LMFDB - Elliptic curves over $\Q$ of conductor 132878

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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	Manin constant

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Results (21 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
132878.a1	132878h1	132878.a	132878h	$1$	$1$	$ 2 \cdot 29^{2} \cdot 79 $	$ 2^{4} \cdot 29^{10} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$1$	$1$		$0$	$7848960$	$2.314186$	$778713392276001/894003184$	$0.91948$	$4.61910$	$[1, -1, 0, -1611934, -786530204]$	$y^2+xy=x^3-x^2-1611934x-786530204$	316.2.0.?	$[ ]$
132878.b1	132878i2	132878.b	132878i	$2$	$2$	$ 2 \cdot 29^{2} \cdot 79 $	$ 2 \cdot 29^{6} \cdot 79^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$632$	$12$	$0$	$1$	$1$		$0$	$280896$	$1.193182$	$81182737/12482$	$0.85973$	$3.25637$	$[1, 0, 1, -7587, 217316]$	$y^2+xy+y=x^3-7587x+217316$	2.3.0.a.1, 8.6.0.b.1, 316.6.0.?, 632.12.0.?	$[ ]$
132878.b2	132878i1	132878.b	132878i	$2$	$2$	$ 2 \cdot 29^{2} \cdot 79 $	$ - 2^{2} \cdot 29^{6} \cdot 79 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$632$	$12$	$0$	$1$	$1$		$1$	$140448$	$0.846608$	$103823/316$	$0.80009$	$2.81451$	$[1, 0, 1, 823, 18840]$	$y^2+xy+y=x^3+823x+18840$	2.3.0.a.1, 8.6.0.c.1, 158.6.0.?, 632.12.0.?	$[ ]$
132878.c1	132878j1	132878.c	132878j	$1$	$1$	$ 2 \cdot 29^{2} \cdot 79 $	$ - 2^{4} \cdot 29^{2} \cdot 79 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$158$	$2$	$0$	$1.653784626$	$1$		$8$	$18720$	$-0.161812$	$198911/1264$	$0.74007$	$1.80008$	$[1, 0, 1, 11, 48]$	$y^2+xy+y=x^3+11x+48$	158.2.0.?	$[(-1, 6), (7, 18)]$
132878.d1	132878k1	132878.d	132878k	$1$	$1$	$ 2 \cdot 29^{2} \cdot 79 $	$ - 2^{4} \cdot 29^{8} \cdot 79^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$158$	$2$	$0$	$1.019227982$	$1$		$2$	$5929920$	$2.682343$	$-349036859307177/7888624$	$0.97963$	$5.12195$	$[1, -1, 0, -11644223, 15296956477]$	$y^2+xy=x^3-x^2-11644223x+15296956477$	158.2.0.?	$[(9882, 925205)]$
132878.e1	132878l1	132878.e	132878l	$1$	$1$	$ 2 \cdot 29^{2} \cdot 79 $	$ - 2^{2} \cdot 29^{9} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$4582$	$2$	$0$	$2.559220351$	$1$		$0$	$725760$	$1.687410$	$1589324463/7706924$	$0.88216$	$3.67791$	$[1, -1, 0, 20447, 3051897]$	$y^2+xy=x^3-x^2+20447x+3051897$	4582.2.0.?	$[(2174/5, 287233/5)]$
132878.f1	132878m2	132878.f	132878m	$2$	$5$	$ 2 \cdot 29^{2} \cdot 79 $	$ 2^{4} \cdot 29^{6} \cdot 79^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$45820$	$48$	$1$	$1$	$1$		$0$	$5376000$	$2.825756$	$1413378216646643521/49232902384$	$1.01962$	$5.25518$	$[1, 0, 1, -19662598, -33559662296]$	$y^2+xy+y=x^3-19662598x-33559662296$	5.12.0.a.2, 145.24.0.?, 316.2.0.?, 1580.24.1.?, 45820.48.1.?	$[ ]$
