LMFDB - Elliptic curves over $\Q$ of conductor 1850

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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 (28 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
1850.a1	1850g1	1850.a	1850g	$2$	$3$	$ 2 \cdot 5^{2} \cdot 37 $	$ - 2^{10} \cdot 5^{4} \cdot 37^{3} $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$444$	$16$	$0$	$0.677837982$	$1$	$8$	$1800$	$0.704188$	$-19026212425/51868672$	$0.95767$	$4.23361$	$[1, 0, 1, -476, 9498]$	$y^2+xy+y=x^3-476x+9498$	3.8.0-3.a.1.2, 148.2.0.?, 444.16.0.?	$[(17, 71)]$
1850.a2	1850g2	1850.a	1850g	$2$	$3$	$ 2 \cdot 5^{2} \cdot 37 $	$ - 2^{30} \cdot 5^{4} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$444$	$16$	$0$	$2.033513947$	$1$	$0$	$5400$	$1.253494$	$12642252501575/39728447488$	$1.00115$	$5.06375$	$[1, 0, 1, 4149, -216202]$	$y^2+xy+y=x^3+4149x-216202$	3.8.0-3.a.1.1, 148.2.0.?, 444.16.0.?	$[(967/3, 31304/3)]$
1850.b1	1850b1	1850.b	1850b	$1$	$1$	$ 2 \cdot 5^{2} \cdot 37 $	$ - 2^{6} \cdot 5^{2} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$148$	$2$	$0$	$0.507639273$	$1$	$4$	$216$	$-0.405339$	$-625/2368$	$1.29119$	$2.45164$	$[1, 0, 1, -1, -12]$	$y^2+xy+y=x^3-x-12$	148.2.0.?	$[(3, 2)]$
1850.c1	1850c1	1850.c	1850c	$1$	$1$	$ 2 \cdot 5^{2} \cdot 37 $	$ - 2 \cdot 5^{8} \cdot 37^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	8.2.0.1		$8$	$2$	$0$	$1$	$1$	$0$	$960$	$0.413319$	$-121945/2738$	$0.85164$	$3.75793$	$[1, 1, 0, -75, -1625]$	$y^2+xy=x^3+x^2-75x-1625$	8.2.0.a.1	$[]$
1850.d1	1850e1	1850.d	1850e	$1$	$1$	$ 2 \cdot 5^{2} \cdot 37 $	$ - 2^{3} \cdot 5^{9} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1480$	$2$	$0$	$0.686718092$	$1$	$4$	$720$	$0.391537$	$-804357/296$	$0.80610$	$3.79837$	$[1, -1, 0, -242, 1916]$	$y^2+xy=x^3-x^2-242x+1916$	1480.2.0.?	$[(19, 53)]$
1850.e1	1850f2	1850.e	1850f	$2$	$2$	$ 2 \cdot 5^{2} \cdot 37 $	$ 2^{9} \cdot 5^{3} \cdot 37^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1480$	$12$	$0$	$5.115691247$	$1$	$2$	$1728$	$0.886325$	$2253707317528029/700928$	$1.14580$	$5.34095$	$[1, -1, 0, -13657, -610899]$	$y^2+xy=x^3-x^2-13657x-610899$	2.3.0.a.1, 40.6.0.b.1, 296.6.0.?, 740.6.0.?, 1480.12.0.?	$[(2199, 101853)]$
1850.e2	1850f1	1850.e	1850f	$2$	$2$	$ 2 \cdot 5^{2} \cdot 37 $	$ 2^{18} \cdot 5^{3} \cdot 37 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1480$	$12$	$0$	$2.557845623$	$1$	$3$	$864$	$0.539751$	$557238592989/9699328$	$1.12880$	$4.23698$	$[1, -1, 0, -857, -9299]$	$y^2+xy=x^3-x^2-857x-9299$	2.3.0.a.1, 40.6.0.c.1, 296.6.0.?, 370.6.0.?, 1480.12.0.?	$[(-15, 4)]$
