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	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
6048.a1	6048u1	6048.a	6048u	$1$	$1$	$ 2^{5} \cdot 3^{3} \cdot 7 $	$ 2^{12} \cdot 3^{3} \cdot 7 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$0.593261292$	$1$	$4$	$768$	$-0.177516$	$13824/7$	$0.78795$	$2.42869$	$[0, 0, 0, -24, 16]$	$y^2=x^3-24x+16$	42.2.0.a.1	$[(0, 4)]$
6048.d1	6048r1	6048.d	6048r	$1$	$1$	$ 2^{5} \cdot 3^{3} \cdot 7 $	$ 2^{12} \cdot 3^{3} \cdot 7 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$0.741757910$	$1$	$4$	$768$	$-0.177516$	$13824/7$	$0.78795$	$2.42869$	$[0, 0, 0, -24, -16]$	$y^2=x^3-24x-16$	42.2.0.a.1	$[(-4, 4)]$
6048.v1	6048d1	6048.v	6048d	$1$	$1$	$ 2^{5} \cdot 3^{3} \cdot 7 $	$ 2^{12} \cdot 3^{9} \cdot 7 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$1.759817104$	$1$	$2$	$2304$	$0.371790$	$13824/7$	$0.78795$	$3.18570$	$[0, 0, 0, -216, -432]$	$y^2=x^3-216x-432$	42.2.0.a.1	$[(-8, 28)]$
6048.w1	6048k1	6048.w	6048k	$1$	$1$	$ 2^{5} \cdot 3^{3} \cdot 7 $	$ 2^{12} \cdot 3^{9} \cdot 7 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$0.545030116$	$1$	$4$	$2304$	$0.371790$	$13824/7$	$0.78795$	$3.18570$	$[0, 0, 0, -216, 432]$	$y^2=x^3-216x+432$	42.2.0.a.1	$[(-12, 36)]$
12096.f1	12096cv1	12096.f	12096cv	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 7 $	$ 2^{6} \cdot 3^{9} \cdot 7 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$0.597369147$	$1$	$2$	$2304$	$0.025217$	$13824/7$	$0.78795$	$2.50840$	$[0, 0, 0, -54, -54]$	$y^2=x^3-54x-54$	42.2.0.a.1	$[(-3, 9)]$
12096.o1	12096cf1	12096.o	12096cf	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 7 $	$ 2^{6} \cdot 3^{9} \cdot 7 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$1.966250482$	$1$	$2$	$2304$	$0.025217$	$13824/7$	$0.78795$	$2.50840$	$[0, 0, 0, -54, 54]$	$y^2=x^3-54x+54$	42.2.0.a.1	$[(1, 1)]$
12096.cu1	12096bq1	12096.cu	12096bq	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 7 $	$ 2^{6} \cdot 3^{3} \cdot 7 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$1$	$1$	$0$	$768$	$-0.524089$	$13824/7$	$0.78795$	$1.80721$	$[0, 0, 0, -6, 2]$	$y^2=x^3-6x+2$	42.2.0.a.1	$[]$
12096.cx1	12096dd1	12096.cx	12096dd	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 7 $	$ 2^{6} \cdot 3^{3} \cdot 7 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$1$	$1$	$0$	$768$	$-0.524089$	$13824/7$	$0.78795$	$1.80721$	$[0, 0, 0, -6, -2]$	$y^2=x^3-6x-2$	42.2.0.a.1	$[]$
42336.a1	42336u1	42336.a	42336u	$1$	$1$	$ 2^{5} \cdot 3^{3} \cdot 7^{2} $	$ 2^{12} \cdot 3^{9} \cdot 7^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$1$	$1$	$0$	$110592$	$1.344746$	$13824/7$	$0.78795$	$3.69975$	$[0, 0, 0, -10584, -148176]$	$y^2=x^3-10584x-148176$	42.2.0.a.1	$[]$
42336.d1	42336bp1	42336.d	42336bp	$1$	$1$	$ 2^{5} \cdot 3^{3} \cdot 7^{2} $	$ 2^{12} \cdot 3^{9} \cdot 7^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$0.380785454$	$1$	$6$	$110592$	$1.344746$	$13824/7$	$0.78795$	$3.69975$	$[0, 0, 0, -10584, 148176]$	$y^2=x^3-10584x+148176$	42.2.0.a.1	$[(168, 1764)]$
42336.dc1	42336cj1	42336.dc	42336cj	$1$	$1$	$ 2^{5} \cdot 3^{3} \cdot 7^{2} $	$ 2^{12} \cdot 3^{3} \cdot 7^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$1.097819566$	$1$	$2$	$36864$	$0.795440$	$13824/7$	$0.78795$	$3.08101$	$[0, 0, 0, -1176, -5488]$	$y^2=x^3-1176x-5488$	42.2.0.a.1	$[(-7, 49)]$
