Elliptic curve search results

Results (36 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
1274.k1	1274l1	1274.k	1274l	$1$	$1$	\( 2 \cdot 7^{2} \cdot 13 \)	\( - 2^{9} \cdot 7^{9} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$1$	$1$		$0$	$6048$	$1.431906$	$-2673465150439/6656$	$0.98079$	$6.45149$	$[1, 1, 1, -99177, -12063017]$	\(y^2+xy+y=x^3+x^2-99177x-12063017\)	728.2.0.?	$[ ]$
1274.m1	1274h1	1274.m	1274h	$1$	$1$	\( 2 \cdot 7^{2} \cdot 13 \)	\( - 2^{9} \cdot 7^{3} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$0.092168486$	$1$		$10$	$864$	$0.458951$	$-2673465150439/6656$	$0.98079$	$4.81854$	$[1, 0, 0, -2024, 34880]$	\(y^2+xy=x^3-2024x+34880\)	728.2.0.?	$[(32, 40)]$
10192.k1	10192x1	10192.k	10192x	$1$	$1$	\( 2^{4} \cdot 7^{2} \cdot 13 \)	\( - 2^{21} \cdot 7^{3} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$2.129875526$	$1$		$2$	$20736$	$1.152098$	$-2673465150439/6656$	$0.98079$	$4.63411$	$[0, -1, 0, -32384, -2232320]$	\(y^2=x^3-x^2-32384x-2232320\)	728.2.0.?	$[(320, 4480)]$
10192.bf1	10192bj1	10192.bf	10192bj	$1$	$1$	\( 2^{4} \cdot 7^{2} \cdot 13 \)	\( - 2^{21} \cdot 7^{9} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$1$	$1$		$0$	$145152$	$2.125053$	$-2673465150439/6656$	$0.98079$	$5.89915$	$[0, 1, 0, -1586832, 768859412]$	\(y^2=x^3+x^2-1586832x+768859412\)	728.2.0.?	$[ ]$
11466.j1	11466bc1	11466.j	11466bc	$1$	$1$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{9} \cdot 3^{6} \cdot 7^{9} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$1$	$1$		$0$	$181440$	$1.981211$	$-2673465150439/6656$	$0.98079$	$5.64015$	$[1, -1, 0, -892593, 324808861]$	\(y^2+xy=x^3-x^2-892593x+324808861\)	728.2.0.?	$[ ]$
11466.ba1	11466q1	11466.ba	11466q	$1$	$1$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{9} \cdot 3^{6} \cdot 7^{3} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$10.17833770$	$1$		$0$	$25920$	$1.008257$	$-2673465150439/6656$	$0.98079$	$4.39105$	$[1, -1, 0, -18216, -941760]$	\(y^2+xy=x^3-x^2-18216x-941760\)	728.2.0.?	$[(56527/13, 11726415/13)]$
16562.g1	16562k1	16562.g	16562k	$1$	$1$	\( 2 \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{9} \cdot 7^{9} \cdot 13^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$1$	$4$	$2$	$0$	$1016064$	$2.714378$	$-2673465150439/6656$	$0.98079$	$6.33228$	$[1, 1, 0, -16760916, -26418643376]$	\(y^2+xy=x^3+x^2-16760916x-26418643376\)	728.2.0.?	$[ ]$
16562.r1	16562g1	16562.r	16562g	$1$	$1$	\( 2 \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{9} \cdot 7^{3} \cdot 13^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$1$	$1$		$0$	$145152$	$1.741425$	$-2673465150439/6656$	$0.98079$	$5.13047$	$[1, 0, 1, -342060, 76973418]$	\(y^2+xy+y=x^3-342060x+76973418\)	728.2.0.?	$[ ]$
31850.k1	31850z1	31850.k	31850z	$1$	$1$	\( 2 \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{9} \cdot 5^{6} \cdot 7^{3} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$0.640266773$	$1$		$4$	$110592$	$1.263670$	$-2673465150439/6656$	$0.98079$	$4.25399$	$[1, 1, 0, -50600, 4360000]$	\(y^2+xy=x^3+x^2-50600x+4360000\)	728.2.0.?	$[(125, 25)]$
