Elliptic curve search results

Results (18 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	Manin constant
3315.b2	3315e2	3315.b	3315e	$4$	$4$	\( 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 3^{4} \cdot 5^{4} \cdot 13^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$884$	$48$	$0$	$1$	$1$		$2$	$2048$	$0.587588$	$104413920565969/2472575625$	$1.15696$	$3.98205$	$[1, 0, 0, -981, -11664]$	\(y^2+xy=x^3-981x-11664\)	2.6.0.a.1, 4.12.0-2.a.1.1, 52.24.0-52.b.1.2, 68.24.0-68.b.1.1, 884.48.0.?	$[ ]$	$1$
9945.k2	9945i2	9945.k	9945i	$4$	$4$	\( 3^{2} \cdot 5 \cdot 13 \cdot 17 \)	\( 3^{10} \cdot 5^{4} \cdot 13^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2652$	$48$	$0$	$1$	$1$		$2$	$16384$	$1.136894$	$104413920565969/2472575625$	$1.15696$	$4.22290$	$[1, -1, 0, -8829, 314928]$	\(y^2+xy=x^3-x^2-8829x+314928\)	2.6.0.a.1, 12.12.0-2.a.1.1, 52.12.0.b.1, 68.12.0.b.1, 156.24.0.?, $\ldots$	$[ ]$	$1$
16575.f2	16575a2	16575.f	16575a	$4$	$4$	\( 3 \cdot 5^{2} \cdot 13 \cdot 17 \)	\( 3^{4} \cdot 5^{10} \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$4420$	$48$	$0$	$4.619127323$	$1$		$2$	$49152$	$1.392307$	$104413920565969/2472575625$	$1.15696$	$4.31634$	$[1, 1, 0, -24525, -1458000]$	\(y^2+xy=x^3+x^2-24525x-1458000\)	2.6.0.a.1, 20.12.0-2.a.1.1, 52.12.0.b.1, 68.12.0.b.1, 260.24.0.?, $\ldots$	$[(-369/2, 1755/2)]$	$1$
43095.p2	43095q2	43095.p	43095q	$4$	$4$	\( 3 \cdot 5 \cdot 13^{2} \cdot 17 \)	\( 3^{4} \cdot 5^{4} \cdot 13^{8} \cdot 17^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$884$	$48$	$0$	$1$	$1$		$2$	$344064$	$1.870062$	$104413920565969/2472575625$	$1.15696$	$4.46709$	$[1, 0, 1, -165793, -25460017]$	\(y^2+xy+y=x^3-165793x-25460017\)	2.6.0.a.1, 4.12.0-2.a.1.1, 52.24.0-52.b.1.2, 68.24.0-68.b.1.3, 884.48.0.?	$[ ]$	$1$
49725.e2	49725j2	49725.e	49725j	$4$	$4$	\( 3^{2} \cdot 5^{2} \cdot 13 \cdot 17 \)	\( 3^{10} \cdot 5^{10} \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$13260$	$48$	$0$	$2.018790369$	$1$		$8$	$393216$	$1.941612$	$104413920565969/2472575625$	$1.15696$	$4.48738$	$[1, -1, 1, -220730, 39145272]$	\(y^2+xy+y=x^3-x^2-220730x+39145272\)	2.6.0.a.1, 52.12.0.b.1, 60.12.0-2.a.1.1, 68.12.0.b.1, 780.24.0.?, $\ldots$	$[(188, 1971)]$	$1$
53040.b2	53040bq2	53040.b	53040bq	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 2^{12} \cdot 3^{4} \cdot 5^{4} \cdot 13^{2} \cdot 17^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$884$	$48$	$0$	$2.464735517$	$1$		$27$	$131072$	$1.280735$	$104413920565969/2472575625$	$1.15696$	$3.73177$	$[0, -1, 0, -15696, 746496]$	\(y^2=x^3-x^2-15696x+746496\)	2.6.0.a.1, 4.12.0-2.a.1.1, 52.24.0-52.b.1.1, 68.24.0-68.b.1.2, 884.48.0.?	$[(90, 234), (0, 864)]$	$1$
