Elliptic curve search results

Results (24 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	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
786.d2	786e2	786.d	786e	$4$	$4$	\( 2 \cdot 3 \cdot 131 \)	\( 2^{6} \cdot 3^{2} \cdot 131^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.1	2Cs	$3144$	$48$	$0$	$1$	$1$		$2$	$288$	$0.227517$	$4722184089433/9884736$	$1.05106$	$4.37730$	$[1, 1, 0, -349, 2365]$	\(y^2+xy=x^3+x^2-349x+2365\)	2.6.0.a.1, 8.12.0-2.a.1.1, 12.12.0-2.a.1.1, 24.24.0-24.a.1.3, 524.12.0.?, $\ldots$	$[]$
2358.m2	2358t2	2358.m	2358t	$4$	$4$	\( 2 \cdot 3^{2} \cdot 131 \)	\( 2^{6} \cdot 3^{8} \cdot 131^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$3144$	$48$	$0$	$2.120322913$	$1$		$8$	$2304$	$0.776823$	$4722184089433/9884736$	$1.05106$	$4.60687$	$[1, -1, 1, -3146, -66999]$	\(y^2+xy+y=x^3-x^2-3146x-66999\)	2.6.0.a.1, 4.12.0-2.a.1.1, 24.24.0-24.a.1.4, 1048.24.0.?, 1572.24.0.?, $\ldots$	$[(-33, 9)]$
6288.n2	6288l2	6288.n	6288l	$4$	$4$	\( 2^{4} \cdot 3 \cdot 131 \)	\( 2^{18} \cdot 3^{2} \cdot 131^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$3144$	$48$	$0$	$9.278962566$	$1$		$3$	$6912$	$0.920664$	$4722184089433/9884736$	$1.05106$	$4.28760$	$[0, 1, 0, -5592, -162540]$	\(y^2=x^3+x^2-5592x-162540\)	2.6.0.a.1, 8.12.0-2.a.1.1, 12.12.0-2.a.1.1, 24.24.0-24.a.1.2, 524.12.0.?, $\ldots$	$[(-46796/33, 572930/33)]$
18864.g2	18864bh2	18864.g	18864bh	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 131 \)	\( 2^{18} \cdot 3^{8} \cdot 131^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$3144$	$48$	$0$	$1$	$1$		$3$	$55296$	$1.469971$	$4722184089433/9884736$	$1.05106$	$4.47869$	$[0, 0, 0, -50331, 4338250]$	\(y^2=x^3-50331x+4338250\)	2.6.0.a.1, 4.12.0-2.a.1.1, 24.24.0-24.a.1.1, 1048.24.0.?, 1572.24.0.?, $\ldots$	$[]$
19650.bc2	19650bf2	19650.bc	19650bf	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 131 \)	\( 2^{6} \cdot 3^{2} \cdot 5^{6} \cdot 131^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$15720$	$48$	$0$	$1$	$1$		$2$	$36864$	$1.032236$	$4722184089433/9884736$	$1.05106$	$3.92885$	$[1, 0, 0, -8738, 313092]$	\(y^2+xy=x^3-8738x+313092\)	2.6.0.a.1, 24.12.0.a.1, 40.12.0-2.a.1.1, 60.12.0-2.a.1.1, 120.24.0.?, $\ldots$	$[]$
25152.g2	25152bg2	25152.g	25152bg	$4$	$4$	\( 2^{6} \cdot 3 \cdot 131 \)	\( 2^{24} \cdot 3^{2} \cdot 131^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$3144$	$48$	$0$	$11.06778182$	$1$		$3$	$55296$	$1.267239$	$4722184089433/9884736$	$1.05106$	$4.11144$	$[0, -1, 0, -22369, -1277951]$	\(y^2=x^3-x^2-22369x-1277951\)	2.6.0.a.1, 4.12.0-2.a.1.1, 24.24.0-24.a.1.1, 1048.24.0.?, 1572.24.0.?, $\ldots$	$[(-280325/57, 8906876/57)]$
