Elliptic curves over $\Q$ of conductor 2480

The results below are complete, since the LMFDB contains all elliptic curves with conductor at most 500000

Results (29 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
2480.a1	2480g1	2480.a	2480g	$1$	$1$	\( 2^{4} \cdot 5 \cdot 31 \)	\( - 2^{8} \cdot 5^{5} \cdot 31^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$310$	$2$	$0$	$0.126347020$	$1$		$6$	$6720$	$1.205755$	$-24560689104608256/93096875$	$1.02659$	$5.53800$	$1$	$[0, 0, 0, -38452, 2902204]$	\(y^2=x^3-38452x+2902204\)	310.2.0.?	$[(153, 775)]$	$1$
2480.b1	2480j2	2480.b	2480j	$2$	$2$	\( 2^{4} \cdot 5 \cdot 31 \)	\( 2^{12} \cdot 5 \cdot 31^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$620$	$12$	$0$	$0.608225200$	$1$		$21$	$1024$	$0.277544$	$1948441249/4805$	$0.86747$	$3.80092$	$1$	$[0, 1, 0, -416, 3124]$	\(y^2=x^3+x^2-416x+3124\)	2.3.0.a.1, 10.6.0.a.1, 124.6.0.?, 620.12.0.?	$[(10, 8), (12, 2)]$	$1$
2480.b2	2480j1	2480.b	2480j	$2$	$2$	\( 2^{4} \cdot 5 \cdot 31 \)	\( - 2^{12} \cdot 5^{2} \cdot 31 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$620$	$12$	$0$	$0.608225200$	$1$		$23$	$512$	$-0.069030$	$-117649/775$	$0.89386$	$2.87993$	$1$	$[0, 1, 0, -16, 84]$	\(y^2=x^3+x^2-16x+84\)	2.3.0.a.1, 20.6.0.c.1, 62.6.0.b.1, 620.12.0.?	$[(2, 8), (10, 32)]$	$1$
2480.c1	2480l2	2480.c	2480l	$2$	$2$	\( 2^{4} \cdot 5 \cdot 31 \)	\( 2^{15} \cdot 5^{2} \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$248$	$12$	$0$	$0.390137886$	$1$		$11$	$2304$	$0.978086$	$133974081659809/192200$	$0.95835$	$5.22599$	$1$	$[0, 1, 0, -17056, 851700]$	\(y^2=x^3+x^2-17056x+851700\)	2.3.0.a.1, 8.6.0.b.1, 124.6.0.?, 248.12.0.?	$[(74, 16)]$	$1$
2480.c2	2480l1	2480.c	2480l	$2$	$2$	\( 2^{4} \cdot 5 \cdot 31 \)	\( - 2^{18} \cdot 5^{4} \cdot 31 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$248$	$12$	$0$	$0.780275773$	$1$		$9$	$1152$	$0.631513$	$-31824875809/1240000$	$0.89741$	$4.16663$	$1$	$[0, 1, 0, -1056, 13300]$	\(y^2=x^3+x^2-1056x+13300\)	2.3.0.a.1, 8.6.0.c.1, 62.6.0.b.1, 248.12.0.?	$[(12, 50)]$	$1$
2480.d1	2480c2	2480.d	2480c	$2$	$2$	\( 2^{4} \cdot 5 \cdot 31 \)	\( 2^{10} \cdot 5 \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$620$	$12$	$0$	$0.707481780$	$1$		$7$	$384$	$0.042985$	$96550276/4805$	$0.93799$	$3.23913$	$1$	$[0, 1, 0, -96, -380]$	\(y^2=x^3+x^2-96x-380\)	2.3.0.a.1, 10.6.0.a.1, 124.6.0.?, 620.12.0.?	$[(-6, 4)]$	$1$
2480.d2	2480c1	2480.d	2480c	$2$	$2$	\( 2^{4} \cdot 5 \cdot 31 \)	\( - 2^{8} \cdot 5^{2} \cdot 31 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$620$	$12$	$0$	$1.414963561$	$1$		$7$	$192$	$-0.303588$	$21296/775$	$0.76112$	$2.51237$	$1$	$[0, 1, 0, 4, -20]$	\(y^2=x^3+x^2+4x-20\)	2.3.0.a.1, 20.6.0.c.1, 62.6.0.b.1, 620.12.0.?	$[(6, 16)]$	$1$
