LMFDB - Elliptic curves over $\Q$ of conductor 4620

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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	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
4620.a1	4620a2	4620.a	4620a	$2$	$2$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{8} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1540$	$12$	$0$	$0.224649595$	$1$	$13$	$1920$	$0.324070$	$59466754384/121275$	$0.84408$	$3.59722$	$[0, -1, 0, -516, 4680]$	$y^2=x^3-x^2-516x+4680$	2.3.0.a.1, 44.6.0.a.1, 140.6.0.?, 1540.12.0.?	$[(6, 42)]$
4620.a2	4620a1	4620.a	4620a	$2$	$2$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{4} \cdot 5 \cdot 7 \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1540$	$12$	$0$	$0.449299190$	$1$	$9$	$960$	$-0.022504$	$-67108864/343035$	$1.21836$	$2.73521$	$[0, -1, 0, -21, 126]$	$y^2=x^3-x^2-21x+126$	2.3.0.a.1, 44.6.0.b.1, 70.6.0.a.1, 1540.12.0.?	$[(3, 9)]$
4620.b1	4620c1	4620.b	4620c	$1$	$1$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 3^{3} \cdot 5 \cdot 7^{5} \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$2310$	$2$	$0$	$0.155762258$	$1$	$8$	$4320$	$0.858641$	$-81756451446784/24958395$	$0.94954$	$4.45364$	$[0, -1, 0, -5741, 169401]$	$y^2=x^3-x^2-5741x+169401$	2310.2.0.?	$[(43, 14)]$
4620.c1	4620b2	4620.c	4620b	$2$	$2$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{8} \cdot 3^{6} \cdot 5^{10} \cdot 7^{2} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1540$	$12$	$0$	$1.463481062$	$1$	$7$	$17280$	$1.593008$	$19288565375865424/3837216796875$	$0.95211$	$5.10105$	$[0, -1, 0, -35476, -2071640]$	$y^2=x^3-x^2-35476x-2071640$	2.3.0.a.1, 44.6.0.a.1, 140.6.0.?, 1540.12.0.?	$[(-74, 378)]$
4620.c2	4620b1	4620.c	4620b	$2$	$2$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{12} \cdot 5^{5} \cdot 7 \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1540$	$12$	$0$	$2.926962125$	$1$	$5$	$8640$	$1.246435$	$681010157060096/1406657896875$	$1.06770$	$4.48805$	$[0, -1, 0, 4619, -195194]$	$y^2=x^3-x^2+4619x-195194$	2.3.0.a.1, 44.6.0.b.1, 70.6.0.a.1, 1540.12.0.?	$[(45, 319)]$
4620.d1	4620d2	4620.d	4620d	$2$	$2$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{8} \cdot 3 \cdot 5^{3} \cdot 7^{4} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$660$	$12$	$0$	$0.316787781$	$1$	$9$	$3456$	$0.769171$	$2605772594896/108945375$	$0.88348$	$4.04519$	$[0, -1, 0, -1820, 29400]$	$y^2=x^3-x^2-1820x+29400$	2.3.0.a.1, 44.6.0.c.1, 60.6.0.a.1, 660.12.0.?	$[(10, 110)]$
4620.d2	4620d1	4620.d	4620d	$2$	$2$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{2} \cdot 5^{6} \cdot 7^{2} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$660$	$12$	$0$	$0.158393890$	$1$	$15$	$1728$	$0.422597$	$1129201664/75796875$	$0.96687$	$3.36119$	$[0, -1, 0, 55, 1650]$	$y^2=x^3-x^2+55x+1650$	2.3.0.a.1, 22.6.0.a.1, 60.6.0.b.1, 660.12.0.?	$[(-5, 35)]$
4620.e1	4620e2	4620.e	4620e	$2$	$2$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{8} \cdot 3^{5} \cdot 5^{7} \cdot 7^{4} \cdot 11^{10} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$660$	$12$	$0$	$1$	$1$	$1$	$873600$	$3.377033$	$414354576760345737269208016/1182266314178222109375$	$1.03557$	$7.92045$	$[0, -1, 0, -98619500, -375994125000]$	$y^2=x^3-x^2-98619500x-375994125000$	2.3.0.a.1, 44.6.0.c.1, 60.6.0.a.1, 660.12.0.?	$[]$
