LMFDB - Elliptic curves over $\Q$ of conductor 232845

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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
232845.a1	232845a1	232845.a	232845a	$1$	$1$	$ 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ 3^{4} \cdot 5^{9} \cdot 19^{2} \cdot 43^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$10$	$2$	$0$	$2.438477537$	$1$		$0$	$1752192$	$1.730064$	$3212716834443833344/292517578125$	$1.04383$	$3.92475$	$[0, -1, 1, -218886, -39340258]$	$y^2+y=x^3-x^2-218886x-39340258$	10.2.0.a.1	$[(-1083/2, 383/2)]$
232845.b1	232845b1	232845.b	232845b	$1$	$1$	$ 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ - 3^{10} \cdot 5^{14} \cdot 19^{10} \cdot 43^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$86$	$2$	$0$	$1$	$9$	$3$	$0$	$1195084800$	$4.888557$	$-5849020933249476332032897024/3734327290213641357421875$	$1.02740$	$6.66332$	$[0, -1, 1, -13550657126, -880504557300784]$	$y^2+y=x^3-x^2-13550657126x-880504557300784$	86.2.0.?	$[ ]$
232845.c1	232845c1	232845.c	232845c	$1$	$1$	$ 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ - 3^{14} \cdot 5^{2} \cdot 19^{6} \cdot 43^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$86$	$2$	$0$	$1$	$1$		$0$	$18579456$	$2.758495$	$-522547125460258816/9506987907075$	$1.00952$	$4.73333$	$[0, 1, 1, -6057700, -5830179044]$	$y^2+y=x^3+x^2-6057700x-5830179044$	86.2.0.?	$[ ]$
232845.d1	232845d1	232845.d	232845d	$1$	$1$	$ 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ - 3 \cdot 5^{4} \cdot 19^{10} \cdot 43 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$516$	$2$	$0$	$10.69069109$	$1$		$0$	$4114944$	$2.084953$	$-42471289/80625$	$0.88203$	$3.92153$	$[1, 0, 0, -133036, 38629241]$	$y^2+xy=x^3-133036x+38629241$	516.2.0.?	$[(27553/9, 4048813/9)]$
232845.e1	232845e4	232845.e	232845e	$4$	$4$	$ 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ 3 \cdot 5^{4} \cdot 19^{6} \cdot 43 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$98040$	$48$	$0$	$1$	$4$	$2$	$0$	$1267200$	$1.658863$	$36097320816649/80625$	$0.94094$	$3.95560$	$[1, 0, 0, -248556, -47716905]$	$y^2+xy=x^3-248556x-47716905$	2.3.0.a.1, 4.6.0.c.1, 120.12.0.?, 228.12.0.?, 258.6.0.?, $\ldots$	$[ ]$
232845.e2	232845e3	232845.e	232845e	$4$	$4$	$ 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ 3 \cdot 5 \cdot 19^{6} \cdot 43^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$98040$	$48$	$0$	$1$	$1$		$0$	$1267200$	$1.658863$	$184122897769/51282015$	$1.05622$	$3.52849$	$[1, 0, 0, -42786, 2449821]$	$y^2+xy=x^3-42786x+2449821$	2.3.0.a.1, 4.6.0.c.1, 60.12.0.h.1, 228.12.0.?, 380.12.0.?, $\ldots$	$[ ]$
232845.e3	232845e2	232845.e	232845e	$4$	$4$	$ 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ 3^{2} \cdot 5^{2} \cdot 19^{6} \cdot 43^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$49020$	$48$	$0$	$1$	$1$		$2$	$633600$	$1.312290$	$9116230969/416025$	$0.87424$	$3.28528$	$[1, 0, 0, -15711, -728784]$	$y^2+xy=x^3-15711x-728784$	2.6.0.a.1, 60.12.0.a.1, 228.12.0.?, 380.12.0.?, 516.12.0.?, $\ldots$	$[ ]$
232845.e4	232845e1	232845.e	232845e	$4$	$4$	$ 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ - 3^{4} \cdot 5 \cdot 19^{6} \cdot 43 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$98040$	$48$	$0$	$1$	$1$		$1$	$316800$	$0.965716$	$357911/17415$	$0.85974$	$2.82199$	$[1, 0, 0, 534, -43245]$	$y^2+xy=x^3+534x-43245$	2.3.0.a.1, 4.6.0.c.1, 120.12.0.?, 380.12.0.?, 430.6.0.?, $\ldots$	$[ ]$
232845.f1	232845f4	232845.f	232845f	$4$	$4$	$ 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ 3^{3} \cdot 5^{2} \cdot 19^{7} \cdot 43^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$19608$	$48$	$0$	$11.98367309$	$1$		$0$	$11888640$	$2.794029$	$35450760458736972649/43846122825$	$0.94531$	$5.07207$	$[1, 0, 0, -24706306, -47269204189]$	$y^2+xy=x^3-24706306x-47269204189$	2.3.0.a.1, 4.12.0-4.c.1.2, 114.6.0.?, 228.24.0.?, 1032.24.0.?, $\ldots$	$[(-2250755/28, 35973127/28)]$
232845.f2	232845f2	232845.f	232845f	$4$	$4$	$ 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ 3^{6} \cdot 5^{4} \cdot 19^{8} \cdot 43^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$9804$	$48$	$0$	$5.991836547$	$1$		$2$	$5944320$	$2.447456$	$8876043294138649/304124675625$	$0.90275$	$4.40105$	$[1, 0, 0, -1557181, -725573464]$	$y^2+xy=x^3-1557181x-725573464$	2.6.0.a.1, 4.12.0-2.a.1.1, 228.24.0.?, 516.24.0.?, 3268.24.0.?, $\ldots$	$[(-10099/4, 176123/4)]$
