LMFDB - Elliptic curve search results

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Conductor	Discriminant	j-invariant	Rank

Bad$\ p$	Curves per isogeny class	Complex multiplication	Torsion

Isogeny class degree	Cyclic isogeny degree	Isogeny class size	Integral points

Analytic order of Ш	$p\ $div$\ $\|Ш\|	Regulator	Reduction	Faltings height

Galois image	Adelic level	Adelic index	Adelic genus

Nonmax$\ \ell$	$abc$ quality	Szpiro ratio

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Results (32 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	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
29400.u1	29400de1	29400.u	29400de	$1$	$1$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{11} \cdot 3^{4} \cdot 5^{3} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$		$0$	$204288$	$1.799393$	$-2390122/81$	$0.94079$	$4.53464$	$[0, -1, 0, -116048, 15694092]$	$y^2=x^3-x^2-116048x+15694092$	40.2.0.a.1	$[]$
29400.v1	29400x1	29400.v	29400x	$1$	$1$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{11} \cdot 3^{4} \cdot 5^{9} \cdot 7^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$		$0$	$145920$	$1.631157$	$-2390122/81$	$0.94079$	$4.33842$	$[0, -1, 0, -59208, -5685588]$	$y^2=x^3-x^2-59208x-5685588$	40.2.0.a.1	$[]$
29400.de1	29400cd1	29400.de	29400cd	$1$	$1$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{11} \cdot 3^{4} \cdot 5^{9} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$		$0$	$1021440$	$2.604111$	$-2390122/81$	$0.94079$	$5.47320$	$[0, 1, 0, -2901208, 1955959088]$	$y^2=x^3+x^2-2901208x+1955959088$	40.2.0.a.1	$[]$
29400.df1	29400eh1	29400.df	29400eh	$1$	$1$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{11} \cdot 3^{4} \cdot 5^{3} \cdot 7^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$		$0$	$29184$	$0.826437$	$-2390122/81$	$0.94079$	$3.39986$	$[0, 1, 0, -2368, -46432]$	$y^2=x^3+x^2-2368x-46432$	40.2.0.a.1	$[]$
58800.df1	58800bn1	58800.df	58800bn	$1$	$1$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{11} \cdot 3^{4} \cdot 5^{3} \cdot 7^{4} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$0.162343597$	$1$		$26$	$58368$	$0.826437$	$-2390122/81$	$0.94079$	$3.18527$	$[0, -1, 0, -2368, 46432]$	$y^2=x^3-x^2-2368x+46432$	40.2.0.a.1	$[(12, 140), (82, 630)]$
58800.dg1	58800bw1	58800.dg	58800bw	$1$	$1$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{11} \cdot 3^{4} \cdot 5^{9} \cdot 7^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$11.49793513$	$1$		$0$	$2042880$	$2.604111$	$-2390122/81$	$0.94079$	$5.12775$	$[0, -1, 0, -2901208, -1955959088]$	$y^2=x^3-x^2-2901208x-1955959088$	40.2.0.a.1	$[(3184657/11, 5670886500/11)]$
58800.ij1	58800dx1	58800.ij	58800dx	$1$	$1$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{11} \cdot 3^{4} \cdot 5^{9} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1.055995812$	$1$		$4$	$291840$	$1.631157$	$-2390122/81$	$0.94079$	$4.06460$	$[0, 1, 0, -59208, 5685588]$	$y^2=x^3+x^2-59208x+5685588$	40.2.0.a.1	$[(108, 750)]$
58800.ik1	58800ef1	58800.ik	58800ef	$1$	$1$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{11} \cdot 3^{4} \cdot 5^{3} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$		$0$	$408576$	$1.799393$	$-2390122/81$	$0.94079$	$4.24843$	$[0, 1, 0, -116048, -15694092]$	$y^2=x^3+x^2-116048x-15694092$	40.2.0.a.1	$[]$
88200.fg1	88200ib1	88200.fg	88200ib	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{11} \cdot 3^{10} \cdot 5^{9} \cdot 7^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$53.84388943$	$1$		$0$	$8171520$	$3.153416$	$-2390122/81$	$0.94079$	$5.52403$	$[0, 0, 0, -26110875, -52837006250]$	$y^2=x^3-26110875x-52837006250$	40.2.0.a.1	$[(5718660980120316244739150/28455742517, 7814304882452113271024152720931786250/28455742517)]$