4620.e2	4620e1	4620.e	4620e	$2$	$2$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{10} \cdot 5^{14} \cdot 7^{2} \cdot 11^{5} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$660$	$12$	$0$	$1$	$1$	$1$	$436800$	$3.030460$	$-349439858058052607328256/2844147488104248046875$	$1.07764$	$7.07448$	$[0, -1, 0, -3697625, -10620843750]$	$y^2=x^3-x^2-3697625x-10620843750$	2.3.0.a.1, 22.6.0.a.1, 60.6.0.b.1, 660.12.0.?	$[]$
4620.f1	4620f2	4620.f	4620f	$2$	$2$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{8} \cdot 3^{4} \cdot 5^{2} \cdot 7^{6} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1540$	$12$	$0$	$0.220312334$	$1$	$11$	$6912$	$1.011469$	$31558509702736/2620631475$	$0.90565$	$4.34077$	$[0, -1, 0, -4180, 97672]$	$y^2=x^3-x^2-4180x+97672$	2.3.0.a.1, 44.6.0.a.1, 140.6.0.?, 1540.12.0.?	$[(22, 126)]$
4620.f2	4620f1	4620.f	4620f	$2$	$2$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{8} \cdot 5 \cdot 7^{3} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1540$	$12$	$0$	$0.440624668$	$1$	$9$	$3456$	$0.664894$	$143225913344/1361505915$	$0.99247$	$3.69706$	$[0, -1, 0, 275, 6790]$	$y^2=x^3-x^2+275x+6790$	2.3.0.a.1, 44.6.0.b.1, 70.6.0.a.1, 1540.12.0.?	$[(-3, 77)]$
4620.g1	4620g1	4620.g	4620g	$1$	$1$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 3 \cdot 5^{5} \cdot 7^{3} \cdot 11^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$2310$	$2$	$0$	$0.062051972$	$1$	$12$	$30240$	$1.788549$	$100715742101504/62663434246875$	$1.10842$	$5.30540$	$[0, -1, 0, 6155, -6092975]$	$y^2=x^3-x^2+6155x-6092975$	2310.2.0.?	$[(2055, 93170)]$
4620.h1	4620h2	4620.h	4620h	$2$	$2$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{8} \cdot 3^{7} \cdot 5^{3} \cdot 7^{8} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$660$	$12$	$0$	$1.400816562$	$1$	$7$	$80640$	$2.217182$	$1314817350433665559504/190690249278375$	$0.99777$	$6.42003$	$[0, 1, 0, -1449196, -671887996]$	$y^2=x^3+x^2-1449196x-671887996$	2.3.0.a.1, 44.6.0.c.1, 60.6.0.a.1, 660.12.0.?	$[(-700, 198)]$
4620.h2	4620h1	4620.h	4620h	$2$	$2$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{14} \cdot 5^{6} \cdot 7^{4} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$660$	$12$	$0$	$0.700408281$	$1$	$11$	$40320$	$1.870609$	$-3856034557002072064/1973796785296875$	$1.02238$	$5.47542$	$[0, 1, 0, -82321, -12507496]$	$y^2=x^3+x^2-82321x-12507496$	2.3.0.a.1, 22.6.0.a.1, 60.6.0.b.1, 660.12.0.?	$[(587, 11907)]$
4620.i1	4620i1	4620.i	4620i	$1$	$1$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$2310$	$2$	$0$	$1.398360550$	$1$	$2$	$480$	$-0.234390$	$-4194304/1155$	$0.85130$	$2.51046$	$[0, 1, 0, -21, 39]$	$y^2=x^3+x^2-21x+39$	2310.2.0.?	$[(2, 3)]$
4620.j1	4620j4	4620.j	4620j	$4$	$6$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{8} \cdot 3^{2} \cdot 5^{6} \cdot 7^{6} \cdot 11^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$4620$	$96$	$1$	$1$	$1$	$1$	$31104$	$1.719421$	$52702650535889104/22020583921875$	$0.96882$	$5.22017$	$[0, 1, 0, -49596, 2224980]$	$y^2=x^3+x^2-49596x+2224980$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 44.6.0.a.1, 132.48.0.?, $\ldots$	$[]$
4620.j2	4620j2	4620.j	4620j	$4$	$6$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{8} \cdot 3^{6} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$4620$	$96$	$1$	$1$	$1$	$5$	$10368$	$1.170115$	$33766427105425744/9823275$	$0.94982$	$5.16741$	$[0, 1, 0, -42756, 3388644]$	$y^2=x^3+x^2-42756x+3388644$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 44.6.0.a.1, 132.48.0.?, $\ldots$	$[]$
