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	Manin constant

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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	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
4704.f1	4704t1	4704.f	4704t	$1$	$1$	$ 2^{5} \cdot 3 \cdot 7^{2} $	$ - 2^{9} \cdot 3^{13} \cdot 7^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$8.065253045$	$1$		$2$	$43680$	$2.021038$	$2731405432/1594323$	$1.19582$	$5.60839$	$[0, -1, 0, 152864, -2188556]$	$y^2=x^3-x^2+152864x-2188556$	24.2.0.b.1	$[(6180, 486758)]$
4704.l1	4704p1	4704.l	4704p	$1$	$1$	$ 2^{5} \cdot 3 \cdot 7^{2} $	$ - 2^{9} \cdot 3^{13} \cdot 7^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$1$		$0$	$6240$	$1.048082$	$2731405432/1594323$	$1.19582$	$4.22769$	$[0, -1, 0, 3120, -7272]$	$y^2=x^3-x^2+3120x-7272$	24.2.0.b.1	$[ ]$
4704.w1	4704bb1	4704.w	4704bb	$1$	$1$	$ 2^{5} \cdot 3 \cdot 7^{2} $	$ - 2^{9} \cdot 3^{13} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$1$		$0$	$43680$	$2.021038$	$2731405432/1594323$	$1.19582$	$5.60839$	$[0, 1, 0, 152864, 2188556]$	$y^2=x^3+x^2+152864x+2188556$	24.2.0.b.1	$[ ]$
4704.bc1	4704z1	4704.bc	4704z	$1$	$1$	$ 2^{5} \cdot 3 \cdot 7^{2} $	$ - 2^{9} \cdot 3^{13} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$0.356098002$	$1$		$6$	$6240$	$1.048082$	$2731405432/1594323$	$1.19582$	$4.22769$	$[0, 1, 0, 3120, 7272]$	$y^2=x^3+x^2+3120x+7272$	24.2.0.b.1	$[(6, 162)]$
9408.o1	9408bo1	9408.o	9408bo	$1$	$1$	$ 2^{6} \cdot 3 \cdot 7^{2} $	$ - 2^{15} \cdot 3^{13} \cdot 7^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$1$		$0$	$24960$	$1.394657$	$2731405432/1594323$	$1.19582$	$4.36196$	$[0, -1, 0, 12479, 45697]$	$y^2=x^3-x^2+12479x+45697$	24.2.0.b.1	$[ ]$
9408.bb1	9408bx1	9408.bb	9408bx	$1$	$1$	$ 2^{6} \cdot 3 \cdot 7^{2} $	$ - 2^{15} \cdot 3^{13} \cdot 7^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$7.548444000$	$1$		$0$	$174720$	$2.367611$	$2731405432/1594323$	$1.19582$	$5.63806$	$[0, -1, 0, 611455, 16896993]$	$y^2=x^3-x^2+611455x+16896993$	24.2.0.b.1	$[(3301/3, 460088/3)]$
9408.cg1	9408cl1	9408.cg	9408cl	$1$	$1$	$ 2^{6} \cdot 3 \cdot 7^{2} $	$ - 2^{15} \cdot 3^{13} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$0.090145189$	$1$		$10$	$24960$	$1.394657$	$2731405432/1594323$	$1.19582$	$4.36196$	$[0, 1, 0, 12479, -45697]$	$y^2=x^3+x^2+12479x-45697$	24.2.0.b.1	$[(23, 504)]$
9408.cp1	9408cs1	9408.cp	9408cs	$1$	$1$	$ 2^{6} \cdot 3 \cdot 7^{2} $	$ - 2^{15} \cdot 3^{13} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$1$		$0$	$174720$	$2.367611$	$2731405432/1594323$	$1.19582$	$5.63806$	$[0, 1, 0, 611455, -16896993]$	$y^2=x^3+x^2+611455x-16896993$	24.2.0.b.1	$[ ]$
14112.v1	14112l1	14112.v	14112l	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 7^{2} $	$ - 2^{9} \cdot 3^{19} \cdot 7^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$1$		$0$	$49920$	$1.597389$	$2731405432/1594323$	$1.19582$	$4.43147$	$[0, 0, 0, 28077, 168266]$	$y^2=x^3+28077x+168266$	24.2.0.b.1	$[ ]$
14112.w1	14112k1	14112.w	14112k	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 7^{2} $	$ - 2^{9} \cdot 3^{19} \cdot 7^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$1$		$0$	$49920$	$1.597389$	$2731405432/1594323$	$1.19582$	$4.43147$	$[0, 0, 0, 28077, -168266]$	$y^2=x^3+28077x-168266$	24.2.0.b.1	$[ ]$
14112.bn1	14112r1	14112.bn	14112r	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 7^{2} $	$ - 2^{9} \cdot 3^{19} \cdot 7^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$11.56538586$	$1$		$0$	$349440$	$2.570343$	$2731405432/1594323$	$1.19582$	$5.65342$	$[0, 0, 0, 1375773, -57715238]$	$y^2=x^3+1375773x-57715238$	24.2.0.b.1	$[(6458918/77, 23870308932/77)]$