25152.bc2	25152l2	25152.bc	25152l	$4$	$4$	\( 2^{6} \cdot 3 \cdot 131 \)	\( 2^{24} \cdot 3^{2} \cdot 131^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$3144$	$48$	$0$	$1$	$1$		$3$	$55296$	$1.267239$	$4722184089433/9884736$	$1.05106$	$4.11144$	$[0, 1, 0, -22369, 1277951]$	\(y^2=x^3+x^2-22369x+1277951\)	2.6.0.a.1, 4.12.0-2.a.1.1, 24.24.0-24.a.1.4, 1048.24.0.?, 1572.24.0.?, $\ldots$	$[]$
38514.l2	38514l2	38514.l	38514l	$4$	$4$	\( 2 \cdot 3 \cdot 7^{2} \cdot 131 \)	\( 2^{6} \cdot 3^{2} \cdot 7^{6} \cdot 131^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$22008$	$48$	$0$	$5.677970481$	$1$		$4$	$110592$	$1.200472$	$4722184089433/9884736$	$1.05106$	$3.86965$	$[1, 0, 1, -17127, -862550]$	\(y^2+xy+y=x^3-17127x-862550\)	2.6.0.a.1, 24.12.0.a.1, 56.12.0-2.a.1.1, 84.12.0.?, 168.24.0.?, $\ldots$	$[(1366/3, 3352/3)]$
58950.m2	58950h2	58950.m	58950h	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 131 \)	\( 2^{6} \cdot 3^{8} \cdot 5^{6} \cdot 131^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$15720$	$48$	$0$	$1$	$1$		$2$	$294912$	$1.581543$	$4722184089433/9884736$	$1.05106$	$4.13599$	$[1, -1, 0, -78642, -8453484]$	\(y^2+xy=x^3-x^2-78642x-8453484\)	2.6.0.a.1, 20.12.0-2.a.1.1, 24.12.0.a.1, 120.24.0.?, 1048.12.0.?, $\ldots$	$[]$
75456.ct2	75456cn2	75456.ct	75456cn	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 131 \)	\( 2^{24} \cdot 3^{8} \cdot 131^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$3144$	$48$	$0$	$8.530392048$	$1$		$3$	$442368$	$1.816544$	$4722184089433/9884736$	$1.05106$	$4.29617$	$[0, 0, 0, -201324, 34706000]$	\(y^2=x^3-201324x+34706000\)	2.6.0.a.1, 8.12.0-2.a.1.1, 12.12.0-2.a.1.1, 24.24.0-24.a.1.2, 524.12.0.?, $\ldots$	$[(39997/11, 2752245/11)]$
75456.cw2	75456bd2	75456.cw	75456bd	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 131 \)	\( 2^{24} \cdot 3^{8} \cdot 131^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$3144$	$48$	$0$	$18.21540791$	$1$		$3$	$442368$	$1.816544$	$4722184089433/9884736$	$1.05106$	$4.29617$	$[0, 0, 0, -201324, -34706000]$	\(y^2=x^3-201324x-34706000\)	2.6.0.a.1, 8.12.0-2.a.1.1, 12.12.0-2.a.1.1, 24.24.0-24.a.1.3, 524.12.0.?, $\ldots$	$[(9568421798/167, 935966050145280/167)]$
95106.t2	95106o2	95106.t	95106o	$4$	$4$	\( 2 \cdot 3 \cdot 11^{2} \cdot 131 \)	\( 2^{6} \cdot 3^{2} \cdot 11^{6} \cdot 131^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$34584$	$48$	$0$	$5.149442923$	$1$		$2$	$368640$	$1.426464$	$4722184089433/9884736$	$1.05106$	$3.80107$	$[1, 1, 1, -42292, -3359179]$	\(y^2+xy+y=x^3+x^2-42292x-3359179\)	2.6.0.a.1, 24.12.0.a.1, 88.12.0.?, 132.12.0.?, 264.24.0.?, $\ldots$	$[(2807/2, 138759/2)]$
