LMFDB - Elliptic curves over $\Q$ of conductor 10780

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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 (26 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	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
10780.a1	10780g2	10780.a	10780g	$2$	$2$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{8} \cdot 5^{2} \cdot 7^{10} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$1.978964725$	$1$		$3$	$27648$	$1.242250$	$1193895376/660275$	$0.85133$	$4.10547$	$[0, 1, 0, -6876, 43924]$	$y^2=x^3+x^2-6876x+43924$	2.3.0.a.1, 20.6.0.c.1, 44.6.0.a.1, 220.12.0.?	$[(-61, 490)]$
10780.a2	10780g1	10780.a	10780g	$2$	$2$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{4} \cdot 5 \cdot 7^{8} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$3.957929450$	$1$		$3$	$13824$	$0.895677$	$4294967296/29645$	$1.07594$	$3.94475$	$[0, 1, 0, -4181, -104840]$	$y^2=x^3+x^2-4181x-104840$	2.3.0.a.1, 10.6.0.a.1, 44.6.0.b.1, 220.12.0.?	$[(136, 1364)]$
10780.b1	10780b1	10780.b	10780b	$2$	$3$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 5 \cdot 7^{8} \cdot 11 $	$0$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$330$	$16$	$0$	$1$	$1$		$2$	$9072$	$0.668248$	$-3937024/55$	$0.69786$	$3.61314$	$[0, 1, 0, -1486, 21825]$	$y^2=x^3+x^2-1486x+21825$	3.8.0-3.a.1.2, 110.2.0.?, 330.16.0.?	$[]$
10780.b2	10780b2	10780.b	10780b	$2$	$3$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 5^{3} \cdot 7^{8} \cdot 11^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$330$	$16$	$0$	$1$	$1$		$0$	$27216$	$1.217554$	$186050816/166375$	$0.81768$	$4.02580$	$[0, 1, 0, 5374, 113749]$	$y^2=x^3+x^2+5374x+113749$	3.8.0-3.a.1.1, 110.2.0.?, 330.16.0.?	$[]$
10780.c1	10780i2	10780.c	10780i	$2$	$2$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{8} \cdot 5^{2} \cdot 7^{6} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$1$	$1$		$1$	$9216$	$0.773882$	$94875856/275$	$0.82986$	$3.83274$	$[0, 1, 0, -2956, -62700]$	$y^2=x^3+x^2-2956x-62700$	2.3.0.a.1, 20.6.0.c.1, 44.6.0.a.1, 220.12.0.?	$[]$
10780.c2	10780i1	10780.c	10780i	$2$	$2$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{4} \cdot 5 \cdot 7^{6} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$1$	$1$		$1$	$4608$	$0.427308$	$1048576/605$	$1.25294$	$3.04896$	$[0, 1, 0, -261, -176]$	$y^2=x^3+x^2-261x-176$	2.3.0.a.1, 10.6.0.a.1, 44.6.0.b.1, 220.12.0.?	$[]$
10780.d1	10780m1	10780.d	10780m	$1$	$1$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 5^{11} \cdot 7^{10} \cdot 11^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$110$	$2$	$0$	$1$	$1$		$0$	$720720$	$3.081882$	$-129084391106508544/7863818359375$	$0.99824$	$6.64815$	$[0, 1, 0, -17408050, -29396334927]$	$y^2=x^3+x^2-17408050x-29396334927$	110.2.0.?	$[]$
10780.e1	10780e2	10780.e	10780e	$2$	$3$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 5 \cdot 7^{2} \cdot 11^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$420$	$16$	$0$	$1.585589316$	$1$		$0$	$10368$	$0.825068$	$-18330740176/8857805$	$0.86618$	$3.62674$	$[0, -1, 0, -1276, 24200]$	$y^2=x^3-x^2-1276x+24200$	3.4.0.a.1, 20.2.0.a.1, 21.8.0-3.a.1.2, 60.8.0.a.1, 420.16.0.?	$[(-11/2, 1331/2)]$
10780.e2	10780e1	10780.e	10780e	$2$	$3$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 5^{3} \cdot 7^{2} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$420$	$16$	$0$	$0.528529772$	$1$		$4$	$3456$	$0.275762$	$16674224/15125$	$0.77919$	$2.80723$	$[0, -1, 0, 124, -440]$	$y^2=x^3-x^2+124x-440$	3.4.0.a.1, 20.2.0.a.1, 21.8.0-3.a.1.1, 60.8.0.a.1, 420.16.0.?	$[(6, 22)]$