56355.f2	56355l2	56355.f	56355l	$4$	$4$	\( 3 \cdot 5 \cdot 13 \cdot 17^{2} \)	\( 3^{4} \cdot 5^{4} \cdot 13^{2} \cdot 17^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$884$	$48$	$0$	$2.833145382$	$1$		$6$	$589824$	$2.004196$	$104413920565969/2472575625$	$1.15696$	$4.50468$	$[1, 1, 1, -283515, -57021720]$	\(y^2+xy+y=x^3+x^2-283515x-57021720\)	2.6.0.a.1, 4.12.0-2.a.1.1, 52.24.0-52.b.1.3, 68.24.0-68.b.1.1, 884.48.0.?	$[(-287, -757)]$	$1$
129285.c2	129285t2	129285.c	129285t	$4$	$4$	\( 3^{2} \cdot 5 \cdot 13^{2} \cdot 17 \)	\( 3^{10} \cdot 5^{4} \cdot 13^{8} \cdot 17^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2652$	$48$	$0$	$6.344624480$	$1$		$20$	$2752512$	$2.419369$	$104413920565969/2472575625$	$1.15696$	$4.61018$	$[1, -1, 1, -1492133, 687420452]$	\(y^2+xy+y=x^3-x^2-1492133x+687420452\)	2.6.0.a.1, 12.12.0-2.a.1.1, 52.12.0.b.1, 68.12.0.b.1, 156.24.0.?, $\ldots$	$[(468, 9328), (790, 703)]$	$1$
159120.cr2	159120d2	159120.cr	159120d	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 13 \cdot 17 \)	\( 2^{12} \cdot 3^{10} \cdot 5^{4} \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2652$	$48$	$0$	$1.619242942$	$1$		$15$	$1048576$	$1.830042$	$104413920565969/2472575625$	$1.15696$	$3.93982$	$[0, 0, 0, -141267, -20014126]$	\(y^2=x^3-141267x-20014126\)	2.6.0.a.1, 12.12.0-2.a.1.1, 52.12.0.b.1, 68.12.0.b.1, 156.24.0.?, $\ldots$	$[(-217, 650)]$	$1$
162435.v2	162435t2	162435.v	162435t	$4$	$4$	\( 3 \cdot 5 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{4} \cdot 5^{4} \cdot 7^{6} \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$6188$	$48$	$0$	$0.788410796$	$1$		$14$	$589824$	$1.560543$	$104413920565969/2472575625$	$1.15696$	$3.66350$	$[1, 1, 1, -48070, 3952682]$	\(y^2+xy+y=x^3+x^2-48070x+3952682\)	2.6.0.a.1, 28.12.0-2.a.1.1, 52.12.0.b.1, 68.12.0.b.1, 364.24.0.?, $\ldots$	$[(-8, 2086)]$	$1$
169065.u2	169065bb2	169065.u	169065bb	$4$	$4$	\( 3^{2} \cdot 5 \cdot 13 \cdot 17^{2} \)	\( 3^{10} \cdot 5^{4} \cdot 13^{2} \cdot 17^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2652$	$48$	$0$	$7.185831433$	$1$		$2$	$4718592$	$2.553501$	$104413920565969/2472575625$	$1.15696$	$4.64115$	$[1, -1, 0, -2551635, 1537034800]$	\(y^2+xy=x^3-x^2-2551635x+1537034800\)	2.6.0.a.1, 12.12.0-2.a.1.1, 52.12.0.b.1, 68.12.0.b.1, 156.24.0.?, $\ldots$	$[(25485/4, 2437555/4)]$	$1$
212160.dq2	212160gx2	212160.dq	212160gx	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 2^{18} \cdot 3^{4} \cdot 5^{4} \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$1768$	$48$	$0$	$3.709016727$	$1$		$7$	$1048576$	$1.627308$	$104413920565969/2472575625$	$1.15696$	$3.64906$	$[0, -1, 0, -62785, -5909183]$	\(y^2=x^3-x^2-62785x-5909183\)	2.6.0.a.1, 8.12.0-2.a.1.1, 52.12.0.b.1, 68.12.0.b.1, 104.24.0.?, $\ldots$	$[(-152, 315)]$	$1$
