Elliptic curve search results

Results (26 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
2730.d4	2730f1	2730.d	2730f	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{4} \cdot 3 \cdot 5^{4} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$1560$	$48$	$0$	$0.580593878$	$1$		$7$	$768$	$0.076193$	$30080231/19110000$	$0.94018$	$3.06109$	$[1, 1, 0, 7, 213]$	\(y^2+xy=x^3+x^2+7x+213\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 40.12.0-4.c.1.4, 52.12.0-4.c.1.2, $\ldots$	$[(-2, 15)]$
8190.bz4	8190by1	8190.bz	8190by	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{4} \cdot 3^{7} \cdot 5^{4} \cdot 7^{2} \cdot 13 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1560$	$48$	$0$	$1$	$1$		$3$	$6144$	$0.625499$	$30080231/19110000$	$0.94018$	$3.41941$	$[1, -1, 1, 58, -5691]$	\(y^2+xy+y=x^3-x^2+58x-5691\)	2.3.0.a.1, 4.12.0-4.c.1.1, 78.6.0.?, 120.24.0.?, 156.24.0.?, $\ldots$	$[]$
13650.cn4	13650cm1	13650.cn	13650cm	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{4} \cdot 3 \cdot 5^{10} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$1560$	$48$	$0$	$1.339751705$	$1$		$3$	$18432$	$0.880912$	$30080231/19110000$	$0.94018$	$3.55786$	$[1, 0, 0, 162, 26292]$	\(y^2+xy=x^3+162x+26292\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 60.12.0-4.c.1.2, 78.6.0.?, $\ldots$	$[(62, 494)]$
19110.bd4	19110bg1	19110.bd	19110bg	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{4} \cdot 3 \cdot 5^{4} \cdot 7^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$10920$	$48$	$0$	$1$	$1$		$1$	$36864$	$1.049149$	$30080231/19110000$	$0.94018$	$3.64122$	$[1, 0, 1, 317, -72082]$	\(y^2+xy+y=x^3+317x-72082\)	2.3.0.a.1, 4.6.0.c.1, 78.6.0.?, 84.12.0.?, 120.12.0.?, $\ldots$	$[]$
21840.bm4	21840bu1	21840.bm	21840bu	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{16} \cdot 3 \cdot 5^{4} \cdot 7^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1$	$1$		$1$	$18432$	$0.769341$	$30080231/19110000$	$0.94018$	$3.25650$	$[0, 1, 0, 104, -13420]$	\(y^2=x^3+x^2+104x-13420\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 40.12.0-4.c.1.4, 52.12.0-4.c.1.1, $\ldots$	$[]$
35490.cq4	35490cn1	35490.cq	35490cn	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13^{2} \)	\( - 2^{4} \cdot 3 \cdot 5^{4} \cdot 7^{2} \cdot 13^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1560$	$48$	$0$	$2.153738364$	$1$		$7$	$129024$	$1.358667$	$30080231/19110000$	$0.94018$	$3.78059$	$[1, 1, 1, 1095, 462327]$	\(y^2+xy+y=x^3+x^2+1095x+462327\)	2.3.0.a.1, 4.12.0-4.c.1.1, 78.6.0.?, 120.24.0.?, 156.24.0.?, $\ldots$	$[(-63, 416)]$
40950.bg4	40950x1	40950.bg	40950x	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{4} \cdot 3^{7} \cdot 5^{10} \cdot 7^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1$	$1$		$1$	$147456$	$1.430218$	$30080231/19110000$	$0.94018$	$3.81049$	$[1, -1, 0, 1458, -709884]$	\(y^2+xy=x^3-x^2+1458x-709884\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 24.12.0-4.c.1.6, 78.6.0.?, $\ldots$	$[]$
57330.ec4	57330ea1	57330.ec	57330ea	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{4} \cdot 3^{7} \cdot 5^{4} \cdot 7^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$10920$	$48$	$0$	$1$	$1$		$1$	$294912$	$1.598454$	$30080231/19110000$	$0.94018$	$3.87773$	$[1, -1, 1, 2857, 1946207]$	\(y^2+xy+y=x^3-x^2+2857x+1946207\)	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.2, 78.6.0.?, 120.12.0.?, $\ldots$	$[]$
65520.ce4	65520dz1	65520.ce	65520dz	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{16} \cdot 3^{7} \cdot 5^{4} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1560$	$48$	$0$	$0.785752037$	$1$		$9$	$147456$	$1.318645$	$30080231/19110000$	$0.94018$	$3.52828$	$[0, 0, 0, 933, 363274]$	\(y^2=x^3+933x+363274\)	2.3.0.a.1, 4.12.0-4.c.1.2, 78.6.0.?, 120.24.0.?, 156.24.0.?, $\ldots$	$[(23, 630)]$