1850.f1	1850a3	1850.f	1850a	$4$	$6$	$ 2 \cdot 5^{2} \cdot 37 $	$ 2^{4} \cdot 5^{7} \cdot 37^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.6.0.3, 3.4.0.1	2B, 3B	$4440$	$384$	$9$	$11.27996712$	$1$	$1$	$6912$	$1.448227$	$16232905099479601/4052240$	$0.97924$	$6.24522$	$[1, 1, 0, -131875, -18487875]$	$y^2+xy=x^3+x^2-131875x-18487875$	2.3.0.a.1, 3.4.0.a.1, 4.6.0.b.1, 6.12.0.a.1, 12.24.0.f.1, $\ldots$	$[(563410/33, 250098685/33)]$
1850.f2	1850a4	1850.f	1850a	$4$	$6$	$ 2 \cdot 5^{2} \cdot 37 $	$ - 2^{2} \cdot 5^{8} \cdot 37^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.6.0.5, 3.4.0.1	2B, 3B	$4440$	$384$	$9$	$5.639983561$	$1$	$2$	$13824$	$1.794800$	$-16048965315233521/256572640900$	$0.97955$	$6.24733$	$[1, 1, 0, -131375, -18634375]$	$y^2+xy=x^3+x^2-131375x-18634375$	2.3.0.a.1, 3.4.0.a.1, 4.6.0.a.1, 6.12.0.a.1, 12.48.0.b.2, $\ldots$	$[(1780, 72535)]$
1850.f3	1850a1	1850.f	1850a	$4$	$6$	$ 2 \cdot 5^{2} \cdot 37 $	$ 2^{12} \cdot 5^{9} \cdot 37 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.6.0.3, 3.4.0.1	2B, 3B	$4440$	$384$	$9$	$3.759989040$	$1$	$3$	$2304$	$0.898921$	$46694890801/18944000$	$0.91392$	$4.54922$	$[1, 1, 0, -1875, -17875]$	$y^2+xy=x^3+x^2-1875x-17875$	2.3.0.a.1, 3.4.0.a.1, 4.6.0.b.1, 6.12.0.a.1, 12.24.0.f.1, $\ldots$	$[(-19, 116)]$
1850.f4	1850a2	1850.f	1850a	$4$	$6$	$ 2 \cdot 5^{2} \cdot 37 $	$ - 2^{6} \cdot 5^{12} \cdot 37^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.6.0.5, 3.4.0.1	2B, 3B	$4440$	$384$	$9$	$1.879994520$	$1$	$2$	$4608$	$1.245495$	$1625964918479/1369000000$	$0.94818$	$5.02114$	$[1, 1, 0, 6125, -121875]$	$y^2+xy=x^3+x^2+6125x-121875$	2.3.0.a.1, 3.4.0.a.1, 4.6.0.a.1, 6.12.0.a.1, 12.48.0.b.1, $\ldots$	$[(30, 285)]$
1850.g1	1850d1	1850.g	1850d	$1$	$1$	$ 2 \cdot 5^{2} \cdot 37 $	$ - 2^{23} \cdot 5^{8} \cdot 37^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	8.2.0.1		$8$	$2$	$0$	$1$	$1$	$0$	$22080$	$1.747602$	$-132384574175625/11484004352$	$1.06229$	$6.05241$	$[1, -1, 0, -77617, 8944541]$	$y^2+xy=x^3-x^2-77617x+8944541$	8.2.0.a.1	$[]$
1850.h1	1850m1	1850.h	1850m	$1$	$1$	$ 2 \cdot 5^{2} \cdot 37 $	$ - 2^{23} \cdot 5^{2} \cdot 37^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	8.2.0.1		$8$	$2$	$0$	$0.062324207$	$1$	$10$	$4416$	$0.942883$	$-132384574175625/11484004352$	$1.06229$	$4.76878$	$[1, -1, 1, -3105, 72177]$	$y^2+xy+y=x^3-x^2-3105x+72177$	8.2.0.a.1	$[(183, 2276)]$
1850.i1	1850l1	1850.i	1850l	$1$	$1$	$ 2 \cdot 5^{2} \cdot 37 $	$ - 2^{11} \cdot 5^{7} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1480$	$2$	$0$	$0.100155033$	$1$	$12$	$1056$	$0.559989$	$214921799/378880$	$0.86906$	$3.92910$	$[1, 0, 0, 312, -3008]$	$y^2+xy=x^3+312x-3008$	1480.2.0.?	$[(12, 44)]$