132878.f2	132878m1	132878.f	132878m	$2$	$5$	$ 2 \cdot 29^{2} \cdot 79 $	$ 2^{20} \cdot 29^{6} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$45820$	$48$	$1$	$1$	$1$		$0$	$1075200$	$2.021038$	$8194759433281/82837504$	$0.96131$	$4.23307$	$[1, 0, 1, -353238, 80068584]$	$y^2+xy+y=x^3-353238x+80068584$	5.12.0.a.1, 145.24.0.?, 316.2.0.?, 1580.24.1.?, 45820.48.1.?	$[ ]$
132878.g1	132878n2	132878.g	132878n	$2$	$3$	$ 2 \cdot 29^{2} \cdot 79 $	$ - 2^{2} \cdot 29^{2} \cdot 79^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$13746$	$16$	$0$	$6.391927270$	$1$		$2$	$96480$	$0.510674$	$-20651536753/1972156$	$0.84540$	$2.59709$	$[1, 1, 0, -539, -5431]$	$y^2+xy=x^3+x^2-539x-5431$	3.4.0.a.1, 87.8.0.?, 158.2.0.?, 474.8.0.?, 13746.16.0.?	$[(583, 13789)]$
132878.g2	132878n1	132878.g	132878n	$2$	$3$	$ 2 \cdot 29^{2} \cdot 79 $	$ - 2^{6} \cdot 29^{2} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$13746$	$16$	$0$	$2.130642423$	$1$		$2$	$32160$	$-0.038631$	$8722127/5056$	$0.99082$	$1.92554$	$[1, 1, 0, 41, 21]$	$y^2+xy=x^3+x^2+41x+21$	3.4.0.a.1, 87.8.0.?, 158.2.0.?, 474.8.0.?, 13746.16.0.?	$[(3, 12)]$
132878.h1	132878o1	132878.h	132878o	$1$	$1$	$ 2 \cdot 29^{2} \cdot 79 $	$ 2^{8} \cdot 29^{6} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$2.006781280$	$1$		$0$	$774144$	$1.217070$	$72511713/20224$	$0.89606$	$3.24679$	$[1, -1, 0, -7306, 174836]$	$y^2+xy=x^3-x^2-7306x+174836$	316.2.0.?	$[(-92/3, 13594/3)]$
132878.i1	132878a2	132878.i	132878a	$2$	$3$	$ 2 \cdot 29^{2} \cdot 79 $	$ - 2^{2} \cdot 29^{8} \cdot 79^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$474$	$16$	$0$	$1$	$4$	$2$	$0$	$2797920$	$2.194324$	$-20651536753/1972156$	$0.84540$	$4.30969$	$[1, 0, 0, -453737, -127013579]$	$y^2+xy=x^3-453737x-127013579$	3.8.0-3.a.1.1, 158.2.0.?, 474.16.0.?	$[ ]$
132878.i2	132878a1	132878.i	132878a	$2$	$3$	$ 2 \cdot 29^{2} \cdot 79 $	$ - 2^{6} \cdot 29^{8} \cdot 79 $	$0$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$474$	$16$	$0$	$1$	$4$	$2$	$2$	$932640$	$1.645016$	$8722127/5056$	$0.99082$	$3.63813$	$[1, 0, 0, 34043, 101889]$	$y^2+xy=x^3+34043x+101889$	3.8.0-3.a.1.2, 158.2.0.?, 474.16.0.?	$[ ]$
132878.j1	132878b3	132878.j	132878b	$3$	$9$	$ 2 \cdot 29^{2} \cdot 79 $	$ 2^{18} \cdot 29^{6} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$82476$	$144$	$3$	$1$	$1$		$0$	$3024000$	$2.363506$	$15698803397448457/20709376$	$1.00146$	$4.87372$	$[1, 1, 1, -4387094, -3538648557]$	$y^2+xy+y=x^3+x^2-4387094x-3538648557$	3.4.0.a.1, 9.12.0.a.1, 87.8.0.?, 261.24.0.?, 316.2.0.?, $\ldots$	$[ ]$