87360.bw4	87360fa1	87360.bw	87360fa	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{22} \cdot 3 \cdot 5^{4} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1.618419543$	$1$		$5$	$147456$	$1.115913$	$30080231/19110000$	$0.94018$	$3.22525$	$[0, -1, 0, 415, -107775]$	\(y^2=x^3-x^2+415x-107775\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 40.12.0-4.c.1.5, 78.6.0.?, $\ldots$	$[(55, 280)]$
87360.he4	87360dn1	87360.he	87360dn	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{22} \cdot 3 \cdot 5^{4} \cdot 7^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1$	$1$		$1$	$147456$	$1.115913$	$30080231/19110000$	$0.94018$	$3.22525$	$[0, 1, 0, 415, 107775]$	\(y^2=x^3+x^2+415x+107775\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 40.12.0-4.c.1.5, 78.6.0.?, $\ldots$	$[]$
95550.gh4	95550hn1	95550.gh	95550hn	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{4} \cdot 3 \cdot 5^{10} \cdot 7^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$10920$	$48$	$0$	$1$	$1$		$1$	$884736$	$1.853867$	$30080231/19110000$	$0.94018$	$3.97227$	$[1, 1, 1, 7937, -9010219]$	\(y^2+xy+y=x^3+x^2+7937x-9010219\)	2.3.0.a.1, 4.6.0.c.1, 56.12.0-4.c.1.4, 78.6.0.?, 120.12.0.?, $\ldots$	$[]$
106470.d4	106470bi1	106470.d	106470bi	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13^{2} \)	\( - 2^{4} \cdot 3^{7} \cdot 5^{4} \cdot 7^{2} \cdot 13^{7} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1.486552992$	$1$		$23$	$1032192$	$1.907974$	$30080231/19110000$	$0.94018$	$3.99123$	$[1, -1, 0, 9855, -12472979]$	\(y^2+xy=x^3-x^2+9855x-12472979\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 40.12.0-4.c.1.6, 52.12.0-4.c.1.2, $\ldots$	$[(335, 5156), (842, 23915)]$
109200.dj4	109200dr1	109200.dj	109200dr	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{16} \cdot 3 \cdot 5^{10} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$1560$	$48$	$0$	$3.481077120$	$1$		$5$	$442368$	$1.574059$	$30080231/19110000$	$0.94018$	$3.63711$	$[0, -1, 0, 2592, -1682688]$	\(y^2=x^3-x^2+2592x-1682688\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 60.12.0-4.c.1.1, 78.6.0.?, $\ldots$	$[(176, 2048)]$
152880.ef4	152880ds1	152880.ef	152880ds	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{16} \cdot 3 \cdot 5^{4} \cdot 7^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$10920$	$48$	$0$	$1$	$1$		$1$	$884736$	$1.742294$	$30080231/19110000$	$0.94018$	$3.70371$	$[0, -1, 0, 5080, 4613232]$	\(y^2=x^3-x^2+5080x+4613232\)	2.3.0.a.1, 4.6.0.c.1, 78.6.0.?, 84.12.0.?, 120.12.0.?, $\ldots$	$[]$
177450.ez4	177450gz1	177450.ez	177450gz	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13^{2} \)	\( - 2^{4} \cdot 3 \cdot 5^{10} \cdot 7^{2} \cdot 13^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1560$	$48$	$0$	$4.463319624$	$1$		$3$	$3096576$	$2.163387$	$30080231/19110000$	$0.94018$	$4.07612$	$[1, 0, 1, 27374, 57736148]$	\(y^2+xy+y=x^3+27374x+57736148\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 24.12.0-4.c.1.4, 78.6.0.?, $\ldots$	$[(5721, 430117)]$
248430.iy4	248430iy1	248430.iy	248430iy	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{4} \cdot 3 \cdot 5^{4} \cdot 7^{8} \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$10920$	$48$	$0$	$1$	$9$	$3$	$1$	$6193152$	$2.331623$	$30080231/19110000$	$0.94018$	$4.12823$	$[1, 0, 0, 53654, -158417260]$	\(y^2+xy=x^3+53654x-158417260\)	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.2, 78.6.0.?, 120.12.0.?, $\ldots$	$[]$
262080.cs4	262080cs1	262080.cs	262080cs	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{22} \cdot 3^{7} \cdot 5^{4} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$1560$	$48$	$0$	$1.476690620$	$1$		$5$	$1179648$	$1.665220$	$30080231/19110000$	$0.94018$	$3.46958$	$[0, 0, 0, 3732, 2906192]$	\(y^2=x^3+3732x+2906192\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 78.6.0.?, 120.24.0.?, $\ldots$	$[(-59, 1575)]$
