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 (27 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
2310.k4	2310j1	2310.k	2310j	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{12} \cdot 3^{4} \cdot 5 \cdot 7^{4} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$0.666885710$	$1$		$7$	$3072$	$0.748379$	$-95575628340361/43812679680$	$[1, 0, 1, -953, 15068]$	\(y^2+xy+y=x^3-953x+15068\)
6930.w4	6930x1	6930.w	6930x	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{12} \cdot 3^{10} \cdot 5 \cdot 7^{4} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$24576$	$1.297686$	$-95575628340361/43812679680$	$[1, -1, 1, -8573, -406843]$	\(y^2+xy+y=x^3-x^2-8573x-406843\)
11550.bt4	11550bq1	11550.bt	11550bq	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( - 2^{12} \cdot 3^{4} \cdot 5^{7} \cdot 7^{4} \cdot 11 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$0.520317837$	$1$		$19$	$73728$	$1.553097$	$-95575628340361/43812679680$	$[1, 1, 1, -23813, 1883531]$	\(y^2+xy+y=x^3+x^2-23813x+1883531\)
16170.c4	16170d1	16170.c	16170d	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \)	\( - 2^{12} \cdot 3^{4} \cdot 5 \cdot 7^{10} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$1$	$1$		$1$	$147456$	$1.721334$	$-95575628340361/43812679680$	$[1, 1, 0, -46673, -5215083]$	\(y^2+xy=x^3+x^2-46673x-5215083\)
18480.bs4	18480cj1	18480.bs	18480cj	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{24} \cdot 3^{4} \cdot 5 \cdot 7^{4} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3.100105865$	$1$		$3$	$73728$	$1.441526$	$-95575628340361/43812679680$	$[0, -1, 0, -15240, -964368]$	\(y^2=x^3-x^2-15240x-964368\)
25410.cw4	25410cx1	25410.cw	25410cx	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{12} \cdot 3^{4} \cdot 5 \cdot 7^{4} \cdot 11^{7} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1$	$1$		$3$	$368640$	$1.947327$	$-95575628340361/43812679680$	$[1, 0, 0, -115255, -20171095]$	\(y^2+xy=x^3-115255x-20171095\)
34650.bw4	34650bj1	34650.bw	34650bj	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \)	\( - 2^{12} \cdot 3^{10} \cdot 5^{7} \cdot 7^{4} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$589824$	$2.102406$	$-95575628340361/43812679680$	$[1, -1, 0, -214317, -51069659]$	\(y^2+xy=x^3-x^2-214317x-51069659\)
48510.dw4	48510ef1	48510.dw	48510ef	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 \)	\( - 2^{12} \cdot 3^{10} \cdot 5 \cdot 7^{10} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$1179648$	$2.270641$	$-95575628340361/43812679680$	$[1, -1, 1, -420062, 140387181]$	\(y^2+xy+y=x^3-x^2-420062x+140387181\)
55440.bv4	55440di1	55440.bv	55440di	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{24} \cdot 3^{10} \cdot 5 \cdot 7^{4} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$589824$	$1.990831$	$-95575628340361/43812679680$	$[0, 0, 0, -137163, 26175098]$	\(y^2=x^3-137163x+26175098\)
73920.u4	73920g1	73920.u	73920g	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{30} \cdot 3^{4} \cdot 5 \cdot 7^{4} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$589824$	$1.788099$	$-95575628340361/43812679680$	$[0, -1, 0, -60961, 7775905]$	\(y^2=x^3-x^2-60961x+7775905\)
73920.fj4	73920gr1	73920.fj	73920gr	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{30} \cdot 3^{4} \cdot 5 \cdot 7^{4} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$589824$	$1.788099$	$-95575628340361/43812679680$	$[0, 1, 0, -60961, -7775905]$	\(y^2=x^3+x^2-60961x-7775905\)
76230.s4	76230bg1	76230.s	76230bg	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{12} \cdot 3^{10} \cdot 5 \cdot 7^{4} \cdot 11^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$2949120$	$2.496632$	$-95575628340361/43812679680$	$[1, -1, 0, -1037295, 544619565]$	\(y^2+xy=x^3-x^2-1037295x+544619565\)
80850.gf4	80850fu1	80850.gf	80850fu	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( - 2^{12} \cdot 3^{4} \cdot 5^{7} \cdot 7^{10} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$3538944$	$2.526054$	$-95575628340361/43812679680$	$[1, 0, 0, -1166838, -649551708]$	\(y^2+xy=x^3-1166838x-649551708\)
92400.fs4	92400gn1	92400.fs	92400gn	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( - 2^{24} \cdot 3^{4} \cdot 5^{7} \cdot 7^{4} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1$	$1$		$1$	$1769472$	$2.246246$	$-95575628340361/43812679680$	$[0, 1, 0, -381008, -121308012]$	\(y^2=x^3+x^2-381008x-121308012\)
