Elliptic curve search results

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
4641.b6	4641b6	4641.b	4641b	$6$	$8$	\( 3 \cdot 7 \cdot 13 \cdot 17 \)	\( - 3^{8} \cdot 7^{8} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.55	2B	$2.086679704$	$1$		$2$	$12288$	$1.381887$	$158346567380527343/108665074944153$	$[1, 1, 1, 11271, -193848]$	\(y^2+xy+y=x^3+x^2+11271x-193848\)
13923.i6	13923f6	13923.i	13923f	$6$	$8$	\( 3^{2} \cdot 7 \cdot 13 \cdot 17 \)	\( - 3^{14} \cdot 7^{8} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$7.473026610$	$1$		$0$	$98304$	$1.931192$	$158346567380527343/108665074944153$	$[1, -1, 0, 101439, 5335330]$	\(y^2+xy=x^3-x^2+101439x+5335330\)
32487.e6	32487m5	32487.e	32487m	$6$	$8$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( - 3^{8} \cdot 7^{14} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$2.064262647$	$1$		$2$	$589824$	$2.354843$	$158346567380527343/108665074944153$	$[1, 0, 0, 552278, 68146637]$	\(y^2+xy=x^3+552278x+68146637\)
60333.l6	60333d5	60333.l	60333d	$6$	$8$	\( 3 \cdot 7 \cdot 13^{2} \cdot 17 \)	\( - 3^{8} \cdot 7^{8} \cdot 13^{8} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.94	2B	$5.697631259$	$1$		$0$	$2064384$	$2.664360$	$158346567380527343/108665074944153$	$[1, 1, 0, 1904796, -435407643]$	\(y^2+xy=x^3+x^2+1904796x-435407643\)
74256.cd6	74256dd5	74256.cd	74256dd	$6$	$8$	\( 2^{4} \cdot 3 \cdot 7 \cdot 13 \cdot 17 \)	\( - 2^{12} \cdot 3^{8} \cdot 7^{8} \cdot 13^{2} \cdot 17 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.45	2B	$1$	$1$		$3$	$786432$	$2.075035$	$158346567380527343/108665074944153$	$[0, 1, 0, 180336, 12766932]$	\(y^2=x^3+x^2+180336x+12766932\)
78897.g6	78897l5	78897.g	78897l	$6$	$8$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( - 3^{8} \cdot 7^{8} \cdot 13^{2} \cdot 17^{7} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.46	2B	$1$	$1$		$2$	$3538944$	$2.798492$	$158346567380527343/108665074944153$	$[1, 0, 0, 3257313, -975175542]$	\(y^2+xy=x^3+3257313x-975175542\)
97461.s6	97461l5	97461.s	97461l	$6$	$8$	\( 3^{2} \cdot 7^{2} \cdot 13 \cdot 17 \)	\( - 3^{14} \cdot 7^{14} \cdot 13^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.14	2B	$1$	$4$	$2$	$0$	$4718592$	$2.904148$	$158346567380527343/108665074944153$	$[1, -1, 0, 4970502, -1839959199]$	\(y^2+xy=x^3-x^2+4970502x-1839959199\)
116025.bq6	116025bg5	116025.bq	116025bg	$6$	$8$	\( 3 \cdot 5^{2} \cdot 7 \cdot 13 \cdot 17 \)	\( - 3^{8} \cdot 5^{6} \cdot 7^{8} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$0.900118052$	$1$		$4$	$1572864$	$2.186607$	$158346567380527343/108665074944153$	$[1, 0, 1, 281774, -24794527]$	\(y^2+xy+y=x^3+281774x-24794527\)
180999.f6	180999e6	180999.f	180999e	$6$	$8$	\( 3^{2} \cdot 7 \cdot 13^{2} \cdot 17 \)	\( - 3^{14} \cdot 7^{8} \cdot 13^{8} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$1.611803890$	$1$		$6$	$16515072$	$3.213669$	$158346567380527343/108665074944153$	$[1, -1, 1, 17143159, 11773149522]$	\(y^2+xy+y=x^3-x^2+17143159x+11773149522\)
222768.fc6	222768bu5	222768.fc	222768bu	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 13 \cdot 17 \)	\( - 2^{12} \cdot 3^{14} \cdot 7^{8} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$2.827982100$	$1$		$3$	$6291456$	$2.624340$	$158346567380527343/108665074944153$	$[0, 0, 0, 1623021, -343084142]$	\(y^2=x^3+1623021x-343084142\)
236691.r6	236691r6	236691.r	236691r	$6$	$8$	\( 3^{2} \cdot 7 \cdot 13 \cdot 17^{2} \)	\( - 3^{14} \cdot 7^{8} \cdot 13^{2} \cdot 17^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$1$	$1$		$0$	$28311552$	$3.347801$	$158346567380527343/108665074944153$	$[1, -1, 0, 29315817, 26329739634]$	\(y^2+xy=x^3-x^2+29315817x+26329739634\)
297024.dd6	297024dd6	297024.dd	297024dd	$6$	$8$	\( 2^{6} \cdot 3 \cdot 7 \cdot 13 \cdot 17 \)	\( - 2^{18} \cdot 3^{8} \cdot 7^{8} \cdot 13^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.97	2B	$1$	$1$		$1$	$6291456$	$2.421608$	$158346567380527343/108665074944153$	$[0, -1, 0, 721343, 101414113]$	\(y^2=x^3-x^2+721343x+101414113\)
297024.gv6	297024gv5	297024.gv	297024gv	$6$	$8$	\( 2^{6} \cdot 3 \cdot 7 \cdot 13 \cdot 17 \)	\( - 2^{18} \cdot 3^{8} \cdot 7^{8} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.95	2B	$3.421622477$	$1$		$5$	$6291456$	$2.421608$	$158346567380527343/108665074944153$	$[0, 1, 0, 721343, -101414113]$	\(y^2=x^3+x^2+721343x-101414113\)
348075.z6	348075z6	348075.z	348075z	$6$	$8$	\( 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 \cdot 17 \)	\( - 3^{14} \cdot 5^{6} \cdot 7^{8} \cdot 13^{2} \cdot 17 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$3.558634080$	$1$		$16$	$12582912$	$2.735912$	$158346567380527343/108665074944153$	$[1, -1, 1, 2535970, 669452222]$	\(y^2+xy+y=x^3-x^2+2535970x+669452222\)
422331.br6	422331br6	422331.br	422331br	$6$	$8$	\( 3 \cdot 7^{2} \cdot 13^{2} \cdot 17 \)	\( - 3^{8} \cdot 7^{14} \cdot 13^{8} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$8.417305205$	$1$		$0$	$99090432$	$3.637318$	$158346567380527343/108665074944153$	$[1, 0, 1, 93334978, 149624826509]$	\(y^2+xy+y=x^3+93334978x+149624826509\)