10780.f1	10780c2	10780.f	10780c	$2$	$2$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{8} \cdot 5^{2} \cdot 7^{8} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1540$	$12$	$0$	$0.901496137$	$1$		$7$	$9216$	$0.932718$	$44851536/13475$	$0.75216$	$3.75205$	$[0, 0, 0, -2303, -29498]$	$y^2=x^3-2303x-29498$	2.3.0.a.1, 44.6.0.a.1, 140.6.0.?, 1540.12.0.?	$[(-21, 98)]$
10780.f2	10780c1	10780.f	10780c	$2$	$2$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 5 \cdot 7^{7} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1540$	$12$	$0$	$1.802992275$	$1$		$5$	$4608$	$0.586144$	$3538944/4235$	$1.07826$	$3.18704$	$[0, 0, 0, 392, -3087]$	$y^2=x^3+392x-3087$	2.3.0.a.1, 44.6.0.b.1, 70.6.0.a.1, 1540.12.0.?	$[(18, 99)]$
10780.g1	10780d1	10780.g	10780d	$1$	$1$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 5 \cdot 7^{2} \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$110$	$2$	$0$	$0.682695681$	$1$		$4$	$720$	$-0.424278$	$48384/55$	$0.51741$	$1.87943$	$[0, 0, 0, 7, -7]$	$y^2=x^3+7x-7$	110.2.0.?	$[(1, 1)]$
10780.h1	10780j1	10780.h	10780j	$1$	$1$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 5 \cdot 7^{8} \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$110$	$2$	$0$	$0.541527483$	$1$		$4$	$5040$	$0.548677$	$48384/55$	$0.51741$	$3.13682$	$[0, 0, 0, 343, 2401]$	$y^2=x^3+343x+2401$	110.2.0.?	$[(0, 49)]$
10780.i1	10780k2	10780.i	10780k	$2$	$3$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 5 \cdot 7^{8} \cdot 11^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$60$	$16$	$0$	$6.144389369$	$1$		$0$	$72576$	$1.798023$	$-18330740176/8857805$	$0.86618$	$4.88413$	$[0, 1, 0, -62540, -8175532]$	$y^2=x^3+x^2-62540x-8175532$	3.8.0-3.a.1.1, 20.2.0.a.1, 60.16.0-60.a.1.5	$[(11413/6, 429913/6)]$
10780.i2	10780k1	10780.i	10780k	$2$	$3$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 5^{3} \cdot 7^{8} \cdot 11^{2} $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$60$	$16$	$0$	$2.048129789$	$1$		$4$	$24192$	$1.248716$	$16674224/15125$	$0.77919$	$4.06462$	$[0, 1, 0, 6060, 138788]$	$y^2=x^3+x^2+6060x+138788$	3.8.0-3.a.1.2, 20.2.0.a.1, 60.16.0-60.a.1.8	$[(136, 1870)]$
10780.j1	10780a1	10780.j	10780a	$1$	$1$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 5^{11} \cdot 7^{4} \cdot 11^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$110$	$2$	$0$	$1$	$1$		$0$	$102960$	$2.108925$	$-129084391106508544/7863818359375$	$0.99824$	$5.39075$	$[0, -1, 0, -355266, 85805105]$	$y^2=x^3-x^2-355266x+85805105$	110.2.0.?	$[]$
10780.k1	10780f4	10780.k	10780f	$4$	$6$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{8} \cdot 5^{2} \cdot 7^{6} \cdot 11^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$4620$	$96$	$1$	$4.351167490$	$1$		$1$	$62208$	$1.687405$	$154639330142416/33275$	$0.97344$	$5.37322$	$[0, -1, 0, -347916, 79103816]$	$y^2=x^3-x^2-347916x+79103816$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 20.6.0.c.1, 21.8.0-3.a.1.2, $\ldots$	$[(2509/3, 51940/3)]$
10780.k2	10780f3	10780.k	10780f	$4$	$6$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{4} \cdot 5 \cdot 7^{6} \cdot 11^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$4620$	$96$	$1$	$8.702334980$	$1$		$1$	$31104$	$1.340832$	$610462990336/8857805$	$1.02612$	$4.47857$	$[0, -1, 0, -21821, 1232330]$	$y^2=x^3-x^2-21821x+1232330$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 10.6.0.a.1, 21.8.0-3.a.1.2, $\ldots$	$[(39721/24, 3113803/24)]$
