Elliptic curve search results

Results (16 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
27225.j1	27225k1	27225.j	27225k	$1$	$1$	\( 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( - 3^{9} \cdot 5^{2} \cdot 11^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.10.0.1	5Nn	$30$	$120$	$7$	$1$	$1$		$0$	$209088$	$1.997501$	$-1273201875$	$1.14877$	$5.21494$		$[1, -1, 1, -1066880, -423885338]$	\(y^2+xy+y=x^3-x^2-1066880x-423885338\)	5.10.0.a.1, 6.6.0.b.1, 10.20.0.a.1, 15.20.0.b.1, 30.120.7.e.1	$[ ]$	$1$
27225.k1	27225y1	27225.k	27225y	$1$	$1$	\( 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( - 3^{9} \cdot 5^{8} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.10.0.1	5Nn	$30$	$120$	$7$	$1.813111906$	$1$		$2$	$95040$	$1.603273$	$-1273201875$	$1.14877$	$4.75168$		$[1, -1, 1, -220430, 39889072]$	\(y^2+xy+y=x^3-x^2-220430x+39889072\)	5.10.0.a.1, 6.6.0.b.1, 10.20.0.a.1, 15.20.0.b.1, 30.120.7.e.1	$[(268, -40)]$	$1$
27225.m1	27225x1	27225.m	27225x	$1$	$1$	\( 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( - 3^{3} \cdot 5^{8} \cdot 11^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.10.0.1	5Nn	$30$	$120$	$7$	$1.452696479$	$1$		$4$	$348480$	$2.252914$	$-1273201875$	$1.14877$	$5.51507$		$[1, -1, 1, -2963555, 1964407822]$	\(y^2+xy+y=x^3-x^2-2963555x+1964407822\)	5.10.0.a.1, 6.6.0.b.1, 10.20.0.a.1, 15.20.0.b.1, 30.120.7.e.1	$[(994, -535)]$	$1$
27225.n1	27225j1	27225.n	27225j	$1$	$1$	\( 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( - 3^{3} \cdot 5^{2} \cdot 11^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.10.0.1	5Nn	$30$	$120$	$7$	$1$	$1$		$0$	$6336$	$0.249248$	$-1273201875$	$1.14877$	$3.16056$		$[1, -1, 1, -980, -11558]$	\(y^2+xy+y=x^3-x^2-980x-11558\)	5.10.0.a.1, 6.6.0.b.1, 10.20.0.a.1, 15.20.0.b.1, 30.120.7.e.1	$[ ]$	$1$
27225.bn1	27225g1	27225.bn	27225g	$1$	$1$	\( 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( - 3^{3} \cdot 5^{2} \cdot 11^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.10.0.1	5Nn	$30$	$120$	$7$	$1$	$1$		$0$	$69696$	$1.448195$	$-1273201875$	$1.14877$	$4.56945$		$[1, -1, 0, -118542, 15738971]$	\(y^2+xy=x^3-x^2-118542x+15738971\)	5.10.0.a.1, 6.6.0.b.1, 10.20.0.a.1, 15.20.0.b.1, 30.120.7.e.1	$[ ]$	$1$
27225.bo1	27225v1	27225.bo	27225v	$1$	$1$	\( 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( - 3^{3} \cdot 5^{8} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.10.0.1	5Nn	$30$	$120$	$7$	$5.244028189$	$1$		$2$	$31680$	$1.053967$	$-1273201875$	$1.14877$	$4.10619$		$[1, -1, 0, -24492, -1469209]$	\(y^2+xy=x^3-x^2-24492x-1469209\)	5.10.0.a.1, 6.6.0.b.1, 10.20.0.a.1, 15.20.0.b.1, 30.120.7.e.1	$[(238, 2359)]$	$1$
27225.bq1	27225u1	27225.bq	27225u	$1$	$1$	\( 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( - 3^{9} \cdot 5^{8} \cdot 11^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.10.0.1	5Nn	$30$	$120$	$7$	$33.92980460$	$1$		$0$	$1045440$	$2.802219$	$-1273201875$	$1.14877$	$6.16056$		$[1, -1, 0, -26671992, -53012339209]$	\(y^2+xy=x^3-x^2-26671992x-53012339209\)	5.10.0.a.1, 6.6.0.b.1, 10.20.0.a.1, 15.20.0.b.1, 30.120.7.e.1	$[(63641093084024278/1358131, 15820107637388569562784313/1358131)]$	$1$
27225.br1	27225f1	27225.br	27225f	$1$	$1$	\( 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( - 3^{9} \cdot 5^{2} \cdot 11^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.10.0.1	5Nn	$30$	$120$	$7$	$1$	$1$		$0$	$19008$	$0.798553$	$-1273201875$	$1.14877$	$3.80605$		$[1, -1, 0, -8817, 320876]$	\(y^2+xy=x^3-x^2-8817x+320876\)	5.10.0.a.1, 6.6.0.b.1, 10.20.0.a.1, 15.20.0.b.1, 30.120.7.e.1	$[ ]$	$1$
