LMFDB - Elliptic curve search results

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Conductor	Discriminant	j-invariant	Rank

Bad$\ p$	Curves per isogeny class	Complex multiplication	Torsion

Isogeny class degree	Cyclic isogeny degree	Isogeny class size	Integral points

Analytic order of Ш	$p\ $div$\ $\|Ш\|	Regulator	Reduction	Faltings height

Galois image	Adelic level	Adelic index	Adelic genus

Nonmax$\ \ell$	$abc$ quality	Szpiro ratio	Manin constant

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Results (23 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	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
4488.e1	4488h2	4488.e	4488h	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{11} \cdot 3^{6} \cdot 11^{6} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$11520$	$1.336094$	$110725946217794/21954955473$	$0.95362$	$4.75228$	$[0, 1, 0, -12704, -451104]$	$y^2=x^3+x^2-12704x-451104$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[ ]$
8976.f1	8976g2	8976.f	8976g	$2$	$2$	$ 2^{4} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{11} \cdot 3^{6} \cdot 11^{6} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$0.903521997$	$1$		$5$	$23040$	$1.336094$	$110725946217794/21954955473$	$0.95362$	$4.39039$	$[0, -1, 0, -12704, 451104]$	$y^2=x^3-x^2-12704x+451104$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[(-6, 726)]$
13464.o1	13464i2	13464.o	13464i	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 11 \cdot 17 $	$ 2^{11} \cdot 3^{12} \cdot 11^{6} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$2.436660061$	$1$		$3$	$92160$	$1.885401$	$110725946217794/21954955473$	$0.95362$	$4.89645$	$[0, 0, 0, -114339, 12065470]$	$y^2=x^3-114339x+12065470$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[(102, 1210)]$
26928.br1	26928i2	26928.br	26928i	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 11 \cdot 17 $	$ 2^{11} \cdot 3^{12} \cdot 11^{6} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$184320$	$1.885401$	$110725946217794/21954955473$	$0.95362$	$4.56374$	$[0, 0, 0, -114339, -12065470]$	$y^2=x^3-114339x-12065470$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[ ]$
35904.bd1	35904u2	35904.bd	35904u	$2$	$2$	$ 2^{6} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{17} \cdot 3^{6} \cdot 11^{6} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1.329104857$	$1$		$7$	$184320$	$1.682667$	$110725946217794/21954955473$	$0.95362$	$4.20662$	$[0, -1, 0, -50817, -3558015]$	$y^2=x^3-x^2-50817x-3558015$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[(497, 9680)]$
35904.db1	35904cn2	35904.db	35904cn	$2$	$2$	$ 2^{6} \cdot 3 \cdot 11 \cdot 17 $	$ 2^{17} \cdot 3^{6} \cdot 11^{6} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$184320$	$1.682667$	$110725946217794/21954955473$	$0.95362$	$4.20662$	$[0, 1, 0, -50817, 3558015]$	$y^2=x^3+x^2-50817x+3558015$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[ ]$
49368.x1	49368p2	49368.x	49368p	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11^{2} \cdot 17 $	$ 2^{11} \cdot 3^{6} \cdot 11^{12} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$6.168736182$	$1$		$3$	$1382400$	$2.535042$	$110725946217794/21954955473$	$0.95362$	$5.02913$	$[0, 1, 0, -1537224, 594270576]$	$y^2=x^3+x^2-1537224x+594270576$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[(-1365, 12294)]$
76296.n1	76296q2	76296.n	76296q	$2$	$2$	$ 2^{3} \cdot 3 \cdot 11 \cdot 17^{2} $	$ 2^{11} \cdot 3^{6} \cdot 11^{6} \cdot 17^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$5.511066454$	$1$		$3$	$3317760$	$2.752701$	$110725946217794/21954955473$	$0.95362$	$5.06672$	$[0, -1, 0, -3671552, -2194244820]$	$y^2=x^3-x^2-3671552x-2194244820$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[(207865, 94765990)]$