31850.y1	31850j1	31850.y	31850j	$1$	$1$	\( 2 \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{9} \cdot 5^{6} \cdot 7^{9} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$1$	$1$		$0$	$774144$	$2.236626$	$-2673465150439/6656$	$0.98079$	$5.38001$	$[1, 0, 1, -2479426, -1502918252]$	\(y^2+xy+y=x^3-2479426x-1502918252\)	728.2.0.?	$[ ]$
40768.bb1	40768ct1	40768.bb	40768ct	$1$	$1$	\( 2^{6} \cdot 7^{2} \cdot 13 \)	\( - 2^{27} \cdot 7^{9} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$2.525199586$	$1$		$2$	$1161216$	$2.471626$	$-2673465150439/6656$	$0.98079$	$5.52055$	$[0, -1, 0, -6347329, 6157222625]$	\(y^2=x^3-x^2-6347329x+6157222625\)	728.2.0.?	$[(1307, 9604)]$
40768.bn1	40768bq1	40768.bn	40768bq	$1$	$1$	\( 2^{6} \cdot 7^{2} \cdot 13 \)	\( - 2^{27} \cdot 7^{3} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$1.908173598$	$1$		$2$	$165888$	$1.498671$	$-2673465150439/6656$	$0.98079$	$4.42072$	$[0, -1, 0, -129537, 17988097]$	\(y^2=x^3-x^2-129537x+17988097\)	728.2.0.?	$[(208, 7)]$
40768.cs1	40768r1	40768.cs	40768r	$1$	$1$	\( 2^{6} \cdot 7^{2} \cdot 13 \)	\( - 2^{27} \cdot 7^{9} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$1$	$9$	$3$	$0$	$1161216$	$2.471626$	$-2673465150439/6656$	$0.98079$	$5.52055$	$[0, 1, 0, -6347329, -6157222625]$	\(y^2=x^3+x^2-6347329x-6157222625\)	728.2.0.?	$[ ]$
40768.dc1	40768dl1	40768.dc	40768dl	$1$	$1$	\( 2^{6} \cdot 7^{2} \cdot 13 \)	\( - 2^{27} \cdot 7^{3} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$1$	$1$		$0$	$165888$	$1.498671$	$-2673465150439/6656$	$0.98079$	$4.42072$	$[0, 1, 0, -129537, -17988097]$	\(y^2=x^3+x^2-129537x-17988097\)	728.2.0.?	$[ ]$
91728.be1	91728fx1	91728.be	91728fx	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{21} \cdot 3^{6} \cdot 7^{9} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$22.26403666$	$1$		$0$	$4354560$	$2.674358$	$-2673465150439/6656$	$0.98079$	$5.34167$	$[0, 0, 0, -14281491, -20773485614]$	\(y^2=x^3-14281491x-20773485614\)	728.2.0.?	$[(133186369575/4267, 40082411260433822/4267)]$
91728.ek1	91728ek1	91728.ek	91728ek	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{21} \cdot 3^{6} \cdot 7^{3} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$1$	$1$		$0$	$622080$	$1.701405$	$-2673465150439/6656$	$0.98079$	$4.31989$	$[0, 0, 0, -291459, 60564098]$	\(y^2=x^3-291459x+60564098\)	728.2.0.?	$[ ]$
132496.bl1	132496bf1	132496.bl	132496bf	$1$	$1$	\( 2^{4} \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{21} \cdot 7^{3} \cdot 13^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$8.857829045$	$1$		$0$	$3483648$	$2.434574$	$-2673465150439/6656$	$0.98079$	$4.93116$	$[0, -1, 0, -5472952, -4926298768]$	\(y^2=x^3-x^2-5472952x-4926298768\)	728.2.0.?	$[(25042/3, 1002806/3)]$
132496.cq1	132496cd1	132496.cq	132496cd	$1$	$1$	\( 2^{4} \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{21} \cdot 7^{9} \cdot 13^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$3.253800129$	$1$		$2$	$24385536$	$3.407528$	$-2673465150439/6656$	$0.98079$	$5.92108$	$[0, 1, 0, -268174664, 1690256826740]$	\(y^2=x^3+x^2-268174664x+1690256826740\)	728.2.0.?	$[(9572, 19942)]$
149058.fb1	149058o1	149058.fb	149058o	$1$	$1$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{9} \cdot 3^{6} \cdot 7^{3} \cdot 13^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$1$	$1$		$0$	$4354560$	$2.290730$	$-2673465150439/6656$	$0.98079$	$4.73750$	$[1, -1, 1, -3078536, -2078282293]$	\(y^2+xy+y=x^3-x^2-3078536x-2078282293\)	728.2.0.?	$[ ]$
