g2	136710.fr	136710g	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 31 \)	\( 2^{13} \cdot 3^{10} \cdot 5 \cdot 7^{6} \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$1.106956838$	$1$		$6$	$9584640$	$3.003986$	$1152829477932246539641/3188367360$	$[1, -1, 1, -96335357, 363961474629]$	\(y^2+xy+y=x^3-x^2-96335357x+363961474629\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
144150.ea1	144150m2	144150.ea	144150m	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 31^{2} \)	\( 2^{13} \cdot 3^{4} \cdot 5^{7} \cdot 31^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$1$	$1$		$0$	$95846400$	$4.003433$	$1152829477932246539641/3188367360$	$[1, 0, 0, -5248201688, -146340719299008]$	\(y^2+xy=x^3-5248201688x-146340719299008\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
148800.fj1	148800fn2	148800.fj	148800fn	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 31 \)	\( 2^{31} \cdot 3^{4} \cdot 5^{7} \cdot 31^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$1$	$9$	$3$	$1$	$19169280$	$3.326164$	$1152829477932246539641/3188367360$	$[0, -1, 0, -349516033, -2514945908063]$	\(y^2=x^3-x^2-349516033x-2514945908063\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
148800.fz1	148800ha2	148800.fz	148800ha	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 31 \)	\( 2^{31} \cdot 3^{4} \cdot 5^{7} \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$2.967824288$	$1$		$5$	$19169280$	$3.326164$	$1152829477932246539641/3188367360$	$[0, 1, 0, -349516033, 2514945908063]$	\(y^2=x^3+x^2-349516033x+2514945908063\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
157170.cl1	157170q2	157170.cl	157170q	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 13^{2} \cdot 31 \)	\( 2^{13} \cdot 3^{4} \cdot 5 \cdot 13^{6} \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$0.352955174$	$1$		$10$	$9584640$	$2.764198$	$1152829477932246539641/3188367360$	$[1, 0, 0, -36917631, 86334300441]$	\(y^2+xy=x^3-36917631x+86334300441\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
227850.iu1	227850bv2	227850.iu	227850bv	$2$	$2$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 31 \)	\( 2^{13} \cdot 3^{4} \cdot 5^{7} \cdot 7^{6} \cdot 31^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$1$	$1$		$0$	$28753920$	$3.259396$	$1152829477932246539641/3188367360$	$[1, 0, 0, -267598213, -1684917627583]$	\(y^2+xy=x^3-267598213x-1684917627583\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
230640.cr1	230640cr2	230640.cr	230640cr	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5 \cdot 31^{2} \)	\( 2^{25} \cdot 3^{4} \cdot 5 \cdot 31^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$11.47724841$	$1$		$1$	$95846400$	$3.891865$	$1152829477932246539641/3188367360$	$[0, 1, 0, -3358849080, 74925104741460]$	\(y^2=x^3+x^2-3358849080x+74925104741460\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
268770.a1	268770a2	268770.a	268770a	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 17^{2} \cdot 31 \)	\( 2^{13} \cdot 3^{4} \cdot 5 \cdot 17^{6} \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$7.181193086$	$1$		$2$	$21565440$	$2.898331$	$1152829477932246539641/3188367360$	$[1, 1, 0, -63131333, 193044033357]$	\(y^2+xy=x^3+x^2-63131333x+193044033357\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
335730.cs1	335730cs2	335730.cs	335730cs	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 19^{2} \cdot 31 \)	\( 2^{13} \cdot 3^{4} \cdot 5 \cdot 19^{6} \cdot 31^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$1$	$4$	$2$	$0$	$29952000$	$2.953941$	$1152829477932246539641/3188367360$	$[1, 1, 1, -78859555, -269576812735]$	\(y^2+xy+y=x^3+x^2-78859555x-269576812735\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
337590.c1	337590c2	337590.c	337590c	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 31 \)	\( 2^{13} \cdot 3^{10} \cdot 5 \cdot 11^{6} \cdot 31^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$1$	$1$		$0$	$46592000$	$3.229977$	$1152829477932246539641/3188367360$	$[1, -1, 0, -237889350, 1412306315316]$	\(y^2+xy=x^3-x^2-237889350x+1412306315316\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
364560.du1	364560du2	364560.du	364560du	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 31 \)	\( 2^{25} \cdot 3^{4} \cdot 5 \cdot 7^{6} \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$6.517370361$	$1$		$3$	$28753920$	$3.147827$	$1152829477932246539641/3188367360$	$[0, 1, 0, -171262856, 862609320180]$	\(y^2=x^3+x^2-171262856x+862609320180\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
432450.d1	432450d2	432450.d	432450d	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 31^{2} \)	\( 2^{13} \cdot 3^{10} \cdot 5^{7} \cdot 31^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$8.060380223$	$1$		$0$	$766771200$	$4.552742$	$1152829477932246539641/3188367360$	$[1, -1, 0, -47233815192, 3951199421073216]$	\(y^2+xy=x^3-x^2-47233815192x+3951199421073216\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
446400.cc1	446400cc2	446400.cc	446400cc	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 \)	\( 2^{31} \cdot 3^{10} \cdot 5^{7} \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$20.12727379$	$1$		$1$	$153354240$	$3.875469$	$1152829477932246539641/3188367360$	$[0, 0, 0, -3145644300, -67906685162000]$	\(y^2=x^3-3145644300x-67906685162000\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
446400.ru1	446400ru2	446400.ru	446400ru	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 \)	\( 2^{31} \cdot 3^{10} \cdot 5^{7} \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$8.177014255$	$1$		$1$	$153354240$	$3.875469$	$1152829477932246539641/3188367360$	$[0, 0, 0, -3145644300, 67906685162000]$	\(y^2=x^3-3145644300x+67906685162000\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
471510.bo1	471510bo2	471510.bo	471510bo	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 13^{2} \cdot 31 \)	\( 2^{13} \cdot 3^{10} \cdot 5 \cdot 13^{6} \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$17.93094034$	$1$		$0$	$76677120$	$3.313503$	$1152829477932246539641/3188367360$	$[1, -1, 0, -332258679, -2331026111907]$	\(y^2+xy=x^3-x^2-332258679x-2331026111907\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?
491970.q1	491970q2	491970.q	491970q	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 23^{2} \cdot 31 \)	\( 2^{13} \cdot 3^{4} \cdot 5 \cdot 23^{6} \cdot 31^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$1$	$1$		$0$	$49420800$	$3.049469$	$1152829477932246539641/3188367360$	$[1, 0, 1, -115558739, -478146573394]$	\(y^2+xy+y=x^3-115558739x-478146573394\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?