10780.k3	10780f2	10780.k	10780f	$4$	$6$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{8} \cdot 5^{6} \cdot 7^{6} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$4620$	$96$	$1$	$1.450389163$	$1$		$3$	$20736$	$1.138100$	$436334416/171875$	$0.87819$	$3.99707$	$[0, -1, 0, -4916, 76616]$	$y^2=x^3-x^2-4916x+76616$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 20.6.0.c.1, 21.8.0-3.a.1.1, $\ldots$	$[(-2, 294)]$
10780.k4	10780f1	10780.k	10780f	$4$	$6$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{4} \cdot 5^{3} \cdot 7^{6} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$4620$	$96$	$1$	$2.900778326$	$1$		$3$	$10368$	$0.791526$	$643956736/15125$	$0.96705$	$3.74039$	$[0, -1, 0, -2221, -38730]$	$y^2=x^3-x^2-2221x-38730$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 10.6.0.a.1, 21.8.0-3.a.1.1, $\ldots$	$[(69, 363)]$
10780.l1	10780h4	10780.l	10780h	$4$	$6$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{8} \cdot 5^{2} \cdot 7^{18} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$4620$	$96$	$1$	$1$	$9$	$3$	$1$	$497664$	$2.761169$	$3259751350395879376/3806353980275$	$0.97311$	$6.44544$	$[0, -1, 0, -9610876, 11459757576]$	$y^2=x^3-x^2-9610876x+11459757576$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 20.6.0.c.1, 21.8.0-3.a.1.2, $\ldots$	$[]$
10780.l2	10780h3	10780.l	10780h	$4$	$6$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{4} \cdot 5 \cdot 7^{12} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$4620$	$96$	$1$	$1$	$9$	$3$	$1$	$248832$	$2.414597$	$52112158467655991296/71177645$	$1.08004$	$6.44535$	$[0, -1, 0, -9608181, 11466509090]$	$y^2=x^3-x^2-9608181x+11466509090$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 10.6.0.a.1, 21.8.0-3.a.1.2, $\ldots$	$[]$
10780.l3	10780h2	10780.l	10780h	$4$	$6$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{8} \cdot 5^{6} \cdot 7^{10} \cdot 11^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$4620$	$96$	$1$	$1$	$1$		$1$	$165888$	$2.211864$	$329890530231376/49933296875$	$0.92505$	$5.45482$	$[0, -1, 0, -447876, -98989624]$	$y^2=x^3-x^2-447876x-98989624$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 20.6.0.c.1, 21.8.0-3.a.1.1, $\ldots$	$[]$
10780.l4	10780h1	10780.l	10780h	$4$	$6$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{4} \cdot 5^{3} \cdot 7^{8} \cdot 11^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$4620$	$96$	$1$	$1$	$1$		$1$	$82944$	$1.865292$	$106110329552896/10850811125$	$1.03569$	$5.03407$	$[0, -1, 0, -121781, 14882750]$	$y^2=x^3-x^2-121781x+14882750$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 10.6.0.a.1, 21.8.0-3.a.1.1, $\ldots$	$[]$
10780.m1	10780l1	10780.m	10780l	$2$	$3$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 5 \cdot 7^{2} \cdot 11 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2310$	$16$	$0$	$1$	$1$		$0$	$1296$	$-0.304707$	$-3937024/55$	$0.69786$	$2.35575$	$[0, -1, 0, -30, -55]$	$y^2=x^3-x^2-30x-55$	3.4.0.a.1, 21.8.0-3.a.1.1, 110.2.0.?, 330.8.0.?, 2310.16.0.?	$[]$
10780.m2	10780l2	10780.m	10780l	$2$	$3$	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 5^{3} \cdot 7^{2} \cdot 11^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2310$	$16$	$0$	$1$	$1$		$0$	$3888$	$0.244599$	$186050816/166375$	$0.81768$	$2.76841$	$[0, -1, 0, 110, -363]$	$y^2=x^3-x^2+110x-363$	3.4.0.a.1, 21.8.0-3.a.1.2, 110.2.0.?, 330.8.0.?, 2310.16.0.?	$[]$

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Elliptic curves over $\Q$
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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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