2480.e1	2480d1	2480.e	2480d	$2$	$2$	\( 2^{4} \cdot 5 \cdot 31 \)	\( 2^{4} \cdot 5^{3} \cdot 31^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$620$	$12$	$0$	$1$	$1$		$1$	$480$	$-0.104249$	$212629504/120125$	$0.91990$	$2.80804$	$1$	$[0, 1, 0, -31, 0]$	\(y^2=x^3+x^2-31x\)	2.3.0.a.1, 10.6.0.a.1, 124.6.0.?, 620.12.0.?	$[ ]$	$1$
2480.e2	2480d2	2480.e	2480d	$2$	$2$	\( 2^{4} \cdot 5 \cdot 31 \)	\( - 2^{8} \cdot 5^{6} \cdot 31 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$620$	$12$	$0$	$1$	$1$		$1$	$960$	$0.242325$	$817036976/484375$	$0.89899$	$3.33500$	$1$	$[0, 1, 0, 124, 124]$	\(y^2=x^3+x^2+124x+124\)	2.3.0.a.1, 20.6.0.c.1, 62.6.0.b.1, 620.12.0.?	$[ ]$	$1$
2480.f1	2480h1	2480.f	2480h	$2$	$3$	\( 2^{4} \cdot 5 \cdot 31 \)	\( - 2^{8} \cdot 5 \cdot 31 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1860$	$16$	$0$	$1$	$1$		$0$	$288$	$-0.146540$	$-449511424/155$	$0.89260$	$3.25862$	$1$	$[0, -1, 0, -101, -359]$	\(y^2=x^3-x^2-101x-359\)	3.4.0.a.1, 12.8.0-3.a.1.1, 310.2.0.?, 930.8.0.?, 1860.16.0.?	$[ ]$	$1$
2480.f2	2480h2	2480.f	2480h	$2$	$3$	\( 2^{4} \cdot 5 \cdot 31 \)	\( - 2^{8} \cdot 5^{3} \cdot 31^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1860$	$16$	$0$	$1$	$1$		$0$	$864$	$0.402767$	$87228416/3723875$	$0.99928$	$3.59730$	$1$	$[0, -1, 0, 59, -1495]$	\(y^2=x^3-x^2+59x-1495\)	3.4.0.a.1, 12.8.0-3.a.1.2, 310.2.0.?, 930.8.0.?, 1860.16.0.?	$[ ]$	$1$
2480.g1	2480a2	2480.g	2480a	$2$	$2$	\( 2^{4} \cdot 5 \cdot 31 \)	\( 2^{11} \cdot 5^{3} \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$5.278740624$	$1$		$3$	$1536$	$0.747733$	$8144476196418/120125$	$1.00788$	$4.77903$	$1$	$[0, 0, 0, -5323, -149478]$	\(y^2=x^3-5323x-149478\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?	$[(154, 1638)]$	$1$
2480.g2	2480a1	2480.g	2480a	$2$	$2$	\( 2^{4} \cdot 5 \cdot 31 \)	\( - 2^{10} \cdot 5^{6} \cdot 31 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$2.639370312$	$1$		$5$	$768$	$0.401160$	$-3639412836/484375$	$0.94117$	$3.72998$	$1$	$[0, 0, 0, -323, -2478]$	\(y^2=x^3-323x-2478\)	2.3.0.a.1, 40.6.0.c.1, 62.6.0.b.1, 1240.12.0.?	$[(29, 112)]$	$1$
2480.h1	2480e3	2480.h	2480e	$4$	$4$	\( 2^{4} \cdot 5 \cdot 31 \)	\( 2^{10} \cdot 5^{3} \cdot 31 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$1240$	$48$	$0$	$1$	$1$		$1$	$3456$	$1.172489$	$61012706050976004/3875$	$1.01415$	$5.83179$	$2$	$[0, 0, 0, -82667, 9148426]$	\(y^2=x^3-82667x+9148426\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 20.12.0-4.c.1.2, 40.24.0-40.z.1.10, $\ldots$	$[ ]$	$1$