212160.gc2	212160f2	212160.gc	212160f	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 2^{18} \cdot 3^{4} \cdot 5^{4} \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$1768$	$48$	$0$	$0.989117169$	$1$		$13$	$1048576$	$1.627308$	$104413920565969/2472575625$	$1.15696$	$3.64906$	$[0, 1, 0, -62785, 5909183]$	\(y^2=x^3+x^2-62785x+5909183\)	2.6.0.a.1, 8.12.0-2.a.1.1, 52.12.0.b.1, 68.12.0.b.1, 104.24.0.?, $\ldots$	$[(191, 960)]$	$1$
215475.p2	215475w2	215475.p	215475w	$4$	$4$	\( 3 \cdot 5^{2} \cdot 13^{2} \cdot 17 \)	\( 3^{4} \cdot 5^{10} \cdot 13^{8} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$4420$	$48$	$0$	$9.004979366$	$1$		$2$	$8257536$	$2.674782$	$104413920565969/2472575625$	$1.15696$	$4.66799$	$[1, 1, 1, -4144813, -3182502094]$	\(y^2+xy+y=x^3+x^2-4144813x-3182502094\)	2.6.0.a.1, 20.12.0-2.a.1.1, 52.12.0.b.1, 68.12.0.b.1, 260.24.0.?, $\ldots$	$[(-27811/5, 981453/5)]$	$1$
265200.gx2	265200gx2	265200.gx	265200gx	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13 \cdot 17 \)	\( 2^{12} \cdot 3^{4} \cdot 5^{10} \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$4420$	$48$	$0$	$2.310961663$	$1$		$9$	$3145728$	$2.085453$	$104413920565969/2472575625$	$1.15696$	$4.02409$	$[0, 1, 0, -392408, 92527188]$	\(y^2=x^3+x^2-392408x+92527188\)	2.6.0.a.1, 20.12.0-2.a.1.1, 52.12.0.b.1, 68.12.0.b.1, 260.24.0.?, $\ldots$	$[(454, 2856)]$	$1$
281775.cf2	281775cf2	281775.cf	281775cf	$4$	$4$	\( 3 \cdot 5^{2} \cdot 13 \cdot 17^{2} \)	\( 3^{4} \cdot 5^{10} \cdot 13^{2} \cdot 17^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$4420$	$48$	$0$	$1$	$9$	$3$	$2$	$14155776$	$2.808914$	$104413920565969/2472575625$	$1.15696$	$4.69646$	$[1, 0, 1, -7087876, -7113539227]$	\(y^2+xy+y=x^3-7087876x-7113539227\)	2.6.0.a.1, 20.12.0-2.a.1.1, 52.12.0.b.1, 68.12.0.b.1, 260.24.0.?, $\ldots$	$[ ]$	$1$
401115.bp2	401115bp2	401115.bp	401115bp	$4$	$4$	\( 3 \cdot 5 \cdot 11^{2} \cdot 13 \cdot 17 \)	\( 3^{4} \cdot 5^{4} \cdot 11^{6} \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$9724$	$48$	$0$	$2.132434439$	$1$		$6$	$2949120$	$1.786535$	$104413920565969/2472575625$	$1.15696$	$3.61702$	$[1, 0, 1, -118704, 15406081]$	\(y^2+xy+y=x^3-118704x+15406081\)	2.6.0.a.1, 44.12.0-2.a.1.1, 52.12.0.b.1, 68.12.0.b.1, 572.24.0.?, $\ldots$	$[(-97, 5148)]$	$1$
487305.cx2	487305cx2	487305.cx	487305cx	$4$	$4$	\( 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{10} \cdot 5^{4} \cdot 7^{6} \cdot 13^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$18564$	$48$	$0$	$1$	$1$		$2$	$4718592$	$2.109848$	$104413920565969/2472575625$	$1.15696$	$3.85950$	$[1, -1, 0, -432630, -107155049]$	\(y^2+xy=x^3-x^2-432630x-107155049\)	2.6.0.a.1, 52.12.0.b.1, 68.12.0.b.1, 84.12.0.?, 884.24.0.?, $\ldots$	$[ ]$	$1$

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