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	Manin constant

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Results (36 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
1664.g1	1664f1	1664.g	1664f	$1$	$1$	$ 2^{7} \cdot 13 $	$ - 2^{7} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$96$	$-0.369132$	$-85939808/13$	$0.88682$	$3.11737$	$[0, -1, 0, -46, -106]$	$y^2=x^3-x^2-46x-106$	104.2.0.?	$[ ]$
1664.i1	1664c1	1664.i	1664c	$1$	$1$	$ 2^{7} \cdot 13 $	$ - 2^{13} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$0.200170704$	$1$		$6$	$192$	$-0.022558$	$-85939808/13$	$0.88682$	$3.67809$	$[0, -1, 0, -185, 1033]$	$y^2=x^3-x^2-185x+1033$	104.2.0.?	$[(9, 4)]$
1664.l1	1664o1	1664.l	1664o	$1$	$1$	$ 2^{7} \cdot 13 $	$ - 2^{7} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$0.685728240$	$1$		$2$	$96$	$-0.369132$	$-85939808/13$	$0.88682$	$3.11737$	$[0, 1, 0, -46, 106]$	$y^2=x^3+x^2-46x+106$	104.2.0.?	$[(3, 2)]$
1664.n1	1664a1	1664.n	1664a	$1$	$1$	$ 2^{7} \cdot 13 $	$ - 2^{13} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$2.533436542$	$1$		$2$	$192$	$-0.022558$	$-85939808/13$	$0.88682$	$3.67809$	$[0, 1, 0, -185, -1033]$	$y^2=x^3+x^2-185x-1033$	104.2.0.?	$[(17, 32)]$
14976.i1	14976ba1	14976.i	14976ba	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 13 $	$ - 2^{13} \cdot 3^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1.153584275$	$1$		$2$	$5760$	$0.526748$	$-85939808/13$	$0.88682$	$3.52312$	$[0, 0, 0, -1668, 26224]$	$y^2=x^3-1668x+26224$	104.2.0.?	$[(24, 4)]$
14976.l1	14976z1	14976.l	14976z	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 13 $	$ - 2^{13} \cdot 3^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$3.258656969$	$1$		$2$	$5760$	$0.526748$	$-85939808/13$	$0.88682$	$3.52312$	$[0, 0, 0, -1668, -26224]$	$y^2=x^3-1668x-26224$	104.2.0.?	$[(50, 124)]$
14976.z1	14976bf1	14976.z	14976bf	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 13 $	$ - 2^{7} \cdot 3^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$2880$	$0.180174$	$-85939808/13$	$0.88682$	$3.09054$	$[0, 0, 0, -417, 3278]$	$y^2=x^3-417x+3278$	104.2.0.?	$[ ]$
14976.ba1	14976o1	14976.ba	14976o	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 13 $	$ - 2^{7} \cdot 3^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$10.46362409$	$1$		$0$	$2880$	$0.180174$	$-85939808/13$	$0.88682$	$3.09054$	$[0, 0, 0, -417, -3278]$	$y^2=x^3-417x-3278$	104.2.0.?	$[(30762/19, 5223424/19)]$
21632.n1	21632bd1	21632.n	21632bd	$1$	$1$	$ 2^{7} \cdot 13^{2} $	$ - 2^{13} \cdot 13^{7} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$0.414016343$	$1$		$14$	$32256$	$1.259916$	$-85939808/13$	$0.88682$	$4.27473$	$[0, -1, 0, -31321, 2144297]$	$y^2=x^3-x^2-31321x+2144297$	104.2.0.?	$[(139, 676), (61, 676)]$
21632.p1	21632bc1	21632.p	21632bc	$1$	$1$	$ 2^{7} \cdot 13^{2} $	$ - 2^{7} \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$16128$	$0.913342$	$-85939808/13$	$0.88682$	$3.85809$	$[0, -1, 0, -7830, -264122]$	$y^2=x^3-x^2-7830x-264122$	104.2.0.?	$[ ]$
21632.y1	21632ba1	21632.y	21632ba	$1$	$1$	$ 2^{7} \cdot 13^{2} $	$ - 2^{13} \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$32256$	$1.259916$	$-85939808/13$	$0.88682$	$4.27473$	$[0, 1, 0, -31321, -2144297]$	$y^2=x^3+x^2-31321x-2144297$	104.2.0.?	$[ ]$
21632.ba1	21632e1	21632.ba	21632e	$1$	$1$	$ 2^{7} \cdot 13^{2} $	$ - 2^{7} \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$2.409022971$	$1$		$0$	$16128$	$0.913342$	$-85939808/13$	$0.88682$	$3.85809$	$[0, 1, 0, -7830, 264122]$	$y^2=x^3+x^2-7830x+264122$	104.2.0.?	$[(439/3, 676/3)]$
41600.t1	41600f1	41600.t	41600f	$1$	$1$	$ 2^{7} \cdot 5^{2} \cdot 13 $	$ - 2^{7} \cdot 5^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1.913793678$	$1$		$2$	$13440$	$0.435587$	$-85939808/13$	$0.88682$	$3.08185$	$[0, -1, 0, -1158, 15562]$	$y^2=x^3-x^2-1158x+15562$	104.2.0.?	$[(21, 8)]$