132878.j2	132878b2	132878.j	132878b	$3$	$9$	$ 2 \cdot 29^{2} \cdot 79 $	$ 2^{6} \cdot 29^{6} \cdot 79^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.12.0.1	3Cs	$82476$	$144$	$3$	$1$	$1$		$0$	$1008000$	$1.814199$	$59914169497/31554496$	$0.96798$	$3.81616$	$[1, 1, 1, -68559, -2100587]$	$y^2+xy+y=x^3+x^2-68559x-2100587$	3.12.0.a.1, 87.24.0.?, 316.2.0.?, 711.36.0.?, 948.24.1.?, $\ldots$	$[ ]$
132878.j3	132878b1	132878.j	132878b	$3$	$9$	$ 2 \cdot 29^{2} \cdot 79 $	$ 2^{2} \cdot 29^{6} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$82476$	$144$	$3$	$1$	$1$		$0$	$336000$	$1.264894$	$11134383337/316$	$0.90937$	$3.67351$	$[1, 1, 1, -39124, 2962233]$	$y^2+xy+y=x^3+x^2-39124x+2962233$	3.4.0.a.1, 9.12.0.a.1, 87.8.0.?, 261.24.0.?, 316.2.0.?, $\ldots$	$[ ]$
132878.k1	132878c1	132878.k	132878c	$1$	$1$	$ 2 \cdot 29^{2} \cdot 79 $	$ - 2^{4} \cdot 29^{2} \cdot 79^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$158$	$2$	$0$	$1$	$1$		$0$	$204480$	$0.998695$	$-349036859307177/7888624$	$0.97963$	$3.40936$	$[1, -1, 1, -13846, 630549]$	$y^2+xy+y=x^3-x^2-13846x+630549$	158.2.0.?	$[ ]$
132878.l1	132878d1	132878.l	132878d	$1$	$1$	$ 2 \cdot 29^{2} \cdot 79 $	$ - 2^{26} \cdot 29^{7} \cdot 79^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$4582$	$2$	$0$	$1$	$1$		$0$	$23063040$	$3.238705$	$-27432397926574857/959531328733184$	$1.05843$	$5.27010$	$[1, -1, 1, -5284161, 36648871889]$	$y^2+xy+y=x^3-x^2-5284161x+36648871889$	4582.2.0.?	$[ ]$
132878.m1	132878e1	132878.m	132878e	$1$	$1$	$ 2 \cdot 29^{2} \cdot 79 $	$ 2^{2} \cdot 29^{6} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$1.931682475$	$1$		$0$	$198016$	$0.913083$	$4826809/316$	$0.94063$	$3.01712$	$[1, 0, 0, -2961, 58157]$	$y^2+xy=x^3-2961x+58157$	316.2.0.?	$[(19/2, 1663/2)]$
132878.n1	132878f1	132878.n	132878f	$1$	$1$	$ 2 \cdot 29^{2} \cdot 79 $	$ 2^{6} \cdot 29^{8} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$1$	$1$		$0$	$725760$	$1.657955$	$12633057289/4252096$	$0.81682$	$3.68421$	$[1, 0, 0, -40806, 2048804]$	$y^2+xy=x^3-40806x+2048804$	316.2.0.?	$[ ]$
132878.o1	132878g1	132878.o	132878g	$1$	$1$	$ 2 \cdot 29^{2} \cdot 79 $	$ - 2^{4} \cdot 29^{8} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$158$	$2$	$0$	$10.08896482$	$1$		$0$	$542880$	$1.521835$	$198911/1264$	$0.74007$	$3.51267$	$[1, 1, 1, 9654, 1157447]$	$y^2+xy+y=x^3+x^2+9654x+1157447$	158.2.0.?	$[(21295/6, 3097913/6)]$

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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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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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