14112.bo1	14112q1	14112.bo	14112q	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 7^{2} $	$ - 2^{9} \cdot 3^{19} \cdot 7^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$11.56340581$	$1$		$0$	$349440$	$2.570343$	$2731405432/1594323$	$1.19582$	$5.65342$	$[0, 0, 0, 1375773, 57715238]$	$y^2=x^3+1375773x+57715238$	24.2.0.b.1	$[(-503/23, 91379826/23)]$
28224.ci1	28224fn1	28224.ci	28224fn	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} $	$ - 2^{15} \cdot 3^{19} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$1$		$0$	$1397760$	$2.916916$	$2731405432/1594323$	$1.19582$	$5.67686$	$[0, 0, 0, 5503092, 461721904]$	$y^2=x^3+5503092x+461721904$	24.2.0.b.1	$[ ]$
28224.ck1	28224fm1	28224.ck	28224fm	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} $	$ - 2^{15} \cdot 3^{19} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$1$		$0$	$1397760$	$2.916916$	$2731405432/1594323$	$1.19582$	$5.67686$	$[0, 0, 0, 5503092, -461721904]$	$y^2=x^3+5503092x-461721904$	24.2.0.b.1	$[ ]$
28224.ef1	28224em1	28224.ef	28224em	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} $	$ - 2^{15} \cdot 3^{19} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$3.741354181$	$1$		$2$	$199680$	$1.943962$	$2731405432/1594323$	$1.19582$	$4.53756$	$[0, 0, 0, 112308, -1346128]$	$y^2=x^3+112308x-1346128$	24.2.0.b.1	$[(382, 9864)]$
28224.eh1	28224el1	28224.eh	28224el	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} $	$ - 2^{15} \cdot 3^{19} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1.300185652$	$1$		$2$	$199680$	$1.943962$	$2731405432/1594323$	$1.19582$	$4.53756$	$[0, 0, 0, 112308, 1346128]$	$y^2=x^3+112308x+1346128$	24.2.0.b.1	$[(1253, 45927)]$
117600.bq1	117600b1	117600.bq	117600b	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{9} \cdot 3^{13} \cdot 5^{6} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$4.680377528$	$1$		$2$	$873600$	$1.852802$	$2731405432/1594323$	$1.19582$	$3.88921$	$[0, -1, 0, 77992, 753012]$	$y^2=x^3-x^2+77992x+753012$	24.2.0.b.1	$[(628, 17234)]$
117600.cm1	117600p1	117600.cm	117600p	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{9} \cdot 3^{13} \cdot 5^{6} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$1$		$0$	$6115200$	$2.825756$	$2731405432/1594323$	$1.19582$	$4.88924$	$[0, -1, 0, 3821592, 265926312]$	$y^2=x^3-x^2+3821592x+265926312$	24.2.0.b.1	$[ ]$
117600.fw1	117600ct1	117600.fw	117600ct	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{9} \cdot 3^{13} \cdot 5^{6} \cdot 7^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$3.514662332$	$1$		$2$	$6115200$	$2.825756$	$2731405432/1594323$	$1.19582$	$4.88924$	$[0, 1, 0, 3821592, -265926312]$	$y^2=x^3+x^2+3821592x-265926312$	24.2.0.b.1	$[(102, 11178)]$
117600.gq1	117600ce1	117600.gq	117600ce	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{9} \cdot 3^{13} \cdot 5^{6} \cdot 7^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$1$		$0$	$873600$	$1.852802$	$2731405432/1594323$	$1.19582$	$3.88921$	$[0, 1, 0, 77992, -753012]$	$y^2=x^3+x^2+77992x-753012$	24.2.0.b.1	$[ ]$
235200.fn1	235200fn1	235200.fn	235200fn	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{15} \cdot 3^{13} \cdot 5^{6} \cdot 7^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$9$	$3$	$0$	$3494400$	$2.199375$	$2731405432/1594323$	$1.19582$	$4.00750$	$[0, -1, 0, 311967, -6336063]$	$y^2=x^3-x^2+311967x-6336063$	24.2.0.b.1	$[ ]$
235200.iy1	235200iy1	235200.iy	235200iy	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{15} \cdot 3^{13} \cdot 5^{6} \cdot 7^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$26.70695714$	$1$		$0$	$24460800$	$3.172329$	$2731405432/1594323$	$1.19582$	$4.95149$	$[0, -1, 0, 15286367, -2142696863]$	$y^2=x^3-x^2+15286367x-2142696863$	24.2.0.b.1	$[(1017641654241/17765, 1592348083886687464/17765)]$