41600.v1	41600bx1	41600.v	41600bx	$1$	$1$	$ 2^{7} \cdot 5^{2} \cdot 13 $	$ - 2^{13} \cdot 5^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$8.427834611$	$1$		$0$	$26880$	$0.782161$	$-85939808/13$	$0.88682$	$3.47287$	$[0, -1, 0, -4633, -119863]$	$y^2=x^3-x^2-4633x-119863$	104.2.0.?	$[(8171/5, 719956/5)]$
41600.bq1	41600bv1	41600.bq	41600bv	$1$	$1$	$ 2^{7} \cdot 5^{2} \cdot 13 $	$ - 2^{13} \cdot 5^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1.190980202$	$1$		$4$	$26880$	$0.782161$	$-85939808/13$	$0.88682$	$3.47287$	$[0, 1, 0, -4633, 119863]$	$y^2=x^3+x^2-4633x+119863$	104.2.0.?	$[(39, 4)]$
41600.bs1	41600bn1	41600.bs	41600bn	$1$	$1$	$ 2^{7} \cdot 5^{2} \cdot 13 $	$ - 2^{7} \cdot 5^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$9$	$3$	$0$	$13440$	$0.435587$	$-85939808/13$	$0.88682$	$3.08185$	$[0, 1, 0, -1158, -15562]$	$y^2=x^3+x^2-1158x-15562$	104.2.0.?	$[ ]$
81536.w1	81536s1	81536.w	81536s	$1$	$1$	$ 2^{7} \cdot 7^{2} \cdot 13 $	$ - 2^{13} \cdot 7^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1.898772812$	$1$		$2$	$72576$	$0.950397$	$-85939808/13$	$0.88682$	$3.44473$	$[0, -1, 0, -9081, 336169]$	$y^2=x^3-x^2-9081x+336169$	104.2.0.?	$[(55, 8)]$
81536.y1	81536bn1	81536.y	81536bn	$1$	$1$	$ 2^{7} \cdot 7^{2} \cdot 13 $	$ - 2^{7} \cdot 7^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$18.06436298$	$1$		$0$	$36288$	$0.603824$	$-85939808/13$	$0.88682$	$3.07698$	$[0, -1, 0, -2270, -40886]$	$y^2=x^3-x^2-2270x-40886$	104.2.0.?	$[(61893425/547, 471467318734/547)]$
81536.bn1	81536r1	81536.bn	81536r	$1$	$1$	$ 2^{7} \cdot 7^{2} \cdot 13 $	$ - 2^{13} \cdot 7^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$6.930392593$	$1$		$0$	$72576$	$0.950397$	$-85939808/13$	$0.88682$	$3.44473$	$[0, 1, 0, -9081, -336169]$	$y^2=x^3+x^2-9081x-336169$	104.2.0.?	$[(2395/3, 108548/3)]$
81536.bp1	81536g1	81536.bp	81536g	$1$	$1$	$ 2^{7} \cdot 7^{2} \cdot 13 $	$ - 2^{7} \cdot 7^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$36288$	$0.603824$	$-85939808/13$	$0.88682$	$3.07698$	$[0, 1, 0, -2270, 40886]$	$y^2=x^3+x^2-2270x+40886$	104.2.0.?	$[ ]$
194688.bf1	194688q1	194688.bf	194688q	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 13^{2} $	$ - 2^{7} \cdot 3^{6} \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$25.10554555$	$1$		$0$	$483840$	$1.462648$	$-85939808/13$	$0.88682$	$3.70328$	$[0, 0, 0, -70473, -7201766]$	$y^2=x^3-70473x-7201766$	104.2.0.?	$[(789342983182/40461, 557787243979896346/40461)]$
194688.bg1	194688cl1	194688.bg	194688cl	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 13^{2} $	$ - 2^{7} \cdot 3^{6} \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$483840$	$1.462648$	$-85939808/13$	$0.88682$	$3.70328$	$[0, 0, 0, -70473, 7201766]$	$y^2=x^3-70473x+7201766$	104.2.0.?	$[ ]$
194688.ck1	194688cw1	194688.ck	194688cw	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 13^{2} $	$ - 2^{13} \cdot 3^{6} \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$967680$	$1.809223$	$-85939808/13$	$0.88682$	$4.04476$	$[0, 0, 0, -281892, -57614128]$	$y^2=x^3-281892x-57614128$	104.2.0.?	$[ ]$
194688.cn1	194688cy1	194688.cn	194688cy	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 13^{2} $	$ - 2^{13} \cdot 3^{6} \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$967680$	$1.809223$	$-85939808/13$	$0.88682$	$4.04476$	$[0, 0, 0, -281892, 57614128]$	$y^2=x^3-281892x+57614128$	104.2.0.?	$[ ]$
201344.w1	201344k1	201344.w	201344k	$1$	$1$	$ 2^{7} \cdot 11^{2} \cdot 13 $	$ - 2^{7} \cdot 11^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1.709696520$	$1$		$2$	$138240$	$0.829816$	$-85939808/13$	$0.88682$	$3.07128$	$[0, -1, 0, -5606, 163462]$	$y^2=x^3-x^2-5606x+163462$	104.2.0.?	$[(81, 484)]$