4620.j3	4620j1	4620.j	4620j	$4$	$6$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{12} \cdot 5 \cdot 7 \cdot 11^{2} $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$4620$	$96$	$1$	$1$	$1$	$5$	$5184$	$0.823541$	$-130287139815424/2250652635$	$1.00810$	$4.18371$	$[0, 1, 0, -2661, 52740]$	$y^2=x^3+x^2-2661x+52740$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 44.6.0.b.1, 70.6.0.a.1, $\ldots$	$[]$
4620.j4	4620j3	4620.j	4620j	$4$	$6$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{4} \cdot 5^{3} \cdot 7^{3} \cdot 11^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$4620$	$96$	$1$	$1$	$1$	$1$	$15552$	$1.372847$	$7549996227362816/6152409907875$	$1.05409$	$4.66132$	$[0, 1, 0, 10299, 260424]$	$y^2=x^3+x^2+10299x+260424$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 44.6.0.b.1, 70.6.0.a.1, $\ldots$	$[]$
4620.k1	4620k2	4620.k	4620k	$2$	$3$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 3 \cdot 5^{9} \cdot 7^{3} \cdot 11 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$2310$	$16$	$0$	$4.635133657$	$1$	$2$	$7776$	$1.132629$	$-5833703071744/22107421875$	$0.96766$	$4.38025$	$[0, 1, 0, -2381, -123681]$	$y^2=x^3+x^2-2381x-123681$	3.8.0-3.a.1.1, 2310.16.0.?	$[(66, 105)]$
4620.k2	4620k1	4620.k	4620k	$2$	$3$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{3} \cdot 7 \cdot 11^{3} $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$2310$	$16$	$0$	$1.545044552$	$1$	$10$	$2592$	$0.583323$	$7476617216/31444875$	$0.91273$	$3.56898$	$[0, 1, 0, 259, 4095]$	$y^2=x^3+x^2+259x+4095$	3.8.0-3.a.1.2, 2310.16.0.?	$[(-11, 6)]$
4620.l1	4620m1	4620.l	4620m	$1$	$1$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 3^{9} \cdot 5^{7} \cdot 7 \cdot 11^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$2310$	$2$	$0$	$0.016251541$	$1$	$24$	$90720$	$2.336140$	$-3273741656681120014336/1733575611796875$	$1.03268$	$6.52825$	$[0, 1, 0, -1964205, 1059396975]$	$y^2=x^3+x^2-1964205x+1059396975$	2310.2.0.?	$[(-1035, 44550)]$
4620.m1	4620l2	4620.m	4620l	$2$	$2$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{8} \cdot 3^{3} \cdot 5 \cdot 7^{4} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$660$	$12$	$0$	$0.469962631$	$1$	$7$	$3456$	$0.608749$	$68150496976/39220335$	$0.93854$	$3.61337$	$[0, 1, 0, -540, -540]$	$y^2=x^3+x^2-540x-540$	2.3.0.a.1, 44.6.0.c.1, 60.6.0.a.1, 660.12.0.?	$[(-12, 66)]$
4620.m2	4620l1	4620.m	4620l	$2$	$2$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{6} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$660$	$12$	$0$	$0.234981315$	$1$	$13$	$1728$	$0.262176$	$16880451584/9823275$	$0.99667$	$3.11941$	$[0, 1, 0, 135, 0]$	$y^2=x^3+x^2+135x$	2.3.0.a.1, 22.6.0.a.1, 60.6.0.b.1, 660.12.0.?	$[(3, 21)]$
4620.n1	4620n1	4620.n	4620n	$2$	$3$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 3^{9} \cdot 5^{3} \cdot 7^{3} \cdot 11 $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$2310$	$16$	$0$	$0.238324444$	$1$	$20$	$7776$	$1.064508$	$-4890195460096/9282994875$	$0.98037$	$4.29211$	$[0, 1, 0, -2245, 83975]$	$y^2=x^3+x^2-2245x+83975$	3.8.0-3.a.1.2, 2310.16.0.?	$[(50, 315)]$
4620.n2	4620n2	4620.n	4620n	$2$	$3$	$ 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 3^{3} \cdot 5 \cdot 7^{9} \cdot 11^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$2310$	$16$	$0$	$0.714973332$	$1$	$4$	$23328$	$1.613813$	$3132137615458304/7250937873795$	$1.02034$	$5.01584$	$[0, 1, 0, 19355, -1788745]$	$y^2=x^3+x^2+19355x-1788745$	3.8.0-3.a.1.1, 2310.16.0.?	$[(98, 1029)]$

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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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