235200.tz1	235200tz1	235200.tz	235200tz	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{15} \cdot 3^{13} \cdot 5^{6} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$1$		$0$	$24460800$	$3.172329$	$2731405432/1594323$	$1.19582$	$4.95149$	$[0, 1, 0, 15286367, 2142696863]$	$y^2=x^3+x^2+15286367x+2142696863$	24.2.0.b.1	$[ ]$
235200.xo1	235200xo1	235200.xo	235200xo	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{15} \cdot 3^{13} \cdot 5^{6} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$0.456062479$	$1$		$6$	$3494400$	$2.199375$	$2731405432/1594323$	$1.19582$	$4.00750$	$[0, 1, 0, 311967, 6336063]$	$y^2=x^3+x^2+311967x+6336063$	24.2.0.b.1	$[(387, 13608)]$
352800.fs1	352800fs1	352800.fs	352800fs	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{9} \cdot 3^{19} \cdot 5^{6} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$11.98803978$	$1$		$0$	$6988800$	$2.402107$	$2731405432/1594323$	$1.19582$	$4.07075$	$[0, 0, 0, 701925, 21033250]$	$y^2=x^3+701925x+21033250$	24.2.0.b.1	$[(6050354/127, 37610420742/127)]$
352800.ft1	352800ft1	352800.ft	352800ft	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{9} \cdot 3^{19} \cdot 5^{6} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$25$	$5$	$0$	$48921600$	$3.375065$	$2731405432/1594323$	$1.19582$	$4.98478$	$[0, 0, 0, 34394325, -7214404750]$	$y^2=x^3+34394325x-7214404750$	24.2.0.b.1	$[ ]$
352800.jm1	352800jm1	352800.jm	352800jm	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{9} \cdot 3^{19} \cdot 5^{6} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$4.612888873$	$1$		$2$	$6988800$	$2.402107$	$2731405432/1594323$	$1.19582$	$4.07075$	$[0, 0, 0, 701925, -21033250]$	$y^2=x^3+701925x-21033250$	24.2.0.b.1	$[(1729, 79758)]$
352800.jn1	352800jn1	352800.jn	352800jn	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{9} \cdot 3^{19} \cdot 5^{6} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$9$	$3$	$0$	$48921600$	$3.375065$	$2731405432/1594323$	$1.19582$	$4.98478$	$[0, 0, 0, 34394325, 7214404750]$	$y^2=x^3+34394325x+7214404750$	24.2.0.b.1	$[ ]$
705600.ua1	-	705600.ua	-	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{15} \cdot 3^{19} \cdot 5^{6} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$2.135026814$	$1$		$2$	$27955200$	$2.748680$	$2731405432/1594323$	$1.19582$	$4.17005$	$[0, 0, 0, 2807700, -168266000]$	$y^2=x^3+2807700x-168266000$	24.2.0.b.1	$[(296, 26244)]$
705600.ub1	-	705600.ub	-	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{15} \cdot 3^{19} \cdot 5^{6} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$25$	$5$	$0$	$195686400$	$3.721638$	$2731405432/1594323$	$1.19582$	$5.03703$	$[0, 0, 0, 137577300, 57715238000]$	$y^2=x^3+137577300x+57715238000$	24.2.0.b.1	$[ ]$
705600.biu1	-	705600.biu	-	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{15} \cdot 3^{19} \cdot 5^{6} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$13.11586872$	$1$		$0$	$27955200$	$2.748680$	$2731405432/1594323$	$1.19582$	$4.17005$	$[0, 0, 0, 2807700, 168266000]$	$y^2=x^3+2807700x+168266000$	24.2.0.b.1	$[(2343506/5, 3588132904/5)]$
705600.biv1	-	705600.biv	-	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{15} \cdot 3^{19} \cdot 5^{6} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$24$	$2$	$0$	$1$	$4$	$2$	$0$	$195686400$	$3.721638$	$2731405432/1594323$	$1.19582$	$5.03703$	$[0, 0, 0, 137577300, -57715238000]$	$y^2=x^3+137577300x-57715238000$	24.2.0.b.1	$[ ]$

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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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