435600.iz1	435600iz1	435600.iz	435600iz	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( - 2^{12} \cdot 3^{9} \cdot 5^{8} \cdot 11^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.10.0.1	5Nn	$30$	$120$	$7$	$1$	$1$		$0$	$6082560$	$2.296421$	$-1273201875$	$1.14877$	$4.37764$		$[0, 0, 0, -3526875, -2549373750]$	\(y^2=x^3-3526875x-2549373750\)	5.10.0.a.1, 6.6.0.b.1, 10.20.0.a.1, 15.20.0.b.1, 30.120.7.e.1	$[ ]$	$1$
435600.ja1	435600ja1	435600.ja	435600ja	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( - 2^{12} \cdot 3^{9} \cdot 5^{2} \cdot 11^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.10.0.1	5Nn	$30$	$120$	$7$	$2.674742180$	$1$		$2$	$13381632$	$2.690647$	$-1273201875$	$1.14877$	$4.74198$		$[0, 0, 0, -17070075, 27145731690]$	\(y^2=x^3-17070075x+27145731690\)	5.10.0.a.1, 6.6.0.b.1, 10.20.0.a.1, 15.20.0.b.1, 30.120.7.e.1	$[(2421, 3024)]$	$1$
435600.jb1	435600jb1	435600.jb	435600jb	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( - 2^{12} \cdot 3^{3} \cdot 5^{8} \cdot 11^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.10.0.1	5Nn	$30$	$120$	$7$	$1.087162224$	$1$		$12$	$2027520$	$1.747114$	$-1273201875$	$1.14877$	$3.86998$		$[0, 0, 0, -391875, 94421250]$	\(y^2=x^3-391875x+94421250\)	5.10.0.a.1, 6.6.0.b.1, 10.20.0.a.1, 15.20.0.b.1, 30.120.7.e.1	$[(375, 450), (225, 4200)]$	$1$
435600.jc1	435600jc1	435600.jc	435600jc	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( - 2^{12} \cdot 3^{3} \cdot 5^{2} \cdot 11^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.10.0.1	5Nn	$30$	$120$	$7$	$5.642268954$	$1$		$0$	$4460544$	$2.141342$	$-1273201875$	$1.14877$	$4.23432$		$[0, 0, 0, -1896675, -1005397470]$	\(y^2=x^3-1896675x-1005397470\)	5.10.0.a.1, 6.6.0.b.1, 10.20.0.a.1, 15.20.0.b.1, 30.120.7.e.1	$[(20449/3, 2162512/3)]$	$1$
435600.lk1	435600lk1	435600.lk	435600lk	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( - 2^{12} \cdot 3^{3} \cdot 5^{2} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.10.0.1	5Nn	$30$	$120$	$7$	$0.732748618$	$1$		$2$	$405504$	$0.942395$	$-1273201875$	$1.14877$	$3.12628$		$[0, 0, 0, -15675, 755370]$	\(y^2=x^3-15675x+755370\)	5.10.0.a.1, 6.6.0.b.1, 10.20.0.a.1, 15.20.0.b.1, 30.120.7.e.1	$[(69, 48)]$	$1$
435600.ll1	435600ll1	435600.ll	435600ll	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( - 2^{12} \cdot 3^{3} \cdot 5^{8} \cdot 11^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.10.0.1	5Nn	$30$	$120$	$7$	$1$	$1$		$0$	$22302720$	$2.946060$	$-1273201875$	$1.14877$	$4.97803$		$[0, 0, 0, -47416875, -125674683750]$	\(y^2=x^3-47416875x-125674683750\)	5.10.0.a.1, 6.6.0.b.1, 10.20.0.a.1, 15.20.0.b.1, 30.120.7.e.1	$[ ]$	$1$
435600.lm1	435600lm1	435600.lm	435600lm	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( - 2^{12} \cdot 3^{9} \cdot 5^{2} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.10.0.1	5Nn	$30$	$120$	$7$	$10.55815904$	$1$		$0$	$1216512$	$1.491701$	$-1273201875$	$1.14877$	$3.63393$		$[0, 0, 0, -141075, -20394990]$	\(y^2=x^3-141075x-20394990\)	5.10.0.a.1, 6.6.0.b.1, 10.20.0.a.1, 15.20.0.b.1, 30.120.7.e.1	$[(105169/15, 13409072/15)]$	$1$
435600.ln1	435600ln1	435600.ln	435600ln	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( - 2^{12} \cdot 3^{9} \cdot 5^{8} \cdot 11^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$5$	5.10.0.1	5Nn	$30$	$120$	$7$	$1$	$4$	$2$	$0$	$66908160$	$3.495369$	$-1273201875$	$1.14877$	$5.48568$		$[0, 0, 0, -426751875, 3393216461250]$	\(y^2=x^3-426751875x+3393216461250\)	5.10.0.a.1, 6.6.0.b.1, 10.20.0.a.1, 15.20.0.b.1, 30.120.7.e.1	$[ ]$	$1$

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