42336.df1	42336de1	42336.df	42336de	$1$	$1$	$ 2^{5} \cdot 3^{3} \cdot 7^{2} $	$ 2^{12} \cdot 3^{3} \cdot 7^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$1$	$1$	$0$	$36864$	$0.795440$	$13824/7$	$0.78795$	$3.08101$	$[0, 0, 0, -1176, 5488]$	$y^2=x^3-1176x+5488$	42.2.0.a.1	$[]$
84672.x1	84672hv1	84672.x	84672hv	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 7^{2} $	$ 2^{6} \cdot 3^{3} \cdot 7^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$1.117520309$	$1$	$2$	$36864$	$0.448866$	$13824/7$	$0.78795$	$2.52626$	$[0, 0, 0, -294, 686]$	$y^2=x^3-294x+686$	42.2.0.a.1	$[(-7, 49)]$
84672.bi1	84672kr1	84672.bi	84672kr	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 7^{2} $	$ 2^{6} \cdot 3^{3} \cdot 7^{7} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$1.901323575$	$1$	$4$	$36864$	$0.448866$	$13824/7$	$0.78795$	$2.52626$	$[0, 0, 0, -294, -686]$	$y^2=x^3-294x-686$	42.2.0.a.1	$[(21, 49), (-63/2, 49/2)]$
84672.jt1	84672hl1	84672.jt	84672hl	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 7^{2} $	$ 2^{6} \cdot 3^{9} \cdot 7^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$2.589370016$	$1$	$2$	$110592$	$0.998172$	$13824/7$	$0.78795$	$3.10720$	$[0, 0, 0, -2646, 18522]$	$y^2=x^3-2646x+18522$	42.2.0.a.1	$[(133, 1421)]$
84672.ke1	84672kk1	84672.ke	84672kk	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 7^{2} $	$ 2^{6} \cdot 3^{9} \cdot 7^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$1$	$1$	$0$	$110592$	$0.998172$	$13824/7$	$0.78795$	$3.10720$	$[0, 0, 0, -2646, -18522]$	$y^2=x^3-2646x-18522$	42.2.0.a.1	$[]$
151200.ba1	151200ck1	151200.ba	151200ck	$1$	$1$	$ 2^{5} \cdot 3^{3} \cdot 5^{2} \cdot 7 $	$ 2^{12} \cdot 3^{9} \cdot 5^{6} \cdot 7 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$1$	$1$	$0$	$248832$	$1.176510$	$13824/7$	$0.78795$	$3.13558$	$[0, 0, 0, -5400, 54000]$	$y^2=x^3-5400x+54000$	42.2.0.a.1	$[]$
151200.bx1	151200dw1	151200.bx	151200dw	$1$	$1$	$ 2^{5} \cdot 3^{3} \cdot 5^{2} \cdot 7 $	$ 2^{12} \cdot 3^{3} \cdot 5^{6} \cdot 7 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$1$	$1$	$0$	$82944$	$0.627203$	$13824/7$	$0.78795$	$2.58288$	$[0, 0, 0, -600, -2000]$	$y^2=x^3-600x-2000$	42.2.0.a.1	$[]$
151200.dq1	151200eq1	151200.dq	151200eq	$1$	$1$	$ 2^{5} \cdot 3^{3} \cdot 5^{2} \cdot 7 $	$ 2^{12} \cdot 3^{3} \cdot 5^{6} \cdot 7 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$1$	$1$	$0$	$82944$	$0.627203$	$13824/7$	$0.78795$	$2.58288$	$[0, 0, 0, -600, 2000]$	$y^2=x^3-600x+2000$	42.2.0.a.1	$[]$
151200.en1	151200s1	151200.en	151200s	$1$	$1$	$ 2^{5} \cdot 3^{3} \cdot 5^{2} \cdot 7 $	$ 2^{12} \cdot 3^{9} \cdot 5^{6} \cdot 7 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$1$	$1$	$0$	$248832$	$1.176510$	$13824/7$	$0.78795$	$3.13558$	$[0, 0, 0, -5400, -54000]$	$y^2=x^3-5400x-54000$	42.2.0.a.1	$[]$
302400.db1	302400db1	302400.db	302400db	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 5^{2} \cdot 7 $	$ 2^{6} \cdot 3^{3} \cdot 5^{6} \cdot 7 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$1$	$1$	$0$	$82944$	$0.280630$	$13824/7$	$0.78795$	$2.11145$	$[0, 0, 0, -150, -250]$	$y^2=x^3-150x-250$	42.2.0.a.1	$[]$
302400.he1	302400he1	302400.he	302400he	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 5^{2} \cdot 7 $	$ 2^{6} \cdot 3^{9} \cdot 5^{6} \cdot 7 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$2.573387957$	$1$	$2$	$248832$	$0.829936$	$13824/7$	$0.78795$	$2.63379$	$[0, 0, 0, -1350, 6750]$	$y^2=x^3-1350x+6750$	42.2.0.a.1	$[(-39, 9)]$
