Elliptic curve search results

Results (14 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	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
12870.u2	12870i2	12870.u	12870i	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( - 2^{27} \cdot 3^{9} \cdot 5 \cdot 11^{3} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$17160$	$16$	$0$	$1$	$1$		$0$	$326592$	$2.437454$	$4074304020054813/1962402098708480$	$1.04067$	$5.55383$	$[1, -1, 0, 89841, -298861075]$	\(y^2+xy=x^3-x^2+89841x-298861075\)	3.8.0-3.a.1.1, 17160.16.0.?	$[ ]$
12870.bg2	12870bd1	12870.bg	12870bd	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( - 2^{27} \cdot 3^{3} \cdot 5 \cdot 11^{3} \cdot 13^{3} \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$17160$	$16$	$0$	$1.302215838$	$1$		$12$	$108864$	$1.888147$	$4074304020054813/1962402098708480$	$1.04067$	$4.85723$	$[1, -1, 1, 9982, 11065601]$	\(y^2+xy+y=x^3-x^2+9982x+11065601\)	3.8.0-3.a.1.2, 17160.16.0.?	$[(-207, 415)]$
64350.bq2	64350a1	64350.bq	64350a	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 13 \)	\( - 2^{27} \cdot 3^{3} \cdot 5^{7} \cdot 11^{3} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$17160$	$16$	$0$	$4.915355711$	$1$		$2$	$2612736$	$2.692867$	$4074304020054813/1962402098708480$	$1.04067$	$5.02334$	$[1, -1, 0, 249558, 1383449716]$	\(y^2+xy=x^3-x^2+249558x+1383449716\)	3.4.0.a.1, 15.8.0-3.a.1.2, 3432.8.0.?, 17160.16.0.?	$[(-151, 36713)]$
64350.ef2	64350cw2	64350.ef	64350cw	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 13 \)	\( - 2^{27} \cdot 3^{9} \cdot 5^{7} \cdot 11^{3} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$17160$	$16$	$0$	$0.755618561$	$1$		$4$	$7838208$	$3.242172$	$4074304020054813/1962402098708480$	$1.04067$	$5.61869$	$[1, -1, 1, 2246020, -37355388353]$	\(y^2+xy+y=x^3-x^2+2246020x-37355388353\)	3.4.0.a.1, 15.8.0-3.a.1.1, 3432.8.0.?, 17160.16.0.?	$[(15349, 1893125)]$
102960.bt2	102960cg1	102960.bt	102960cg	$2$	$3$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( - 2^{39} \cdot 3^{3} \cdot 5 \cdot 11^{3} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$17160$	$16$	$0$	$1$	$1$		$0$	$2612736$	$2.581295$	$4074304020054813/1962402098708480$	$1.04067$	$4.70279$	$[0, 0, 0, 159717, -708358198]$	\(y^2=x^3+159717x-708358198\)	3.4.0.a.1, 12.8.0-3.a.1.1, 17160.16.0.?	$[ ]$
102960.dv2	102960ck2	102960.dv	102960ck	$2$	$3$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( - 2^{39} \cdot 3^{9} \cdot 5 \cdot 11^{3} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$17160$	$16$	$0$	$1$	$1$		$0$	$7838208$	$3.130600$	$4074304020054813/1962402098708480$	$1.04067$	$5.27389$	$[0, 0, 0, 1437453, 19125671346]$	\(y^2=x^3+1437453x+19125671346\)	3.4.0.a.1, 12.8.0-3.a.1.2, 17160.16.0.?	$[ ]$
141570.s2	141570ey1	141570.s	141570ey	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 13 \)	\( - 2^{27} \cdot 3^{3} \cdot 5 \cdot 11^{9} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$17160$	$16$	$0$	$1$	$1$		$0$	$13063680$	$3.087093$	$4074304020054813/1962402098708480$	$1.04067$	$5.08827$	$[1, -1, 0, 1207860, -14731938864]$	\(y^2+xy=x^3-x^2+1207860x-14731938864\)	3.4.0.a.1, 33.8.0-3.a.1.2, 1560.8.0.?, 17160.16.0.?	$[ ]$