88200.fh1	88200dc1	88200.fh	88200dc	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{11} \cdot 3^{10} \cdot 5^{3} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$2.711469487$	$1$		$2$	$233472$	$1.375744$	$-2390122/81$	$0.94079$	$3.65071$	$[0, 0, 0, -21315, 1232350]$	$y^2=x^3-21315x+1232350$	40.2.0.a.1	$[(50, 540)]$
88200.fi1	88200dm1	88200.fi	88200dm	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{11} \cdot 3^{10} \cdot 5^{3} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$		$0$	$1634304$	$2.348698$	$-2390122/81$	$0.94079$	$4.67601$	$[0, 0, 0, -1044435, -422696050]$	$y^2=x^3-1044435x-422696050$	40.2.0.a.1	$[]$
88200.fj1	88200hr1	88200.fj	88200hr	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{11} \cdot 3^{10} \cdot 5^{9} \cdot 7^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$		$0$	$1167360$	$2.180462$	$-2390122/81$	$0.94079$	$4.49873$	$[0, 0, 0, -532875, 154043750]$	$y^2=x^3-532875x+154043750$	40.2.0.a.1	$[]$
176400.hi1	176400ne1	176400.hi	176400ne	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{11} \cdot 3^{10} \cdot 5^{3} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1.666260004$	$1$		$4$	$466944$	$1.375744$	$-2390122/81$	$0.94079$	$3.44125$	$[0, 0, 0, -21315, -1232350]$	$y^2=x^3-21315x-1232350$	40.2.0.a.1	$[(175, 630)]$
176400.hj1	176400lw1	176400.hj	176400lw	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{11} \cdot 3^{10} \cdot 5^{9} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$		$0$	$16343040$	$3.153416$	$-2390122/81$	$0.94079$	$5.20707$	$[0, 0, 0, -26110875, 52837006250]$	$y^2=x^3-26110875x+52837006250$	40.2.0.a.1	$[]$
176400.hk1	176400nf1	176400.hk	176400nf	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{11} \cdot 3^{10} \cdot 5^{9} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$3.895200284$	$1$		$2$	$2334720$	$2.180462$	$-2390122/81$	$0.94079$	$4.24060$	$[0, 0, 0, -532875, -154043750]$	$y^2=x^3-532875x-154043750$	40.2.0.a.1	$[(1425, 44500)]$
176400.hl1	176400lx1	176400.hl	176400lx	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{11} \cdot 3^{10} \cdot 5^{3} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$		$0$	$3268608$	$2.348698$	$-2390122/81$	$0.94079$	$4.40772$	$[0, 0, 0, -1044435, 422696050]$	$y^2=x^3-1044435x+422696050$	40.2.0.a.1	$[]$
235200.fl1	235200fl1	235200.fl	235200fl	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{17} \cdot 3^{4} \cdot 5^{3} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$		$0$	$3268608$	$2.145966$	$-2390122/81$	$0.94079$	$4.10850$	$[0, -1, 0, -464193, -125088543]$	$y^2=x^3-x^2-464193x-125088543$	40.2.0.a.1	$[]$
235200.fm1	235200fm1	235200.fm	235200fm	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{17} \cdot 3^{4} \cdot 5^{9} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$2.512900049$	$1$		$2$	$2334720$	$1.977730$	$-2390122/81$	$0.94079$	$3.94527$	$[0, -1, 0, -236833, 45721537]$	$y^2=x^3-x^2-236833x+45721537$	40.2.0.a.1	$[(-533, 4500)]$
235200.iz1	235200iz1	235200.iz	235200iz	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{17} \cdot 3^{4} \cdot 5^{3} \cdot 7^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$		$0$	$466944$	$1.173012$	$-2390122/81$	$0.94079$	$3.16451$	$[0, -1, 0, -9473, -361983]$	$y^2=x^3-x^2-9473x-361983$	40.2.0.a.1	$[]$
235200.ja1	235200ja1	235200.ja	235200ja	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{17} \cdot 3^{4} \cdot 5^{9} \cdot 7^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$2.532392661$	$1$		$2$	$16343040$	$2.950684$	$-2390122/81$	$0.94079$	$4.88926$	$[0, -1, 0, -11604833, 15659277537]$	$y^2=x^3-x^2-11604833x+15659277537$	40.2.0.a.1	$[(3017, 90000)]$
235200.ua1	235200ua1	235200.ua	235200ua	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{17} \cdot 3^{4} \cdot 5^{9} \cdot 7^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$14.91183089$	$1$		$0$	$16343040$	$2.950684$	$-2390122/81$	$0.94079$	$4.88926$	$[0, 1, 0, -11604833, -15659277537]$	$y^2=x^3+x^2-11604833x-15659277537$	40.2.0.a.1	$[(51003802/113, 60048521625/113)]$