127050.q4	127050d1	127050.q	127050d	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( - 2^{12} \cdot 3^{4} \cdot 5^{7} \cdot 7^{4} \cdot 11^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$8847360$	$2.752045$	$-95575628340361/43812679680$	$[1, 1, 0, -2881375, -2521386875]$	\(y^2+xy=x^3+x^2-2881375x-2521386875\)
129360.ey4	129360gn1	129360.ey	129360gn	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \)	\( - 2^{24} \cdot 3^{4} \cdot 5 \cdot 7^{10} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$2.379257921$	$1$		$5$	$3538944$	$2.414482$	$-95575628340361/43812679680$	$[0, 1, 0, -746776, 332271764]$	\(y^2=x^3+x^2-746776x+332271764\)
177870.fg4	177870dz1	177870.fg	177870dz	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11^{2} \)	\( - 2^{12} \cdot 3^{4} \cdot 5 \cdot 7^{10} \cdot 11^{7} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1.393480839$	$1$		$25$	$17694720$	$2.920280$	$-95575628340361/43812679680$	$[1, 1, 1, -5647496, 6913038089]$	\(y^2+xy+y=x^3+x^2-5647496x+6913038089\)
203280.cm4	203280cu1	203280.cm	203280cu	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{24} \cdot 3^{4} \cdot 5 \cdot 7^{4} \cdot 11^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1$	$1$		$1$	$8847360$	$2.640472$	$-95575628340361/43812679680$	$[0, -1, 0, -1844080, 1290950080]$	\(y^2=x^3-x^2-1844080x+1290950080\)
221760.gz4	221760jw1	221760.gz	221760jw	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{30} \cdot 3^{10} \cdot 5 \cdot 7^{4} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$24.77628163$	$1$		$1$	$4718592$	$2.337406$	$-95575628340361/43812679680$	$[0, 0, 0, -548652, -209400784]$	\(y^2=x^3-548652x-209400784\)
221760.mw4	221760d1	221760.mw	221760d	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)	\( - 2^{30} \cdot 3^{10} \cdot 5 \cdot 7^{4} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$4718592$	$2.337406$	$-95575628340361/43812679680$	$[0, 0, 0, -548652, 209400784]$	\(y^2=x^3-548652x+209400784\)
242550.gr4	242550gr1	242550.gr	242550gr	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( - 2^{12} \cdot 3^{10} \cdot 5^{7} \cdot 7^{10} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$28311552$	$3.075359$	$-95575628340361/43812679680$	$[1, -1, 0, -10501542, 17537896116]$	\(y^2+xy=x^3-x^2-10501542x+17537896116\)
277200.x4	277200x1	277200.x	277200x	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 \)	\( - 2^{24} \cdot 3^{10} \cdot 5^{7} \cdot 7^{4} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$7.354080745$	$1$		$1$	$14155776$	$2.795551$	$-95575628340361/43812679680$	$[0, 0, 0, -3429075, 3271887250]$	\(y^2=x^3-3429075x+3271887250\)
369600.ci4	369600ci1	369600.ci	369600ci	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( - 2^{30} \cdot 3^{4} \cdot 5^{7} \cdot 7^{4} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$1$	$1$		$1$	$14155776$	$2.592819$	$-95575628340361/43812679680$	$[0, -1, 0, -1524033, -968940063]$	\(y^2=x^3-x^2-1524033x-968940063\)
369600.wu4	369600wu1	369600.wu	369600wu	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 \)	\( - 2^{30} \cdot 3^{4} \cdot 5^{7} \cdot 7^{4} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$1$	$1$		$1$	$14155776$	$2.592819$	$-95575628340361/43812679680$	$[0, 1, 0, -1524033, 968940063]$	\(y^2=x^3+x^2-1524033x+968940063\)
381150.lr4	381150lr1	381150.lr	381150lr	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( - 2^{12} \cdot 3^{10} \cdot 5^{7} \cdot 7^{4} \cdot 11^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$70778880$	$3.301350$	$-95575628340361/43812679680$	$[1, -1, 1, -25932380, 68051513247]$	\(y^2+xy+y=x^3-x^2-25932380x+68051513247\)
388080.im4	388080im1	388080.im	388080im	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 \)	\( - 2^{24} \cdot 3^{10} \cdot 5 \cdot 7^{10} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$16.55716924$	$1$		$1$	$28311552$	$2.963787$	$-95575628340361/43812679680$	$[0, 0, 0, -6720987, -8978058614]$	\(y^2=x^3-6720987x-8978058614\)
390390.ei4	390390ei1	390390.ei	390390ei	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13^{2} \)	\( - 2^{12} \cdot 3^{4} \cdot 5 \cdot 7^{4} \cdot 11 \cdot 13^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$0.289848291$	$1$		$11$	$7077888$	$2.030853$	$-95575628340361/43812679680$	$[1, 0, 0, -160976, 33265920]$	\(y^2+xy=x^3-160976x+33265920\)