302400.oe1	302400oe1	302400.oe	302400oe	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 5^{2} \cdot 7 $	$ 2^{6} \cdot 3^{9} \cdot 5^{6} \cdot 7 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$10.34610551$	$1$	$0$	$248832$	$0.829936$	$13824/7$	$0.78795$	$2.63379$	$[0, 0, 0, -1350, -6750]$	$y^2=x^3-1350x-6750$	42.2.0.a.1	$[(-7331/29, 1609597/29)]$
302400.sb1	302400sb1	302400.sb	302400sb	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 5^{2} \cdot 7 $	$ 2^{6} \cdot 3^{3} \cdot 5^{6} \cdot 7 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$1$	$1$	$0$	$82944$	$0.280630$	$13824/7$	$0.78795$	$2.11145$	$[0, 0, 0, -150, 250]$	$y^2=x^3-150x+250$	42.2.0.a.1	$[]$
1058400.ew1	-	1058400.ew	-	$1$	$1$	$ 2^{5} \cdot 3^{3} \cdot 5^{2} \cdot 7^{2} $	$ 2^{12} \cdot 3^{9} \cdot 5^{6} \cdot 7^{7} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$3.305144810$	$1$	$8$	$11943936$	$2.149464$	$13824/7$	$0.78795$	$3.53738$	$[0, 0, 0, -264600, -18522000]$	$y^2=x^3-264600x-18522000$	42.2.0.a.1	$[(-84, 1764), (924, 22932)]$
1058400.ex1	-	1058400.ex	-	$1$	$1$	$ 2^{5} \cdot 3^{3} \cdot 5^{2} \cdot 7^{2} $	$ 2^{12} \cdot 3^{3} \cdot 5^{6} \cdot 7^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$4.075382224$	$1$	$2$	$3981312$	$1.600159$	$13824/7$	$0.78795$	$3.06221$	$[0, 0, 0, -29400, -686000]$	$y^2=x^3-29400x-686000$	42.2.0.a.1	$[(-24, 76)]$
1058400.mc1	-	1058400.mc	-	$1$	$1$	$ 2^{5} \cdot 3^{3} \cdot 5^{2} \cdot 7^{2} $	$ 2^{12} \cdot 3^{9} \cdot 5^{6} \cdot 7^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$8.465942056$	$1$	$0$	$11943936$	$2.149464$	$13824/7$	$0.78795$	$3.53738$	$[0, 0, 0, -264600, 18522000]$	$y^2=x^3-264600x+18522000$	42.2.0.a.1	$[(-61376/11, 6275332/11)]$
1058400.md1	-	1058400.md	-	$1$	$1$	$ 2^{5} \cdot 3^{3} \cdot 5^{2} \cdot 7^{2} $	$ 2^{12} \cdot 3^{3} \cdot 5^{6} \cdot 7^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$1$	$1$	$0$	$3981312$	$1.600159$	$13824/7$	$0.78795$	$3.06221$	$[0, 0, 0, -29400, 686000]$	$y^2=x^3-29400x+686000$	42.2.0.a.1	$[]$
2116800.xg1	-	2116800.xg	-	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 5^{2} \cdot 7^{2} $	$ 2^{6} \cdot 3^{9} \cdot 5^{6} \cdot 7^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$1$	$1$	$0$	$11943936$	$1.802891$	$13824/7$	$0.78795$	$3.08351$	$[0, 0, 0, -66150, 2315250]$	$y^2=x^3-66150x+2315250$	42.2.0.a.1	$[]$
2116800.xn1	-	2116800.xn	-	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 5^{2} \cdot 7^{2} $	$ 2^{6} \cdot 3^{3} \cdot 5^{6} \cdot 7^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$1$	$1$	$0$	$3981312$	$1.253584$	$13824/7$	$0.78795$	$2.63096$	$[0, 0, 0, -7350, 85750]$	$y^2=x^3-7350x+85750$	42.2.0.a.1	$[]$
2116800.bys1	-	2116800.bys	-	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 5^{2} \cdot 7^{2} $	$ 2^{6} \cdot 3^{9} \cdot 5^{6} \cdot 7^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$9.606198957$	$1$	$0$	$11943936$	$1.802891$	$13824/7$	$0.78795$	$3.08351$	$[0, 0, 0, -66150, -2315250]$	$y^2=x^3-66150x-2315250$	42.2.0.a.1	$[(-25151/26, 5400143/26)]$
2116800.byz1	-	2116800.byz	-	$1$	$1$	$ 2^{6} \cdot 3^{3} \cdot 5^{2} \cdot 7^{2} $	$ 2^{6} \cdot 3^{3} \cdot 5^{6} \cdot 7^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$42$	$2$	$0$	$10.14762906$	$1$	$0$	$3981312$	$1.253584$	$13824/7$	$0.78795$	$2.63096$	$[0, 0, 0, -7350, -85750]$	$y^2=x^3-7350x-85750$	42.2.0.a.1	$[(-7411/17, 1439663/17)]$

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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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