262080.dy4	262080dy1	262080.dy	262080dy	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{22} \cdot 3^{7} \cdot 5^{4} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$1560$	$48$	$0$	$3.383617947$	$1$		$3$	$1179648$	$1.665220$	$30080231/19110000$	$0.94018$	$3.46958$	$[0, 0, 0, 3732, -2906192]$	\(y^2=x^3+3732x-2906192\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 78.6.0.?, 120.24.0.?, $\ldots$	$[(1158, 39424)]$
283920.hr4	283920hr1	283920.hr	283920hr	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 13^{2} \)	\( - 2^{16} \cdot 3 \cdot 5^{4} \cdot 7^{2} \cdot 13^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1560$	$48$	$0$	$2.308106382$	$1$		$3$	$3096576$	$2.051815$	$30080231/19110000$	$0.94018$	$3.81692$	$[0, 1, 0, 17520, -29553900]$	\(y^2=x^3+x^2+17520x-29553900\)	2.3.0.a.1, 4.12.0-4.c.1.2, 78.6.0.?, 120.24.0.?, 156.24.0.?, $\ldots$	$[(1460, 55770)]$
286650.ho4	286650ho1	286650.ho	286650ho	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{4} \cdot 3^{7} \cdot 5^{10} \cdot 7^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$10920$	$48$	$0$	$1$	$1$		$1$	$7077888$	$2.403172$	$30080231/19110000$	$0.94018$	$4.14955$	$[1, -1, 0, 71433, 243347341]$	\(y^2+xy=x^3-x^2+71433x+243347341\)	2.3.0.a.1, 4.6.0.c.1, 78.6.0.?, 120.12.0.?, 140.12.0.?, $\ldots$	$[]$
327600.hn4	327600hn1	327600.hn	327600hn	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{16} \cdot 3^{7} \cdot 5^{10} \cdot 7^{2} \cdot 13 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1560$	$48$	$0$	$2.146615062$	$1$		$21$	$3538944$	$2.123363$	$30080231/19110000$	$0.94018$	$3.84152$	$[0, 0, 0, 23325, 45409250]$	\(y^2=x^3+23325x+45409250\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 24.12.0-4.c.1.6, 78.6.0.?, $\ldots$	$[(145, 7200), (-305, 3150)]$
330330.du4	330330du1	330330.du	330330du	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \cdot 13 \)	\( - 2^{4} \cdot 3 \cdot 5^{4} \cdot 7^{2} \cdot 11^{6} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$17160$	$48$	$0$	$1.953443276$	$1$		$5$	$983040$	$1.275141$	$30080231/19110000$	$0.94018$	$3.03804$	$[1, 1, 1, 784, -279487]$	\(y^2+xy+y=x^3+x^2+784x-279487\)	2.3.0.a.1, 4.6.0.c.1, 78.6.0.?, 120.12.0.?, 132.12.0.?, $\ldots$	$[(83, 563)]$
436800.ew4	436800ew1	436800.ew	436800ew	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{22} \cdot 3 \cdot 5^{10} \cdot 7^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$1560$	$48$	$0$	$1$	$1$		$1$	$3538944$	$1.920633$	$30080231/19110000$	$0.94018$	$3.56911$	$[0, -1, 0, 10367, 13451137]$	\(y^2=x^3-x^2+10367x+13451137\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 78.6.0.?, 120.24.0.?, $\ldots$	$[]$
436800.qh4	436800qh1	436800.qh	436800qh	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{22} \cdot 3 \cdot 5^{10} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$1560$	$48$	$0$	$9.310183657$	$1$		$1$	$3538944$	$1.920633$	$30080231/19110000$	$0.94018$	$3.56911$	$[0, 1, 0, 10367, -13451137]$	\(y^2=x^3+x^2+10367x-13451137\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 78.6.0.?, 120.24.0.?, $\ldots$	$[(412279/19, 264692736/19)]$
458640.r4	458640r1	458640.r	458640r	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{16} \cdot 3^{7} \cdot 5^{4} \cdot 7^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$10920$	$48$	$0$	$1$	$1$		$1$	$7077888$	$2.291603$	$30080231/19110000$	$0.94018$	$3.89723$	$[0, 0, 0, 45717, -124602982]$	\(y^2=x^3+45717x-124602982\)	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.1, 78.6.0.?, 120.12.0.?, $\ldots$	$[]$