2480.h2	2480e2	2480.h	2480e	$4$	$4$	\( 2^{4} \cdot 5 \cdot 31 \)	\( 2^{8} \cdot 5^{6} \cdot 31^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$620$	$48$	$0$	$1$	$1$		$3$	$1728$	$0.825915$	$59593532744016/15015625$	$1.00733$	$4.76762$	$1$	$[0, 0, 0, -5167, 142926]$	\(y^2=x^3-5167x+142926\)	2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.b.1.2, 124.24.0.?, 620.48.0.?	$[ ]$	$1$
2480.h3	2480e4	2480.h	2480e	$4$	$4$	\( 2^{4} \cdot 5 \cdot 31 \)	\( - 2^{10} \cdot 5^{12} \cdot 31 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1240$	$48$	$0$	$1$	$1$		$3$	$3456$	$1.172489$	$-10153098934884/7568359375$	$0.97891$	$4.82445$	$1$	$[0, 0, 0, -4547, 178514]$	\(y^2=x^3-4547x+178514\)	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.z.1.4, 62.6.0.b.1, 124.24.0.?, $\ldots$	$[ ]$	$1$
2480.h4	2480e1	2480.h	2480e	$4$	$4$	\( 2^{4} \cdot 5 \cdot 31 \)	\( 2^{4} \cdot 5^{3} \cdot 31^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1240$	$48$	$0$	$1$	$1$		$1$	$864$	$0.479342$	$327890958336/115440125$	$1.03881$	$3.74725$	$2$	$[0, 0, 0, -362, 1659]$	\(y^2=x^3-362x+1659\)	2.3.0.a.1, 4.12.0-4.c.1.2, 10.6.0.a.1, 20.24.0-20.g.1.1, 248.24.0.?, $\ldots$	$[ ]$	$1$
2480.i1	2480n2	2480.i	2480n	$2$	$2$	\( 2^{4} \cdot 5 \cdot 31 \)	\( 2^{8} \cdot 5^{10} \cdot 31 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$620$	$12$	$0$	$1$	$1$		$1$	$1440$	$0.787681$	$759636032976/302734375$	$1.00201$	$4.20947$	$1$	$[0, 0, 0, -1207, -9006]$	\(y^2=x^3-1207x-9006\)	2.3.0.a.1, 20.6.0.c.1, 124.6.0.?, 620.12.0.?	$[ ]$	$1$
2480.i2	2480n1	2480.i	2480n	$2$	$2$	\( 2^{4} \cdot 5 \cdot 31 \)	\( 2^{4} \cdot 5^{5} \cdot 31^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$620$	$12$	$0$	$1$	$1$		$1$	$720$	$0.441107$	$8047314026496/3003125$	$1.01698$	$4.15672$	$1$	$[0, 0, 0, -1052, -13129]$	\(y^2=x^3-1052x-13129\)	2.3.0.a.1, 10.6.0.a.1, 124.6.0.?, 620.12.0.?	$[ ]$	$1$
2480.j1	2480b1	2480.j	2480b	$1$	$1$	\( 2^{4} \cdot 5 \cdot 31 \)	\( - 2^{8} \cdot 5^{11} \cdot 31 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$310$	$2$	$0$	$3.615373782$	$1$		$2$	$2112$	$1.045130$	$-161332732109824/1513671875$	$0.96151$	$4.89709$	$1$	$[0, 1, 0, -7201, 234715]$	\(y^2=x^3+x^2-7201x+234715\)	310.2.0.?	$[(54, 79)]$	$1$
2480.k1	2480k1	2480.k	2480k	$1$	$1$	\( 2^{4} \cdot 5 \cdot 31 \)	\( - 2^{12} \cdot 5 \cdot 31 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$310$	$2$	$0$	$3.226622604$	$1$		$2$	$288$	$-0.184094$	$-262144/155$	$0.79514$	$2.75055$	$1$	$[0, 1, 0, -21, -61]$	\(y^2=x^3+x^2-21x-61\)	310.2.0.?	$[(22, 103)]$	$1$
2480.l1	2480f1	2480.l	2480f	$1$	$1$	\( 2^{4} \cdot 5 \cdot 31 \)	\( - 2^{8} \cdot 5^{3} \cdot 31 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$310$	$2$	$0$	$1.175946083$	$1$		$2$	$192$	$-0.145869$	$-7023616/3875$	$0.77120$	$2.81211$	$1$	$[0, 1, 0, -25, -77]$	\(y^2=x^3+x^2-25x-77\)	310.2.0.?	$[(6, 5)]$	$1$
