LMFDB - Elliptic curve search results

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Conductor	j-invariant	Rank	Torsion	Complex multiplication

Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image

Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $\|Ш\|	Nonmax$\ \ell$

Curves per isogeny class	Reduction	Integral points	Faltings height

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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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
6240.d1	6240a3	6240.d	6240a	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5 \cdot 13 $	$ 2^{12} \cdot 3 \cdot 5 \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$2.486877264$	$1$		$3$	$1536$	$0.317203$	$30488290624/195$	$[0, -1, 0, -1041, 13281]$	$y^2=x^3-x^2-1041x+13281$
6240.u1	6240ba2	6240.u	6240ba	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5 \cdot 13 $	$ 2^{12} \cdot 3 \cdot 5 \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$5.415464264$	$1$		$1$	$1536$	$0.317203$	$30488290624/195$	$[0, 1, 0, -1041, -13281]$	$y^2=x^3+x^2-1041x-13281$
12480.bj3	12480o1	12480.bj	12480o	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13 $	$ 2^{6} \cdot 3 \cdot 5 \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$3.583022007$	$4$	$2$	$3$	$1536$	$-0.029371$	$30488290624/195$	$[0, -1, 0, -260, -1530]$	$y^2=x^3-x^2-260x-1530$
12480.cx3	12480bh1	12480.cx	12480bh	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13 $	$ 2^{6} \cdot 3 \cdot 5 \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$1$	$4$	$2$	$1$	$1536$	$-0.029371$	$30488290624/195$	$[0, 1, 0, -260, 1530]$	$y^2=x^3+x^2-260x+1530$
18720.bh1	18720bj2	18720.bh	18720bj	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13 $	$ 2^{12} \cdot 3^{7} \cdot 5 \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$1$		$1$	$12288$	$0.866508$	$30488290624/195$	$[0, 0, 0, -9372, -349216]$	$y^2=x^3-9372x-349216$
18720.bi1	18720n3	18720.bi	18720n	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13 $	$ 2^{12} \cdot 3^{7} \cdot 5 \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$3.802975703$	$1$		$3$	$12288$	$0.866508$	$30488290624/195$	$[0, 0, 0, -9372, 349216]$	$y^2=x^3-9372x+349216$
31200.k1	31200d4	31200.k	31200d	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{12} \cdot 3 \cdot 5^{7} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$36864$	$1.121922$	$30488290624/195$	$[0, -1, 0, -26033, -1608063]$	$y^2=x^3-x^2-26033x-1608063$
31200.bz1	31200cb4	31200.bz	31200cb	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{12} \cdot 3 \cdot 5^{7} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$1$		$1$	$36864$	$1.121922$	$30488290624/195$	$[0, 1, 0, -26033, 1608063]$	$y^2=x^3+x^2-26033x+1608063$
37440.bl3	37440bk1	37440.bl	37440bk	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13 $	$ 2^{6} \cdot 3^{7} \cdot 5 \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2.444114752$	$1$		$3$	$12288$	$0.519935$	$30488290624/195$	$[0, 0, 0, -2343, 43652]$	$y^2=x^3-2343x+43652$
37440.bo3	37440bj1	37440.bo	37440bj	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13 $	$ 2^{6} \cdot 3^{7} \cdot 5 \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$3.870828347$	$4$	$2$	$3$	$12288$	$0.519935$	$30488290624/195$	$[0, 0, 0, -2343, -43652]$	$y^2=x^3-2343x-43652$
62400.cp3	62400a1	62400.cp	62400a	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{6} \cdot 3 \cdot 5^{7} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$3.210375889$	$1$		$3$	$36864$	$0.775348$	$30488290624/195$	$[0, -1, 0, -6508, 204262]$	$y^2=x^3-x^2-6508x+204262$
62400.fp3	62400ca1	62400.fp	62400ca	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{6} \cdot 3 \cdot 5^{7} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$36864$	$0.775348$	$30488290624/195$	$[0, 1, 0, -6508, -204262]$	$y^2=x^3+x^2-6508x-204262$
81120.v1	81120bg4	81120.v	81120bg	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5 \cdot 13^{2} $	$ 2^{12} \cdot 3 \cdot 5 \cdot 13^{7} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$8.963245492$	$1$		$3$	$258048$	$1.599678$	$30488290624/195$	$[0, -1, 0, -175985, 28474497]$	$y^2=x^3-x^2-175985x+28474497$
