Elliptic curve search results

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 (15 matches)

 

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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
17160.a2	17160b3	17160.a	17160b	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{11} \cdot 3^{28} \cdot 5^{2} \cdot 11 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$688128$	$2.587345$	$287849398425814280018/81784533026485575$	$[0, -1, 0, -1746856, 634609900]$	\(y^2=x^3-x^2-1746856x+634609900\)
34320.bw2	34320t3	34320.bw	34320t	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{11} \cdot 3^{28} \cdot 5^{2} \cdot 11 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$1376256$	$2.587345$	$287849398425814280018/81784533026485575$	$[0, 1, 0, -1746856, -634609900]$	\(y^2=x^3+x^2-1746856x-634609900\)
51480.bb2	51480bu3	51480.bb	51480bu	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{11} \cdot 3^{34} \cdot 5^{2} \cdot 11 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$1$	$16$	$2$	$1$	$5505024$	$3.136654$	$287849398425814280018/81784533026485575$	$[0, 0, 0, -15721707, -17118745594]$	\(y^2=x^3-15721707x-17118745594\)
85800.cy2	85800cp3	85800.cy	85800cp	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13 \)	\( 2^{11} \cdot 3^{28} \cdot 5^{8} \cdot 11 \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$4.895653091$	$1$		$1$	$16515072$	$3.392067$	$287849398425814280018/81784533026485575$	$[0, 1, 0, -43671408, 79238894688]$	\(y^2=x^3+x^2-43671408x+79238894688\)
102960.eq2	102960bi3	102960.eq	102960bi	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{11} \cdot 3^{34} \cdot 5^{2} \cdot 11 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$1$	$4$	$2$	$1$	$11010048$	$3.136654$	$287849398425814280018/81784533026485575$	$[0, 0, 0, -15721707, 17118745594]$	\(y^2=x^3-15721707x+17118745594\)
137280.dk2	137280cu3	137280.dk	137280cu	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{17} \cdot 3^{28} \cdot 5^{2} \cdot 11 \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$19.91955825$	$1$		$1$	$11010048$	$2.933918$	$287849398425814280018/81784533026485575$	$[0, -1, 0, -6987425, -5069891775]$	\(y^2=x^3-x^2-6987425x-5069891775\)
137280.fu2	137280dw4	137280.fu	137280dw	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{17} \cdot 3^{28} \cdot 5^{2} \cdot 11 \cdot 13 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$4.285761096$	$1$		$13$	$11010048$	$2.933918$	$287849398425814280018/81784533026485575$	$[0, 1, 0, -6987425, 5069891775]$	\(y^2=x^3+x^2-6987425x+5069891775\)
171600.k2	171600hb3	171600.k	171600hb	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13 \)	\( 2^{11} \cdot 3^{28} \cdot 5^{8} \cdot 11 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$33030144$	$3.392067$	$287849398425814280018/81784533026485575$	$[0, -1, 0, -43671408, -79238894688]$	\(y^2=x^3-x^2-43671408x-79238894688\)
188760.ba2	188760bn3	188760.ba	188760bn	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 13 \)	\( 2^{11} \cdot 3^{28} \cdot 5^{2} \cdot 11^{7} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$82.21584678$	$1$		$1$	$82575360$	$3.786293$	$287849398425814280018/81784533026485575$	$[0, -1, 0, -211369616, -843820298484]$	\(y^2=x^3-x^2-211369616x-843820298484\)
223080.cb2	223080be4	223080.cb	223080be	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 11 \cdot 13^{2} \)	\( 2^{11} \cdot 3^{28} \cdot 5^{2} \cdot 11 \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1$	$16$	$2$	$1$	$115605504$	$3.869820$	$287849398425814280018/81784533026485575$	$[0, -1, 0, -295218720, 1393057075500]$	\(y^2=x^3-x^2-295218720x+1393057075500\)
257400.ej2	257400ej3	257400.ej	257400ej	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 13 \)	\( 2^{11} \cdot 3^{34} \cdot 5^{8} \cdot 11 \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$70.17004512$	$1$		$1$	$132120576$	$3.941372$	$287849398425814280018/81784533026485575$	$[0, 0, 0, -393042675, -2139843199250]$	\(y^2=x^3-393042675x-2139843199250\)
377520.dy2	377520dy4	377520.dy	377520dy	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 13 \)	\( 2^{11} \cdot 3^{28} \cdot 5^{2} \cdot 11^{7} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$0.747998340$	$1$		$11$	$165150720$	$3.786293$	$287849398425814280018/81784533026485575$	$[0, 1, 0, -211369616, 843820298484]$	\(y^2=x^3+x^2-211369616x+843820298484\)
411840.i2	411840i3	411840.i	411840i	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{17} \cdot 3^{34} \cdot 5^{2} \cdot 11 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$1$	$1$		$1$	$88080384$	$3.483227$	$287849398425814280018/81784533026485575$	$[0, 0, 0, -62886828, -136949964752]$	\(y^2=x^3-62886828x-136949964752\)
411840.gi2	411840gi4	411840.gi	411840gi	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 13 \)	\( 2^{17} \cdot 3^{34} \cdot 5^{2} \cdot 11 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$1$	$16$	$2$	$1$	$88080384$	$3.483227$	$287849398425814280018/81784533026485575$	$[0, 0, 0, -62886828, 136949964752]$	\(y^2=x^3-62886828x+136949964752\)
446160.gw2	446160gw3	446160.gw	446160gw	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 11 \cdot 13^{2} \)	\( 2^{11} \cdot 3^{28} \cdot 5^{2} \cdot 11 \cdot 13^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$4.632856628$	$1$		$7$	$231211008$	$3.869820$	$287849398425814280018/81784533026485575$	$[0, 1, 0, -295218720, -1393057075500]$	\(y^2=x^3+x^2-295218720x-1393057075500\)