LMFDB - Elliptic curves over $\Q$ of conductor 6672

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Isogeny class degree	Cyclic isogeny degree	Isogeny class size	Integral points

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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
6672.a1	6672m2	6672.a	6672m	$2$	$5$	$ 2^{4} \cdot 3 \cdot 139 $	$ - 2^{14} \cdot 3 \cdot 139^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$8340$	$48$	$1$	$0.691054745$	$1$	$2$	$48000$	$1.641232$	$-143228059472161/622666136388$	$1.04157$	$4.88943$	$[0, -1, 0, -17440, 2592256]$	$y^2=x^3-x^2-17440x+2592256$	5.12.0.a.2, 20.24.0-5.a.2.2, 1668.2.0.?, 4170.24.0.?, 8340.48.1.?	$[(42, 1390)]$
6672.a2	6672m1	6672.a	6672m	$2$	$5$	$ 2^{4} \cdot 3 \cdot 139 $	$ - 2^{22} \cdot 3^{5} \cdot 139 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$8340$	$48$	$1$	$3.455273726$	$1$	$2$	$9600$	$0.836512$	$-37966934881/34587648$	$1.04223$	$3.81837$	$[0, -1, 0, -1120, -22784]$	$y^2=x^3-x^2-1120x-22784$	5.12.0.a.1, 20.24.0-5.a.1.2, 1668.2.0.?, 4170.24.0.?, 8340.48.1.?	$[(42, 50)]$
6672.b1	6672i1	6672.b	6672i	$1$	$1$	$ 2^{4} \cdot 3 \cdot 139 $	$ - 2^{14} \cdot 3^{4} \cdot 139 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$278$	$2$	$0$	$0.599375098$	$1$	$20$	$2304$	$0.265018$	$12167/45036$	$0.95901$	$3.00801$	$[0, -1, 0, 8, -656]$	$y^2=x^3-x^2+8x-656$	278.2.0.?	$[(28, 144), (10, 18)]$
6672.c1	6672j1	6672.c	6672j	$1$	$1$	$ 2^{4} \cdot 3 \cdot 139 $	$ - 2^{4} \cdot 3^{4} \cdot 139 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$278$	$2$	$0$	$1.568848267$	$1$	$2$	$576$	$-0.264657$	$-67108864/11259$	$1.02412$	$2.39039$	$[0, -1, 0, -21, -36]$	$y^2=x^3-x^2-21x-36$	278.2.0.?	$[(12, 36)]$
6672.d1	6672b1	6672.d	6672b	$2$	$2$	$ 2^{4} \cdot 3 \cdot 139 $	$ 2^{10} \cdot 3^{3} \cdot 139 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.4	2B	$3336$	$12$	$0$	$1$	$1$	$1$	$2688$	$0.390516$	$210094874500/3753$	$1.00904$	$3.74784$	$[0, -1, 0, -1248, -16560]$	$y^2=x^3-x^2-1248x-16560$	2.3.0.a.1, 8.6.0.d.1, 834.6.0.?, 3336.12.0.?	$[]$
6672.d2	6672b2	6672.d	6672b	$2$	$2$	$ 2^{4} \cdot 3 \cdot 139 $	$ - 2^{11} \cdot 3^{6} \cdot 139^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.5	2B	$3336$	$12$	$0$	$1$	$1$	$1$	$5376$	$0.737090$	$-95269531250/14085009$	$1.02921$	$3.76259$	$[0, -1, 0, -1208, -17712]$	$y^2=x^3-x^2-1208x-17712$	2.3.0.a.1, 8.6.0.a.1, 1668.6.0.?, 3336.12.0.?	$[]$
6672.e1	6672a1	6672.e	6672a	$1$	$1$	$ 2^{4} \cdot 3 \cdot 139 $	$ - 2^{10} \cdot 3^{3} \cdot 139 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1668$	$2$	$0$	$1$	$1$	$0$	$768$	$-0.022882$	$-12194500/3753$	$0.79234$	$2.68854$	$[0, -1, 0, -48, -144]$	$y^2=x^3-x^2-48x-144$	1668.2.0.?	$[]$
6672.f1	6672g2	6672.f	6672g	$2$	$2$	$ 2^{4} \cdot 3 \cdot 139 $	$ 2^{8} \cdot 3^{6} \cdot 139 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1668$	$12$	$0$	$1$	$1$	$1$	$3024$	$0.366688$	$169671989968/101331$	$1.20085$	$3.56614$	$[0, -1, 0, -732, -7380]$	$y^2=x^3-x^2-732x-7380$	2.3.0.a.1, 12.6.0.c.1, 556.6.0.?, 1668.12.0.?	$[]$