81120.bw1	81120u4	81120.bw	81120u	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5 \cdot 13^{2} $	$ 2^{12} \cdot 3 \cdot 5 \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$19.09953496$	$1$		$1$	$258048$	$1.599678$	$30488290624/195$	$[0, 1, 0, -175985, -28474497]$	$y^2=x^3+x^2-175985x-28474497$
93600.co1	93600bh4	93600.co	93600bh	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{12} \cdot 3^{7} \cdot 5^{7} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$8.370807812$	$1$		$1$	$294912$	$1.671228$	$30488290624/195$	$[0, 0, 0, -234300, -43652000]$	$y^2=x^3-234300x-43652000$
93600.cp1	93600dt4	93600.cp	93600dt	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{12} \cdot 3^{7} \cdot 5^{7} \cdot 13 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$1$	$1$		$3$	$294912$	$1.671228$	$30488290624/195$	$[0, 0, 0, -234300, 43652000]$	$y^2=x^3-234300x+43652000$
162240.w3	162240hx1	162240.w	162240hx	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$8.746394472$	$4$	$2$	$1$	$258048$	$1.253103$	$30488290624/195$	$[0, -1, 0, -43996, -3537314]$	$y^2=x^3-x^2-43996x-3537314$
162240.fl3	162240gi1	162240.fl	162240gi	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$1$	$4$	$2$	$1$	$258048$	$1.253103$	$30488290624/195$	$[0, 1, 0, -43996, 3537314]$	$y^2=x^3+x^2-43996x+3537314$
187200.hz3	187200ml1	187200.hz	187200ml	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{6} \cdot 3^{7} \cdot 5^{7} \cdot 13 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$14.91770545$	$1$		$3$	$294912$	$1.324654$	$30488290624/195$	$[0, 0, 0, -58575, 5456500]$	$y^2=x^3-58575x+5456500$
187200.ic3	187200mn1	187200.ic	187200mn	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{6} \cdot 3^{7} \cdot 5^{7} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$1$	$4$	$2$	$1$	$294912$	$1.324654$	$30488290624/195$	$[0, 0, 0, -58575, -5456500]$	$y^2=x^3-58575x-5456500$
243360.bj1	243360bj2	243360.bj	243360bj	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ 2^{12} \cdot 3^{7} \cdot 5 \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2.141564135$	$1$		$3$	$2064384$	$2.148983$	$30488290624/195$	$[0, 0, 0, -1583868, 767227552]$	$y^2=x^3-1583868x+767227552$
243360.bk1	243360bk4	243360.bk	243360bk	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ 2^{12} \cdot 3^{7} \cdot 5 \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$1$		$1$	$2064384$	$2.148983$	$30488290624/195$	$[0, 0, 0, -1583868, -767227552]$	$y^2=x^3-1583868x-767227552$
305760.da1	305760da2	305760.da	305760da	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 $	$ 2^{12} \cdot 3 \cdot 5 \cdot 7^{6} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$3.210580390$	$1$		$3$	$589824$	$1.290157$	$30488290624/195$	$[0, -1, 0, -51025, 4453345]$	$y^2=x^3-x^2-51025x+4453345$
305760.gs1	305760gs4	305760.gs	305760gs	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 $	$ 2^{12} \cdot 3 \cdot 5 \cdot 7^{6} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9.056005388$	$4$	$2$	$1$	$589824$	$1.290157$	$30488290624/195$	$[0, 1, 0, -51025, -4453345]$	$y^2=x^3+x^2-51025x-4453345$
405600.ca1	405600ca4	405600.ca	405600ca	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ 2^{12} \cdot 3 \cdot 5^{7} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$1$		$1$	$6193152$	$2.404396$	$30488290624/195$	$[0, -1, 0, -4399633, -3550512863]$	$y^2=x^3-x^2-4399633x-3550512863$
405600.fg1	405600fg2	405600.fg	405600fg	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ 2^{12} \cdot 3 \cdot 5^{7} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1$	$1$		$1$	$6193152$	$2.404396$	$30488290624/195$	$[0, 1, 0, -4399633, 3550512863]$	$y^2=x^3+x^2-4399633x+3550512863$
486720.mq3	486720mq1	486720.mq	486720mq	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ 2^{6} \cdot 3^{7} \cdot 5 \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9.148697619$	$4$	$2$	$1$	$2064384$	$1.802410$	$30488290624/195$	$[0, 0, 0, -395967, -95903444]$	$y^2=x^3-395967x-95903444$
486720.mt3	486720mt1	486720.mt	486720mt	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ 2^{6} \cdot 3^{7} \cdot 5 \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$8.645341221$	$1$		$1$	$2064384$	$1.802410$	$30488290624/195$	$[0, 0, 0, -395967, 95903444]$	$y^2=x^3-395967x+95903444$

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