141570.ek2	141570cg2	141570.ek	141570cg	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 13 \)	\( - 2^{27} \cdot 3^{9} \cdot 5 \cdot 11^{9} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$17160$	$16$	$0$	$1$	$1$		$0$	$39191040$	$3.636402$	$4074304020054813/1962402098708480$	$1.04067$	$5.64403$	$[1, -1, 1, 10870738, 397751478589]$	\(y^2+xy+y=x^3-x^2+10870738x+397751478589\)	3.4.0.a.1, 33.8.0-3.a.1.1, 1560.8.0.?, 17160.16.0.?	$[ ]$
167310.cg2	167310fb1	167310.cg	167310fb	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13^{2} \)	\( - 2^{27} \cdot 3^{3} \cdot 5 \cdot 11^{3} \cdot 13^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$17160$	$16$	$0$	$6.182950093$	$1$		$0$	$18289152$	$3.170624$	$4074304020054813/1962402098708480$	$1.04067$	$5.10093$	$[1, -1, 0, 1687011, 24316187013]$	\(y^2+xy=x^3-x^2+1687011x+24316187013\)	3.4.0.a.1, 39.8.0-3.a.1.1, 1320.8.0.?, 17160.16.0.?	$[(45891/2, 9925785/2)]$
167310.dq2	167310cs2	167310.dq	167310cs	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13^{2} \)	\( - 2^{27} \cdot 3^{9} \cdot 5 \cdot 11^{3} \cdot 13^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$17160$	$16$	$0$	$1$	$1$		$0$	$54867456$	$3.719929$	$4074304020054813/1962402098708480$	$1.04067$	$5.64898$	$[1, -1, 1, 15183097, -656552232449]$	\(y^2+xy+y=x^3-x^2+15183097x-656552232449\)	3.4.0.a.1, 39.8.0-3.a.1.2, 1320.8.0.?, 17160.16.0.?	$[ ]$
411840.cp2	411840cp2	411840.cp	411840cp	$2$	$3$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( - 2^{45} \cdot 3^{9} \cdot 5 \cdot 11^{3} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$17160$	$16$	$0$	$38.10358274$	$1$		$0$	$62705664$	$3.477173$	$4074304020054813/1962402098708480$	$1.04067$	$5.03006$	$[0, 0, 0, 5749812, -153005370768]$	\(y^2=x^3+5749812x-153005370768\)	3.4.0.a.1, 24.8.0-3.a.1.1, 8580.8.0.?, 17160.16.0.?	$[(232907321895470664/5898949, 88367778044459283531753612/5898949)]$
411840.ee2	411840ee2	411840.ee	411840ee	$2$	$3$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( - 2^{45} \cdot 3^{9} \cdot 5 \cdot 11^{3} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$17160$	$16$	$0$	$5.488032448$	$1$		$0$	$62705664$	$3.477173$	$4074304020054813/1962402098708480$	$1.04067$	$5.03006$	$[0, 0, 0, 5749812, 153005370768]$	\(y^2=x^3+5749812x+153005370768\)	3.4.0.a.1, 24.8.0-3.a.1.3, 4290.8.0.?, 17160.16.0.?	$[(669106/9, 637272064/9)]$
411840.ji2	411840ji1	411840.ji	411840ji	$2$	$3$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( - 2^{45} \cdot 3^{3} \cdot 5 \cdot 11^{3} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$17160$	$16$	$0$	$2.935942389$	$1$		$0$	$20901888$	$2.927868$	$4074304020054813/1962402098708480$	$1.04067$	$4.52020$	$[0, 0, 0, 638868, 5666865584]$	\(y^2=x^3+638868x+5666865584\)	3.4.0.a.1, 24.8.0-3.a.1.2, 8580.8.0.?, 17160.16.0.?	$[(4390/7, 25952256/7)]$
411840.li2	411840li1	411840.li	411840li	$2$	$3$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( - 2^{45} \cdot 3^{3} \cdot 5 \cdot 11^{3} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$17160$	$16$	$0$	$44.04804152$	$1$		$0$	$20901888$	$2.927868$	$4074304020054813/1962402098708480$	$1.04067$	$4.52020$	$[0, 0, 0, 638868, -5666865584]$	\(y^2=x^3+638868x-5666865584\)	3.4.0.a.1, 24.8.0-3.a.1.4, 4290.8.0.?, 17160.16.0.?	$[(17712919596731954165/68021843, 72376118452950034723654599873/68021843)]$

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