201344.y1	201344l1	201344.y	201344l	$1$	$1$	$ 2^{7} \cdot 11^{2} \cdot 13 $	$ - 2^{13} \cdot 11^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$276480$	$1.176390$	$-85939808/13$	$0.88682$	$3.41181$	$[0, -1, 0, -22425, -1285271]$	$y^2=x^3-x^2-22425x-1285271$	104.2.0.?	$[ ]$
201344.bf1	201344bt1	201344.bf	201344bt	$1$	$1$	$ 2^{7} \cdot 11^{2} \cdot 13 $	$ - 2^{7} \cdot 11^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$138240$	$0.829816$	$-85939808/13$	$0.88682$	$3.07128$	$[0, 1, 0, -5606, -163462]$	$y^2=x^3+x^2-5606x-163462$	104.2.0.?	$[ ]$
201344.bj1	201344s1	201344.bj	201344s	$1$	$1$	$ 2^{7} \cdot 11^{2} \cdot 13 $	$ - 2^{13} \cdot 11^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$276480$	$1.176390$	$-85939808/13$	$0.88682$	$3.41181$	$[0, 1, 0, -22425, 1285271]$	$y^2=x^3+x^2-22425x+1285271$	104.2.0.?	$[ ]$
374400.em1	374400em1	374400.em	374400em	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{7} \cdot 3^{6} \cdot 5^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$18.33227251$	$1$		$0$	$403200$	$0.984894$	$-85939808/13$	$0.88682$	$3.06783$	$[0, 0, 0, -10425, -409750]$	$y^2=x^3-10425x-409750$	104.2.0.?	$[(77557454/487, 644650777658/487)]$
374400.en1	374400en1	374400.en	374400en	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{13} \cdot 3^{6} \cdot 5^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$10.49933613$	$1$		$0$	$806400$	$1.331467$	$-85939808/13$	$0.88682$	$3.39191$	$[0, 0, 0, -41700, -3278000]$	$y^2=x^3-41700x-3278000$	104.2.0.?	$[(68574/17, 2123132/17)]$
374400.ha1	374400ha1	374400.ha	374400ha	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{7} \cdot 3^{6} \cdot 5^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$403200$	$0.984894$	$-85939808/13$	$0.88682$	$3.06783$	$[0, 0, 0, -10425, 409750]$	$y^2=x^3-10425x+409750$	104.2.0.?	$[ ]$
374400.hb1	374400hb1	374400.hb	374400hb	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{13} \cdot 3^{6} \cdot 5^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$4.432837276$	$1$		$2$	$806400$	$1.331467$	$-85939808/13$	$0.88682$	$3.39191$	$[0, 0, 0, -41700, 3278000]$	$y^2=x^3-41700x+3278000$	104.2.0.?	$[(-4, 1856)]$
480896.i1	480896i1	480896.i	480896i	$1$	$1$	$ 2^{7} \cdot 13 \cdot 17^{2} $	$ - 2^{13} \cdot 13 \cdot 17^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$13.16612272$	$1$		$0$	$844800$	$1.394049$	$-85939808/13$	$0.88682$	$3.38441$	$[0, -1, 0, -53561, -4753943]$	$y^2=x^3-x^2-53561x-4753943$	104.2.0.?	$[(985951/21, 973311704/21)]$
480896.k1	480896k1	480896.k	480896k	$1$	$1$	$ 2^{7} \cdot 13 \cdot 17^{2} $	$ - 2^{7} \cdot 13 \cdot 17^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$3.935111724$	$1$		$2$	$422400$	$1.047476$	$-85939808/13$	$0.88682$	$3.06654$	$[0, -1, 0, -13390, 600938]$	$y^2=x^3-x^2-13390x+600938$	104.2.0.?	$[(89, 326)]$
480896.v1	480896v1	480896.v	480896v	$1$	$1$	$ 2^{7} \cdot 13 \cdot 17^{2} $	$ - 2^{13} \cdot 13 \cdot 17^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$2.530731790$	$1$		$2$	$844800$	$1.394049$	$-85939808/13$	$0.88682$	$3.38441$	$[0, 1, 0, -53561, 4753943]$	$y^2=x^3+x^2-53561x+4753943$	104.2.0.?	$[(131, 52)]$
480896.x1	480896x1	480896.x	480896x	$1$	$1$	$ 2^{7} \cdot 13 \cdot 17^{2} $	$ - 2^{7} \cdot 13 \cdot 17^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$9$	$3$	$0$	$422400$	$1.047476$	$-85939808/13$	$0.88682$	$3.06654$	$[0, 1, 0, -13390, -600938]$	$y^2=x^3+x^2-13390x-600938$	104.2.0.?	$[ ]$

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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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