235200.ub1	235200ub1	235200.ub	235200ub	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{17} \cdot 3^{4} \cdot 5^{3} \cdot 7^{4} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$0.226271970$	$1$		$24$	$466944$	$1.173012$	$-2390122/81$	$0.94079$	$3.16451$	$[0, 1, 0, -9473, 361983]$	$y^2=x^3+x^2-9473x+361983$	40.2.0.a.1	$[(79, 336), (-17, 720)]$
235200.xm1	235200xm1	235200.xm	235200xm	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{17} \cdot 3^{4} \cdot 5^{9} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$0.914665865$	$1$		$4$	$2334720$	$1.977730$	$-2390122/81$	$0.94079$	$3.94527$	$[0, 1, 0, -236833, -45721537]$	$y^2=x^3+x^2-236833x-45721537$	40.2.0.a.1	$[(1283, 42000)]$
235200.xn1	235200xn1	235200.xn	235200xn	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{17} \cdot 3^{4} \cdot 5^{3} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$		$0$	$3268608$	$2.145966$	$-2390122/81$	$0.94079$	$4.10850$	$[0, 1, 0, -464193, 125088543]$	$y^2=x^3+x^2-464193x+125088543$	40.2.0.a.1	$[]$
705600.tw1	-	705600.tw	-	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{17} \cdot 3^{10} \cdot 5^{9} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1.695698447$	$1$		$2$	$18677760$	$2.527035$	$-2390122/81$	$0.94079$	$4.11289$	$[0, 0, 0, -2131500, 1232350000]$	$y^2=x^3-2131500x+1232350000$	40.2.0.a.1	$[(1400, 31500)]$
705600.tx1	-	705600.tx	-	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{17} \cdot 3^{10} \cdot 5^{3} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$		$0$	$26148864$	$2.695271$	$-2390122/81$	$0.94079$	$4.26280$	$[0, 0, 0, -4177740, -3381568400]$	$y^2=x^3-4177740x-3381568400$	40.2.0.a.1	$[]$
705600.ug1	-	705600.ug	-	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{17} \cdot 3^{10} \cdot 5^{3} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1.305554081$	$1$		$4$	$3735552$	$1.722317$	$-2390122/81$	$0.94079$	$3.39582$	$[0, 0, 0, -85260, 9858800]$	$y^2=x^3-85260x+9858800$	40.2.0.a.1	$[(190, 720)]$
705600.uh1	-	705600.uh	-	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{17} \cdot 3^{10} \cdot 5^{9} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$9$	$3$	$0$	$130744320$	$3.499992$	$-2390122/81$	$0.94079$	$4.97987$	$[0, 0, 0, -104443500, -422696050000]$	$y^2=x^3-104443500x-422696050000$	40.2.0.a.1	$[]$
705600.biq1	-	705600.biq	-	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{17} \cdot 3^{10} \cdot 5^{3} \cdot 7^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$6.263740855$	$1$		$2$	$26148864$	$2.695271$	$-2390122/81$	$0.94079$	$4.26280$	$[0, 0, 0, -4177740, 3381568400]$	$y^2=x^3-4177740x+3381568400$	40.2.0.a.1	$[(-2315, 25425)]$
705600.bir1	-	705600.bir	-	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{17} \cdot 3^{10} \cdot 5^{9} \cdot 7^{4} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$17.81052125$	$1$		$6$	$18677760$	$2.527035$	$-2390122/81$	$0.94079$	$4.11289$	$[0, 0, 0, -2131500, -1232350000]$	$y^2=x^3-2131500x-1232350000$	40.2.0.a.1	$[(1850, 34000), (2074, 57168)]$
705600.bja1	-	705600.bja	-	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{17} \cdot 3^{10} \cdot 5^{9} \cdot 7^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$7.768734413$	$1$		$2$	$130744320$	$3.499992$	$-2390122/81$	$0.94079$	$4.97987$	$[0, 0, 0, -104443500, 422696050000]$	$y^2=x^3-104443500x+422696050000$	40.2.0.a.1	$[(47114, 10004112)]$
705600.bjb1	-	705600.bjb	-	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{17} \cdot 3^{10} \cdot 5^{3} \cdot 7^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$		$0$	$3735552$	$1.722317$	$-2390122/81$	$0.94079$	$3.39582$	$[0, 0, 0, -85260, -9858800]$	$y^2=x^3-85260x-9858800$	40.2.0.a.1	$[]$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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