232845.f3	232845f1	232845.f	232845f	$4$	$4$	$ 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ 3^{12} \cdot 5^{2} \cdot 19^{7} \cdot 43 $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$19608$	$48$	$0$	$2.995918273$	$1$		$7$	$2972160$	$2.100883$	$33042169120969/10854682425$	$0.87371$	$3.94845$	$[1, 0, 0, -241336, 29984735]$	$y^2+xy=x^3-241336x+29984735$	2.3.0.a.1, 4.12.0-4.c.1.1, 456.24.0.?, 1032.24.0.?, 1634.6.0.?, $\ldots$	$[(-22, 5951)]$
232845.f4	232845f3	232845.f	232845f	$4$	$4$	$ 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ - 3^{3} \cdot 5^{8} \cdot 19^{10} \cdot 43 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$19608$	$48$	$0$	$11.98367309$	$1$		$0$	$11888640$	$2.794029$	$366923296278071/59102609765625$	$0.95837$	$4.59844$	$[1, 0, 0, 538424, -2532404095]$	$y^2+xy=x^3+538424x-2532404095$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 228.12.0.?, 456.24.0.?, $\ldots$	$[(3882997/12, 7630646393/12)]$
232845.g1	232845g1	232845.g	232845g	$1$	$1$	$ 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ - 3^{7} \cdot 5^{3} \cdot 19^{2} \cdot 43^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$2580$	$2$	$0$	$0.562341548$	$1$		$6$	$598752$	$1.342562$	$-7061909557328281/21735226125$	$0.92310$	$3.42994$	$[1, 0, 0, -28460, -1855275]$	$y^2+xy=x^3-28460x-1855275$	2580.2.0.?	$[(205, 865)]$
232845.h1	232845h1	232845.h	232845h	$2$	$2$	$ 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ 3^{3} \cdot 5^{2} \cdot 19^{6} \cdot 43 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$1$	$471744$	$1.114872$	$1263214441/29025$	$0.85169$	$3.12536$	$[1, 0, 0, -8130, -277173]$	$y^2+xy=x^3-8130x-277173$	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[ ]$
232845.h2	232845h2	232845.h	232845h	$2$	$2$	$ 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ - 3^{6} \cdot 5 \cdot 19^{6} \cdot 43^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1$	$1$		$0$	$943488$	$1.461445$	$1685159/6739605$	$1.19354$	$3.30509$	$[1, 0, 0, 895, -856578]$	$y^2+xy=x^3+895x-856578$	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[ ]$
232845.i1	232845i1	232845.i	232845i	$1$	$1$	$ 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ - 3^{12} \cdot 5^{8} \cdot 19^{6} \cdot 43 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$86$	$2$	$0$	$1.375989942$	$1$		$4$	$10063872$	$2.637981$	$660867352100864/8926548046875$	$1.07121$	$4.44223$	$[0, -1, 1, 655095, -964829194]$	$y^2+y=x^3-x^2+655095x-964829194$	86.2.0.?	$[(22110, 3289612)]$
232845.j1	232845j1	232845.j	232845j	$1$	$1$	$ 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ - 3 \cdot 5^{4} \cdot 19^{4} \cdot 43 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$516$	$2$	$0$	$1.941074372$	$1$		$2$	$216576$	$0.612732$	$-42471289/80625$	$0.88203$	$2.49197$	$[1, 1, 0, -368, -5787]$	$y^2+xy=x^3+x^2-368x-5787$	516.2.0.?	$[(36, 153)]$
232845.k1	232845k1	232845.k	232845k	$1$	$1$	$ 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ - 3^{7} \cdot 5^{3} \cdot 19^{8} \cdot 43^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$2580$	$2$	$0$	$4.426812605$	$1$		$2$	$11376288$	$2.814781$	$-7061909557328281/21735226125$	$0.92310$	$4.85950$	$[1, 1, 0, -10274067, 12704783094]$	$y^2+xy=x^3+x^2-10274067x+12704783094$	2580.2.0.?	$[(-242, 123316)]$
232845.l1	232845l1	232845.l	232845l	$1$	$1$	$ 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ - 3^{6} \cdot 5^{2} \cdot 19^{6} \cdot 43 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$86$	$2$	$0$	$1.912060635$	$1$		$0$	$1382400$	$1.284664$	$99897344/783675$	$0.89128$	$3.12478$	$[0, -1, 1, 3490, -282319]$	$y^2+y=x^3-x^2+3490x-282319$	86.2.0.?	$[(1325/2, 48731/2)]$
232845.m1	232845m1	232845.m	232845m	$1$	$1$	$ 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ 3^{4} \cdot 5^{9} \cdot 19^{8} \cdot 43^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$10$	$2$	$0$	$16.64085709$	$1$		$0$	$33291648$	$3.202282$	$3212716834443833344/292517578125$	$1.04383$	$5.35430$	$[0, 1, 1, -79017966, 270308935451]$	$y^2+y=x^3+x^2-79017966x+270308935451$	10.2.0.a.1	$[(-152273811/134, 1383456785447/134)]$
232845.n1	232845n1	232845.n	232845n	$1$	$1$	$ 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ - 3^{6} \cdot 5^{2} \cdot 19^{6} \cdot 43 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$86$	$2$	$0$	$1$	$1$		$0$	$8294400$	$2.314686$	$-645008376471556096/783675$	$1.01002$	$4.74786$	$[0, 1, 1, -6498120, 6373561331]$	$y^2+y=x^3+x^2-6498120x+6373561331$	86.2.0.?	$[ ]$

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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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