1850.j1	1850o2	1850.j	1850o	$2$	$2$	$ 2 \cdot 5^{2} \cdot 37 $	$ 2^{9} \cdot 5^{9} \cdot 37^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1480$	$12$	$0$	$2.217067129$	$1$	$4$	$8640$	$1.691044$	$2253707317528029/700928$	$1.14580$	$6.62458$	$[1, -1, 1, -341430, -76703803]$	$y^2+xy+y=x^3-x^2-341430x-76703803$	2.3.0.a.1, 40.6.0.b.1, 296.6.0.?, 740.6.0.?, 1480.12.0.?	$[(-337, 171)]$
1850.j2	1850o1	1850.j	1850o	$2$	$2$	$ 2 \cdot 5^{2} \cdot 37 $	$ 2^{18} \cdot 5^{9} \cdot 37 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1480$	$12$	$0$	$1.108533564$	$1$	$7$	$4320$	$1.344471$	$557238592989/9699328$	$1.12880$	$5.52061$	$[1, -1, 1, -21430, -1183803]$	$y^2+xy+y=x^3-x^2-21430x-1183803$	2.3.0.a.1, 40.6.0.c.1, 296.6.0.?, 370.6.0.?, 1480.12.0.?	$[(-87, 171)]$
1850.k1	1850j3	1850.k	1850j	$4$	$4$	$ 2 \cdot 5^{2} \cdot 37 $	$ 2 \cdot 5^{10} \cdot 37 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$1480$	$48$	$0$	$8.348155895$	$1$	$0$	$1536$	$0.881229$	$6825481747209/46250$	$0.96373$	$5.21183$	$[1, -1, 1, -9880, -375503]$	$y^2+xy+y=x^3-x^2-9880x-375503$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 40.24.0-40.y.1.13, 296.24.0.?, $\ldots$	$[(72649/24, 7563175/24)]$
1850.k2	1850j2	1850.k	1850j	$4$	$4$	$ 2 \cdot 5^{2} \cdot 37 $	$ 2^{2} \cdot 5^{8} \cdot 37^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$1480$	$48$	$0$	$4.174077947$	$1$	$2$	$768$	$0.534657$	$1767172329/136900$	$0.99471$	$4.11399$	$[1, -1, 1, -630, -5503]$	$y^2+xy+y=x^3-x^2-630x-5503$	2.6.0.a.1, 4.12.0-2.a.1.1, 40.24.0-40.b.1.4, 296.24.0.?, 740.24.0.?, $\ldots$	$[(-53/2, 205/2)]$
1850.k3	1850j1	1850.k	1850j	$4$	$4$	$ 2 \cdot 5^{2} \cdot 37 $	$ 2^{4} \cdot 5^{7} \cdot 37 $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$1480$	$48$	$0$	$2.087038973$	$1$	$7$	$384$	$0.188082$	$15438249/2960$	$0.81779$	$3.48388$	$[1, -1, 1, -130, 497]$	$y^2+xy+y=x^3-x^2-130x+497$	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.y.1.2, 296.24.0.?, 370.6.0.?, $\ldots$	$[(-7, 35)]$
1850.k4	1850j4	1850.k	1850j	$4$	$4$	$ 2 \cdot 5^{2} \cdot 37 $	$ - 2 \cdot 5^{7} \cdot 37^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$1480$	$48$	$0$	$2.087038973$	$1$	$0$	$1536$	$0.881229$	$1689410871/18741610$	$1.06786$	$4.49346$	$[1, -1, 1, 620, -25503]$	$y^2+xy+y=x^3-x^2+620x-25503$	2.3.0.a.1, 4.12.0-4.c.1.2, 40.24.0-40.s.1.1, 296.24.0.?, 1480.48.0.?	$[(831/2, 23215/2)]$
1850.l1	1850n1	1850.l	1850n	$1$	$1$	$ 2 \cdot 5^{2} \cdot 37 $	$ - 2^{3} \cdot 5^{3} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1480$	$2$	$0$	$0.196247114$	$1$	$6$	$144$	$-0.413182$	$-804357/296$	$0.80610$	$2.51475$	$[1, -1, 1, -10, 17]$	$y^2+xy+y=x^3-x^2-10x+17$	1480.2.0.?	$[(-1, 5)]$