2480.m1	2480m2	2480.m	2480m	$2$	$5$	\( 2^{4} \cdot 5 \cdot 31 \)	\( - 2^{12} \cdot 5 \cdot 31^{5} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.2	5B.4.2	$620$	$48$	$1$	$4.170141597$	$1$		$2$	$4000$	$1.141684$	$-65626385453056/143145755$	$0.97061$	$5.13517$	$1$	$[0, 1, 0, -13445, 596723]$	\(y^2=x^3+x^2-13445x+596723\)	5.12.0.a.2, 20.24.0-5.a.2.2, 310.24.1.?, 620.48.1.?	$[(38, 377)]$	$1$
2480.m2	2480m1	2480.m	2480m	$2$	$5$	\( 2^{4} \cdot 5 \cdot 31 \)	\( - 2^{12} \cdot 5^{5} \cdot 31 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.1	5B.4.1	$620$	$48$	$1$	$0.834028319$	$1$		$2$	$800$	$0.336965$	$99897344/96875$	$0.86229$	$3.42085$	$1$	$[0, 1, 0, 155, -557]$	\(y^2=x^3+x^2+155x-557\)	5.12.0.a.1, 20.24.0-5.a.1.2, 310.24.1.?, 620.48.1.?	$[(6, 25)]$	$1$
2480.n1	2480i4	2480.n	2480i	$4$	$6$	\( 2^{4} \cdot 5 \cdot 31 \)	\( 2^{14} \cdot 5^{3} \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1860$	$96$	$1$	$1$	$4$	$2$	$1$	$13824$	$1.622370$	$947226559343329/443751840500$	$0.99256$	$5.47623$	$1$	$[0, -1, 0, -32736, -984064]$	\(y^2=x^3-x^2-32736x-984064\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 10.6.0.a.1, 12.24.0-6.a.1.9, $\ldots$	$[ ]$	$1$
2480.n2	2480i2	2480.n	2480i	$4$	$6$	\( 2^{4} \cdot 5 \cdot 31 \)	\( 2^{18} \cdot 5 \cdot 31^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1860$	$96$	$1$	$1$	$4$	$2$	$1$	$4608$	$1.073063$	$549131937598369/307520$	$0.96644$	$5.40648$	$1$	$[0, -1, 0, -27296, -1726720]$	\(y^2=x^3-x^2-27296x-1726720\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 10.6.0.a.1, 12.24.0-6.a.1.3, $\ldots$	$[ ]$	$1$
2480.n3	2480i1	2480.n	2480i	$4$	$6$	\( 2^{4} \cdot 5 \cdot 31 \)	\( - 2^{24} \cdot 5^{2} \cdot 31 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1860$	$96$	$1$	$1$	$4$	$2$	$1$	$2304$	$0.726490$	$-131794519969/3174400$	$0.90964$	$4.34532$	$1$	$[0, -1, 0, -1696, -26880]$	\(y^2=x^3-x^2-1696x-26880\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0-6.a.1.3, 20.6.0.c.1, $\ldots$	$[ ]$	$1$
2480.n4	2480i3	2480.n	2480i	$4$	$6$	\( 2^{4} \cdot 5 \cdot 31 \)	\( - 2^{16} \cdot 5^{6} \cdot 31^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1860$	$96$	$1$	$1$	$4$	$2$	$1$	$6912$	$1.275795$	$10347405816671/7447750000$	$0.97053$	$4.89834$	$1$	$[0, -1, 0, 7264, -120064]$	\(y^2=x^3-x^2+7264x-120064\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0-6.a.1.9, 20.6.0.c.1, $\ldots$	$[ ]$	$1$
2480.o1	2480o1	2480.o	2480o	$1$	$1$	\( 2^{4} \cdot 5 \cdot 31 \)	\( - 2^{8} \cdot 5 \cdot 31 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$310$	$2$	$0$	$1$	$1$		$0$	$288$	$-0.429105$	$221184/155$	$0.73786$	$2.28402$	$1$	$[0, 0, 0, 8, -4]$	\(y^2=x^3+8x-4\)	310.2.0.?	$[ ]$	$1$

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