149058.hi1	149058by1	149058.hi	149058by	$1$	$1$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{9} \cdot 3^{6} \cdot 7^{9} \cdot 13^{7} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$2.047988569$	$1$		$10$	$30481920$	$3.263687$	$-2673465150439/6656$	$0.98079$	$5.71763$	$[1, -1, 1, -150848249, 713152522905]$	\(y^2+xy+y=x^3-x^2-150848249x+713152522905\)	728.2.0.?	$[(7485, 54224), (7095, -2196)]$
154154.m1	154154bw1	154154.m	154154bw	$1$	$1$	\( 2 \cdot 7^{2} \cdot 11^{2} \cdot 13 \)	\( - 2^{9} \cdot 7^{9} \cdot 11^{6} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$6.378353029$	$1$		$2$	$7197120$	$2.630852$	$-2673465150439/6656$	$0.98079$	$5.06583$	$[1, 1, 0, -12000419, 15995873293]$	\(y^2+xy=x^3+x^2-12000419x+15995873293\)	728.2.0.?	$[(11829, 1230772)]$
154154.bd1	154154cm1	154154.bd	154154cm	$1$	$1$	\( 2 \cdot 7^{2} \cdot 11^{2} \cdot 13 \)	\( - 2^{9} \cdot 7^{3} \cdot 11^{6} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$1$	$9$	$3$	$0$	$1028160$	$1.657898$	$-2673465150439/6656$	$0.98079$	$4.08846$	$[1, 0, 1, -244907, -46670186]$	\(y^2+xy+y=x^3-244907x-46670186\)	728.2.0.?	$[ ]$
254800.cw1	254800cw1	254800.cw	254800cw	$1$	$1$	\( 2^{4} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{21} \cdot 5^{6} \cdot 7^{9} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$3.543716491$	$1$		$0$	$18579456$	$2.929771$	$-2673465150439/6656$	$0.98079$	$5.14948$	$[0, -1, 0, -39670808, 96186768112]$	\(y^2=x^3-x^2-39670808x+96186768112\)	728.2.0.?	$[(32833/3, 34300/3)]$
254800.ga1	254800ga1	254800.ga	254800ga	$1$	$1$	\( 2^{4} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{21} \cdot 5^{6} \cdot 7^{3} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$1$	$9$	$3$	$0$	$2654208$	$1.956816$	$-2673465150439/6656$	$0.98079$	$4.21156$	$[0, 1, 0, -809608, -280659212]$	\(y^2=x^3+x^2-809608x-280659212\)	728.2.0.?	$[ ]$
286650.ra1	286650ra1	286650.ra	286650ra	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{9} \cdot 3^{6} \cdot 5^{6} \cdot 7^{9} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$1$	$1$		$0$	$23224320$	$2.785931$	$-2673465150439/6656$	$0.98079$	$4.96386$	$[1, -1, 1, -22314830, 40578792797]$	\(y^2+xy+y=x^3-x^2-22314830x+40578792797\)	728.2.0.?	$[ ]$
286650.rb1	286650rb1	286650.rb	286650rb	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{9} \cdot 3^{6} \cdot 5^{6} \cdot 7^{3} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$3.923025350$	$1$		$2$	$3317760$	$1.812975$	$-2673465150439/6656$	$0.98079$	$4.03473$	$[1, -1, 1, -455405, -118175403]$	\(y^2+xy+y=x^3-x^2-455405x-118175403\)	728.2.0.?	$[(849, 9900)]$
366912.cr1	366912cr1	366912.cr	366912cr	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{27} \cdot 3^{6} \cdot 7^{3} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$1$	$4$	$2$	$0$	$4976640$	$2.047977$	$-2673465150439/6656$	$0.98079$	$4.17708$	$[0, 0, 0, -1165836, -484512784]$	\(y^2=x^3-1165836x-484512784\)	728.2.0.?	$[ ]$
366912.fd1	366912fd1	366912.fd	366912fd	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{27} \cdot 3^{6} \cdot 7^{3} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$2.221722327$	$1$		$2$	$4976640$	$2.047977$	$-2673465150439/6656$	$0.98079$	$4.17708$	$[0, 0, 0, -1165836, 484512784]$	\(y^2=x^3-1165836x+484512784\)	728.2.0.?	$[(-126, 25088)]$