1850.m1	1850k1	1850.m	1850k	$1$	$1$	$ 2 \cdot 5^{2} \cdot 37 $	$ - 2 \cdot 5^{2} \cdot 37^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2$	8.2.0.1		$8$	$2$	$0$	$1.449379421$	$1$	$0$	$192$	$-0.391400$	$-121945/2738$	$0.85164$	$2.47430$	$[1, 0, 0, -3, -13]$	$y^2+xy=x^3-3x-13$	8.2.0.a.1	$[(19/2, 55/2)]$
1850.n1	1850p1	1850.n	1850p	$1$	$1$	$ 2 \cdot 5^{2} \cdot 37 $	$ - 2^{6} \cdot 5^{8} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$148$	$2$	$0$	$1$	$1$	$0$	$1080$	$0.399380$	$-625/2368$	$1.29119$	$3.73526$	$[1, 1, 1, -13, -1469]$	$y^2+xy+y=x^3+x^2-13x-1469$	148.2.0.?	$[]$
1850.o1	1850h1	1850.o	1850h	$3$	$9$	$ 2 \cdot 5^{2} \cdot 37 $	$ - 2 \cdot 5^{7} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$13320$	$144$	$3$	$1$	$1$	$0$	$864$	$0.413506$	$-16954786009/370$	$0.88414$	$4.41456$	$[1, 1, 1, -1338, 18281]$	$y^2+xy+y=x^3+x^2-1338x+18281$	3.4.0.a.1, 9.12.0.a.1, 15.8.0-3.a.1.2, 45.24.0-9.a.1.1, 333.36.0.?, $\ldots$	$[]$
1850.o2	1850h2	1850.o	1850h	$3$	$9$	$ 2 \cdot 5^{2} \cdot 37 $	$ - 2^{3} \cdot 5^{9} \cdot 37^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.12.0.1	3Cs	$13320$	$144$	$3$	$1$	$1$	$0$	$2592$	$0.962812$	$-702595369/50653000$	$0.95453$	$4.63381$	$[1, 1, 1, -463, 42781]$	$y^2+xy+y=x^3+x^2-463x+42781$	3.12.0.a.1, 15.24.0-3.a.1.1, 333.36.0.?, 888.24.0.?, 1480.2.0.?, $\ldots$	$[]$
1850.o3	1850h3	1850.o	1850h	$3$	$9$	$ 2 \cdot 5^{2} \cdot 37 $	$ - 2^{9} \cdot 5^{15} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$13320$	$144$	$3$	$1$	$1$	$0$	$7776$	$1.512117$	$510273943271/37000000000$	$0.99687$	$5.50815$	$[1, 1, 1, 4162, -1150469]$	$y^2+xy+y=x^3+x^2+4162x-1150469$	3.4.0.a.1, 9.12.0.a.1, 15.8.0-3.a.1.1, 45.24.0-9.a.1.2, 333.36.0.?, $\ldots$	$[]$
1850.p1	1850i1	1850.p	1850i	$2$	$3$	$ 2 \cdot 5^{2} \cdot 37 $	$ - 2^{10} \cdot 5^{10} \cdot 37^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2220$	$16$	$0$	$1$	$1$	$0$	$9000$	$1.508907$	$-19026212425/51868672$	$0.95767$	$5.51723$	$[1, 1, 1, -11888, 1187281]$	$y^2+xy+y=x^3+x^2-11888x+1187281$	3.4.0.a.1, 15.8.0-3.a.1.2, 148.2.0.?, 444.8.0.?, 2220.16.0.?	$[]$
1850.p2	1850i2	1850.p	1850i	$2$	$3$	$ 2 \cdot 5^{2} \cdot 37 $	$ - 2^{30} \cdot 5^{10} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2220$	$16$	$0$	$1$	$1$	$0$	$27000$	$2.058212$	$12642252501575/39728447488$	$1.00115$	$6.34737$	$[1, 1, 1, 103737, -27025219]$	$y^2+xy+y=x^3+x^2+103737x-27025219$	3.4.0.a.1, 15.8.0-3.a.1.1, 148.2.0.?, 444.8.0.?, 2220.16.0.?	$[]$

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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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