6672.f2	6672g1	6672.f	6672g	$2$	$2$	$ 2^{4} \cdot 3 \cdot 139 $	$ - 2^{4} \cdot 3^{3} \cdot 139^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1668$	$12$	$0$	$1$	$1$	$1$	$1512$	$0.020115$	$-359661568/521667$	$0.98395$	$2.69461$	$[0, -1, 0, -37, -152]$	$y^2=x^3-x^2-37x-152$	2.3.0.a.1, 6.6.0.a.1, 556.6.0.?, 1668.12.0.?	$[]$
6672.g1	6672l1	6672.g	6672l	$1$	$1$	$ 2^{4} \cdot 3 \cdot 139 $	$ - 2^{16} \cdot 3 \cdot 139 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1668$	$2$	$0$	$0.929394619$	$1$	$4$	$2304$	$0.407350$	$-23320116793/6672$	$0.89680$	$3.65569$	$[0, -1, 0, -952, 11632]$	$y^2=x^3-x^2-952x+11632$	1668.2.0.?	$[(18, 2)]$
6672.h1	6672k3	6672.h	6672k	$4$	$4$	$ 2^{4} \cdot 3 \cdot 139 $	$ 2^{19} \cdot 3^{7} \cdot 139^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$3336$	$48$	$0$	$14.52684329$	$1$	$1$	$225792$	$2.751015$	$368338718602320108230953/104500400213376$	$1.09517$	$7.10690$	$[0, -1, 0, -23894312, -44948257680]$	$y^2=x^3-x^2-23894312x-44948257680$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 12.12.0-4.c.1.2, 24.24.0-24.s.1.3, $\ldots$	$[(1107813508/23, 36872169934400/23)]$
6672.h2	6672k2	6672.h	6672k	$4$	$4$	$ 2^{4} \cdot 3 \cdot 139 $	$ 2^{26} \cdot 3^{14} \cdot 139^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$3336$	$48$	$0$	$29.05368659$	$1$	$3$	$112896$	$2.404438$	$91021581897882444073/1514074014498816$	$1.07852$	$6.16368$	$[0, -1, 0, -1499432, -695974800]$	$y^2=x^3-x^2-1499432x-695974800$	2.6.0.a.1, 8.12.0-2.a.1.1, 12.12.0-2.a.1.1, 24.24.0-24.b.1.3, 556.12.0.?, $\ldots$	$[(-9896556015806/124689, 760847204462025050/124689)]$
6672.h3	6672k1	6672.h	6672k	$4$	$4$	$ 2^{4} \cdot 3 \cdot 139 $	$ 2^{40} \cdot 3^{7} \cdot 139 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$3336$	$48$	$0$	$14.52684329$	$1$	$1$	$56448$	$2.057865$	$181453194188333353/81602499575808$	$1.06982$	$5.45756$	$[0, -1, 0, -188712, 14959728]$	$y^2=x^3-x^2-188712x+14959728$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 12.12.0-4.c.1.1, 24.24.0-24.y.1.10, $\ldots$	$[(-852254/89, 4111057974/89)]$
6672.h4	6672k4	6672.h	6672k	$4$	$4$	$ 2^{4} \cdot 3 \cdot 139 $	$ - 2^{19} \cdot 3^{28} \cdot 139 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$3336$	$48$	$0$	$58.10737319$	$1$	$1$	$225792$	$2.751015$	$-11886225803094313/407023891358666112$	$1.11464$	$6.39589$	$[0, -1, 0, -76072, -1964473232]$	$y^2=x^3-x^2-76072x-1964473232$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 24.24.0-24.y.1.16, 556.12.0.?, $\ldots$	$[(34363675714060590126861826/8101667775, 201441496898504757936562295718489517574/8101667775)]$
6672.i1	6672h2	6672.i	6672h	$2$	$3$	$ 2^{4} \cdot 3 \cdot 139 $	$ - 2^{4} \cdot 3^{4} \cdot 139^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1668$	$16$	$0$	$1$	$1$	$0$	$9792$	$0.970531$	$-15288691386744832/217535139$	$1.06519$	$4.54690$	$[0, -1, 0, -13029, 576792]$	$y^2=x^3-x^2-13029x+576792$	3.4.0.a.1, 12.8.0-3.a.1.2, 278.2.0.?, 834.8.0.?, 1668.16.0.?	$[]$
6672.i2	6672h1	6672.i	6672h	$2$	$3$	$ 2^{4} \cdot 3 \cdot 139 $	$ - 2^{4} \cdot 3^{12} \cdot 139 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1668$	$16$	$0$	$1$	$1$	$0$	$3264$	$0.421224$	$-2303721472/73870299$	$1.07120$	$3.22099$	$[0, -1, 0, -69, 1692]$	$y^2=x^3-x^2-69x+1692$	3.4.0.a.1, 12.8.0-3.a.1.1, 278.2.0.?, 834.8.0.?, 1668.16.0.?	$[]$