102966.q2	102966q2	102966.q	102966q	$4$	$4$	\( 2 \cdot 3 \cdot 131^{2} \)	\( 2^{6} \cdot 3^{2} \cdot 131^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$3144$	$48$	$0$	$38.43546904$	$1$		$2$	$4942080$	$2.665115$	$4722184089433/9884736$	$1.05106$	$5.06270$	$[1, 1, 1, -5998127, -5646469579]$	\(y^2+xy+y=x^3+x^2-5998127x-5646469579\)	2.6.0.a.1, 4.12.0-2.a.1.1, 24.24.0-24.a.1.6, 1048.24.0.?, 1572.24.0.?, $\ldots$	$[(-190904886028527143/11666121, 6046285790418392538527396/11666121)]$
115542.cc2	115542ce2	115542.cc	115542ce	$4$	$4$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 131 \)	\( 2^{6} \cdot 3^{8} \cdot 7^{6} \cdot 131^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$22008$	$48$	$0$	$1.974163003$	$1$		$8$	$884736$	$1.749779$	$4722184089433/9884736$	$1.05106$	$4.07042$	$[1, -1, 1, -154139, 23288843]$	\(y^2+xy+y=x^3-x^2-154139x+23288843\)	2.6.0.a.1, 24.12.0.a.1, 28.12.0-2.a.1.1, 168.24.0.?, 1048.12.0.?, $\ldots$	$[(247, 366)]$
132834.p2	132834m2	132834.p	132834m	$4$	$4$	\( 2 \cdot 3 \cdot 13^{2} \cdot 131 \)	\( 2^{6} \cdot 3^{2} \cdot 13^{6} \cdot 131^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$40872$	$48$	$0$	$1.370133221$	$1$		$8$	$663552$	$1.509991$	$4722184089433/9884736$	$1.05106$	$3.77838$	$[1, 1, 1, -59069, 5491091]$	\(y^2+xy+y=x^3+x^2-59069x+5491091\)	2.6.0.a.1, 24.12.0.a.1, 104.12.0.?, 156.12.0.?, 312.24.0.?, $\ldots$	$[(187, 920)]$
157200.t2	157200ca2	157200.t	157200ca	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 131 \)	\( 2^{18} \cdot 3^{2} \cdot 5^{6} \cdot 131^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$15720$	$48$	$0$	$1$	$1$		$3$	$884736$	$1.725384$	$4722184089433/9884736$	$1.05106$	$3.94121$	$[0, -1, 0, -139808, -20037888]$	\(y^2=x^3-x^2-139808x-20037888\)	2.6.0.a.1, 24.12.0.a.1, 40.12.0-2.a.1.1, 60.12.0-2.a.1.1, 120.24.0.?, $\ldots$	$[]$
227154.g2	227154p2	227154.g	227154p	$4$	$4$	\( 2 \cdot 3 \cdot 17^{2} \cdot 131 \)	\( 2^{6} \cdot 3^{2} \cdot 17^{6} \cdot 131^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$53448$	$48$	$0$	$1$	$1$		$2$	$1474560$	$1.644123$	$4722184089433/9884736$	$1.05106$	$3.74452$	$[1, 0, 1, -101012, 12325970]$	\(y^2+xy+y=x^3-101012x+12325970\)	2.6.0.a.1, 24.12.0.a.1, 136.12.0.?, 204.12.0.?, 408.24.0.?, $\ldots$	$[]$
283746.bg2	283746bg2	283746.bg	283746bg	$4$	$4$	\( 2 \cdot 3 \cdot 19^{2} \cdot 131 \)	\( 2^{6} \cdot 3^{2} \cdot 19^{6} \cdot 131^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$59736$	$48$	$0$	$14.02691727$	$1$		$2$	$1741824$	$1.699736$	$4722184089433/9884736$	$1.05106$	$3.73133$	$[1, 0, 0, -126177, -17230455]$	\(y^2+xy=x^3-126177x-17230455\)	2.6.0.a.1, 24.12.0.a.1, 152.12.0.?, 228.12.0.?, 456.24.0.?, $\ldots$	$[(-4928360/153, -36886645/153)]$