366912.lt1	366912lt1	366912.lt	366912lt	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{27} \cdot 3^{6} \cdot 7^{9} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$3.788693291$	$1$		$2$	$34836480$	$3.020931$	$-2673465150439/6656$	$0.98079$	$5.08831$	$[0, 0, 0, -57125964, 166187884912]$	\(y^2=x^3-57125964x+166187884912\)	728.2.0.?	$[(3726, 71168)]$
366912.nv1	366912nv1	366912.nv	366912nv	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{27} \cdot 3^{6} \cdot 7^{9} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$1$	$25$	$5$	$0$	$34836480$	$3.020931$	$-2673465150439/6656$	$0.98079$	$5.08831$	$[0, 0, 0, -57125964, -166187884912]$	\(y^2=x^3-57125964x-166187884912\)	728.2.0.?	$[ ]$
368186.ca1	368186ca1	368186.ca	368186ca	$1$	$1$	\( 2 \cdot 7^{2} \cdot 13 \cdot 17^{2} \)	\( - 2^{9} \cdot 7^{3} \cdot 13 \cdot 17^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$0.560011353$	$1$		$4$	$3594240$	$1.875557$	$-2673465150439/6656$	$0.98079$	$4.01452$	$[1, 1, 1, -584942, 171950379]$	\(y^2+xy+y=x^3+x^2-584942x+171950379\)	728.2.0.?	$[(409, 951)]$
368186.ck1	368186ck1	368186.ck	368186ck	$1$	$1$	\( 2 \cdot 7^{2} \cdot 13 \cdot 17^{2} \)	\( - 2^{9} \cdot 7^{9} \cdot 13 \cdot 17^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$1$	$4$	$2$	$0$	$25159680$	$2.848511$	$-2673465150439/6656$	$0.98079$	$4.92550$	$[1, 0, 0, -28662159, -59064966535]$	\(y^2+xy=x^3-28662159x-59064966535\)	728.2.0.?	$[ ]$
414050.fk1	414050fk1	414050.fk	414050fk	$1$	$1$	\( 2 \cdot 5^{2} \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{9} \cdot 5^{6} \cdot 7^{3} \cdot 13^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$0.322776828$	$1$		$8$	$18579456$	$2.546143$	$-2673465150439/6656$	$0.98079$	$4.60025$	$[1, 1, 1, -8551488, 9621677281]$	\(y^2+xy+y=x^3+x^2-8551488x+9621677281\)	728.2.0.?	$[(1721, 1505)]$
414050.gw1	414050gw1	414050.gw	414050gw	$1$	$1$	\( 2 \cdot 5^{2} \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{9} \cdot 5^{6} \cdot 7^{9} \cdot 13^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$12.01634456$	$1$		$0$	$130056192$	$3.519100$	$-2673465150439/6656$	$0.98079$	$5.50296$	$[1, 0, 0, -419022913, -3301492376183]$	\(y^2+xy=x^3-419022913x-3301492376183\)	728.2.0.?	$[(469578862/99, 9006446438981/99)]$
459914.k1	459914k1	459914.k	459914k	$1$	$1$	\( 2 \cdot 7^{2} \cdot 13 \cdot 19^{2} \)	\( - 2^{9} \cdot 7^{3} \cdot 13 \cdot 19^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$1$	$1$		$0$	$5225472$	$1.931170$	$-2673465150439/6656$	$0.98079$	$3.99721$	$[1, 1, 0, -730671, -240703259]$	\(y^2+xy=x^3+x^2-730671x-240703259\)	728.2.0.?	$[ ]$
459914.u1	459914u1	459914.u	459914u	$1$	$1$	\( 2 \cdot 7^{2} \cdot 13 \cdot 19^{2} \)	\( - 2^{9} \cdot 7^{9} \cdot 13 \cdot 19^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$728$	$2$	$0$	$10.68711677$	$1$		$0$	$36578304$	$2.904125$	$-2673465150439/6656$	$0.98079$	$4.89265$	$[1, 0, 1, -35802905, 82453809148]$	\(y^2+xy+y=x^3-35802905x+82453809148\)	728.2.0.?	$[(55286548/131, 49082062161/131)]$

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