6672.j1	6672d1	6672.j	6672d	$1$	$1$	$ 2^{4} \cdot 3 \cdot 139 $	$ - 2^{10} \cdot 3^{8} \cdot 139 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$278$	$2$	$0$	$0.096141697$	$1$	$32$	$6656$	$0.536062$	$-82013318212/911979$	$0.89596$	$3.64318$	$[0, 1, 0, -912, 10404]$	$y^2=x^3+x^2-912x+10404$	278.2.0.?	$[(24, 54), (6, 72)]$
6672.k1	6672p1	6672.k	6672p	$1$	$1$	$ 2^{4} \cdot 3 \cdot 139 $	$ - 2^{26} \cdot 3^{4} \cdot 139 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$278$	$2$	$0$	$1.120622602$	$1$	$4$	$16128$	$1.178638$	$-119801283921073/184467456$	$0.96082$	$4.62625$	$[0, 1, 0, -16432, -817324]$	$y^2=x^3+x^2-16432x-817324$	278.2.0.?	$[(242, 3072)]$
6672.l1	6672f1	6672.l	6672f	$1$	$1$	$ 2^{4} \cdot 3 \cdot 139 $	$ - 2^{8} \cdot 3^{2} \cdot 139 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$278$	$2$	$0$	$0.920719066$	$1$	$2$	$896$	$-0.252139$	$-810448/1251$	$0.73962$	$2.32236$	$[0, 1, 0, -12, -36]$	$y^2=x^3+x^2-12x-36$	278.2.0.?	$[(6, 12)]$
6672.m1	6672q1	6672.m	6672q	$2$	$2$	$ 2^{4} \cdot 3 \cdot 139 $	$ 2^{14} \cdot 3 \cdot 139 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.4	2B	$3336$	$12$	$0$	$1$	$1$	$1$	$1536$	$0.088956$	$57066625/1668$	$0.82747$	$2.97280$	$[0, 1, 0, -128, -588]$	$y^2=x^3+x^2-128x-588$	2.3.0.a.1, 8.6.0.d.1, 834.6.0.?, 3336.12.0.?	$[]$
6672.m2	6672q2	6672.m	6672q	$2$	$2$	$ 2^{4} \cdot 3 \cdot 139 $	$ - 2^{13} \cdot 3^{2} \cdot 139^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.5	2B	$3336$	$12$	$0$	$1$	$1$	$1$	$3072$	$0.435529$	$857375/347778$	$0.94518$	$3.24000$	$[0, 1, 0, 32, -1804]$	$y^2=x^3+x^2+32x-1804$	2.3.0.a.1, 8.6.0.a.1, 1668.6.0.?, 3336.12.0.?	$[]$
6672.n1	6672n1	6672.n	6672n	$1$	$1$	$ 2^{4} \cdot 3 \cdot 139 $	$ - 2^{14} \cdot 3 \cdot 139 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1668$	$2$	$0$	$1.596352383$	$1$	$2$	$1152$	$-0.004024$	$857375/1668$	$0.80224$	$2.59365$	$[0, 1, 0, 32, 116]$	$y^2=x^3+x^2+32x+116$	1668.2.0.?	$[(4, 18)]$
6672.o1	6672c1	6672.o	6672c	$1$	$1$	$ 2^{4} \cdot 3 \cdot 139 $	$ - 2^{4} \cdot 3^{2} \cdot 139 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$278$	$2$	$0$	$1$	$1$	$0$	$576$	$-0.489820$	$702464/1251$	$0.76172$	$1.92672$	$[0, 1, 0, 5, -4]$	$y^2=x^3+x^2+5x-4$	278.2.0.?	$[]$
6672.p1	6672o1	6672.p	6672o	$1$	$1$	$ 2^{4} \cdot 3 \cdot 139 $	$ - 2^{12} \cdot 3^{9} \cdot 139 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1668$	$2$	$0$	$0.438668354$	$1$	$6$	$4608$	$0.613714$	$1829276567/2735937$	$0.90083$	$3.41884$	$[0, 1, 0, 408, -3852]$	$y^2=x^3+x^2+408x-3852$	1668.2.0.?	$[(12, 54)]$
6672.q1	6672e1	6672.q	6672e	$1$	$1$	$ 2^{4} \cdot 3 \cdot 139 $	$ - 2^{10} \cdot 3^{11} \cdot 139 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$1668$	$2$	$0$	$1$	$1$	$0$	$25344$	$1.174126$	$-3439147732759876/24623433$	$0.97188$	$4.84977$	$[0, 1, 0, -31696, -2182588]$	$y^2=x^3+x^2-31696x-2182588$	1668.2.0.?	$[]$

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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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