285318.c2	285318c2	285318.c	285318c	$4$	$4$	\( 2 \cdot 3^{2} \cdot 11^{2} \cdot 131 \)	\( 2^{6} \cdot 3^{8} \cdot 11^{6} \cdot 131^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$34584$	$48$	$0$	$5.825981286$	$1$		$20$	$2949120$	$1.975771$	$4722184089433/9884736$	$1.05106$	$3.99338$	$[1, -1, 0, -380628, 90317200]$	\(y^2+xy=x^3-x^2-380628x+90317200\)	2.6.0.a.1, 24.12.0.a.1, 44.12.0-2.a.1.1, 264.24.0.?, 1048.12.0.?, $\ldots$	$[(377, 356), (371, 71)]$
308112.h2	308112h2	308112.h	308112h	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 131 \)	\( 2^{18} \cdot 3^{2} \cdot 7^{6} \cdot 131^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$22008$	$48$	$0$	$1$	$1$		$3$	$2654208$	$1.893620$	$4722184089433/9884736$	$1.05106$	$3.89110$	$[0, -1, 0, -274024, 55203184]$	\(y^2=x^3-x^2-274024x+55203184\)	2.6.0.a.1, 24.12.0.a.1, 56.12.0-2.a.1.1, 84.12.0.?, 168.24.0.?, $\ldots$	$[]$
308898.d2	308898d2	308898.d	308898d	$4$	$4$	\( 2 \cdot 3^{2} \cdot 131^{2} \)	\( 2^{6} \cdot 3^{8} \cdot 131^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.2	2Cs	$3144$	$48$	$0$	$8.988136926$	$1$		$2$	$39536640$	$3.214420$	$4722184089433/9884736$	$1.05106$	$5.14416$	$[1, -1, 0, -53983143, 152400695485]$	\(y^2+xy=x^3-x^2-53983143x+152400695485\)	2.6.0.a.1, 8.12.0-2.a.1.2, 12.12.0-2.a.1.1, 24.24.0-24.a.1.5, 524.12.0.?, $\ldots$	$[(45779/2, 8087269/2)]$
398502.u2	398502u2	398502.u	398502u	$4$	$4$	\( 2 \cdot 3^{2} \cdot 13^{2} \cdot 131 \)	\( 2^{6} \cdot 3^{8} \cdot 13^{6} \cdot 131^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$40872$	$48$	$0$	$1$	$4$	$2$	$2$	$5308416$	$2.059299$	$4722184089433/9884736$	$1.05106$	$3.96765$	$[1, -1, 0, -531621, -148791083]$	\(y^2+xy=x^3-x^2-531621x-148791083\)	2.6.0.a.1, 24.12.0.a.1, 52.12.0-2.a.1.1, 312.24.0.?, 1048.12.0.?, $\ldots$	$[]$
415794.c2	415794c2	415794.c	415794c	$4$	$4$	\( 2 \cdot 3 \cdot 23^{2} \cdot 131 \)	\( 2^{6} \cdot 3^{2} \cdot 23^{6} \cdot 131^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$72312$	$48$	$0$	$3.787980328$	$1$		$6$	$3649536$	$1.795263$	$4722184089433/9884736$	$1.05106$	$3.70973$	$[1, 1, 0, -184896, -30623040]$	\(y^2+xy=x^3+x^2-184896x-30623040\)	2.6.0.a.1, 24.12.0.a.1, 184.12.0.?, 276.12.0.?, 552.24.0.?, $\ldots$	$[(627, 9708)]$
471600.de2	471600de2	471600.de	471600de	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 131 \)	\( 2^{18} \cdot 3^{8} \cdot 5^{6} \cdot 131^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$15720$	$48$	$0$	$1$	$1$		$3$	$7077888$	$2.274689$	$4722184089433/9884736$	$1.05106$	$4.11435$	$[0, 0, 0, -1258275, 542281250]$	\(y^2=x^3-1258275x+542281250\)	2.6.0.a.1, 20.12.0-2.a.1.1, 24.12.0.a.1, 120.24.0.?, 1048.12.0.?, $\ldots$	$[]$