98736.j1	98736k2	98736.j	98736k	$2$	$2$	$ 2^{4} \cdot 3 \cdot 11^{2} \cdot 17 $	$ 2^{11} \cdot 3^{6} \cdot 11^{12} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$2764800$	$2.535042$	$110725946217794/21954955473$	$0.95362$	$4.72601$	$[0, -1, 0, -1537224, -594270576]$	$y^2=x^3-x^2-1537224x-594270576$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[ ]$
107712.q1	107712bb2	107712.q	107712bb	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 11 \cdot 17 $	$ 2^{17} \cdot 3^{12} \cdot 11^{6} \cdot 17 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$10.20669029$	$1$		$11$	$1474560$	$2.231976$	$110725946217794/21954955473$	$0.95362$	$4.37666$	$[0, 0, 0, -457356, 96523760]$	$y^2=x^3-457356x+96523760$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[(532, 1944), (-440, 14580)]$
107712.bp1	107712eq2	107712.bp	107712eq	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 11 \cdot 17 $	$ 2^{17} \cdot 3^{12} \cdot 11^{6} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$1474560$	$2.231976$	$110725946217794/21954955473$	$0.95362$	$4.37666$	$[0, 0, 0, -457356, -96523760]$	$y^2=x^3-457356x-96523760$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[ ]$
112200.y1	112200b2	112200.y	112200b	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 17 $	$ 2^{11} \cdot 3^{6} \cdot 5^{6} \cdot 11^{6} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$8.816314200$	$1$		$1$	$1474560$	$2.140812$	$110725946217794/21954955473$	$0.95362$	$4.26721$	$[0, -1, 0, -317608, -55752788]$	$y^2=x^3-x^2-317608x-55752788$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[(-135083/19, 22288500/19)]$
148104.cg1	148104w2	148104.cg	148104w	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 11^{2} \cdot 17 $	$ 2^{11} \cdot 3^{12} \cdot 11^{12} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$32.85050586$	$1$		$1$	$11059200$	$3.084347$	$110725946217794/21954955473$	$0.95362$	$5.11872$	$[0, 0, 0, -13835019, -16059140570]$	$y^2=x^3-13835019x-16059140570$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[(31566625512131105/248498, 5608293248590960133721735/248498)]$
152592.cv1	152592cw2	152592.cv	152592cw	$2$	$2$	$ 2^{4} \cdot 3 \cdot 11 \cdot 17^{2} $	$ 2^{11} \cdot 3^{6} \cdot 11^{6} \cdot 17^{7} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$4.508514537$	$1$		$9$	$6635520$	$2.752701$	$110725946217794/21954955473$	$0.95362$	$4.77247$	$[0, 1, 0, -3671552, 2194244820]$	$y^2=x^3+x^2-3671552x+2194244820$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[(1660, 26010), (436, 26010)]$
219912.w1	219912w2	219912.w	219912w	$2$	$2$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 11 \cdot 17 $	$ 2^{11} \cdot 3^{6} \cdot 7^{6} \cdot 11^{6} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$14.96255560$	$1$		$1$	$4147200$	$2.309048$	$110725946217794/21954955473$	$0.95362$	$4.19789$	$[0, -1, 0, -622512, 153483660]$	$y^2=x^3-x^2-622512x+153483660$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[(-798155/57, 3162004840/57)]$
224400.fp1	224400gu2	224400.fp	224400gu	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 11 \cdot 17 $	$ 2^{11} \cdot 3^{6} \cdot 5^{6} \cdot 11^{6} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$0.224584773$	$1$		$13$	$2949120$	$2.140812$	$110725946217794/21954955473$	$0.95362$	$4.02716$	$[0, 1, 0, -317608, 55752788]$	$y^2=x^3+x^2-317608x+55752788$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[(-142, 9900)]$
228888.q1	228888bo2	228888.q	228888bo	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 11 \cdot 17^{2} $	$ 2^{11} \cdot 3^{12} \cdot 11^{6} \cdot 17^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$4$	$2$	$1$	$26542080$	$3.302006$	$110725946217794/21954955473$	$0.95362$	$5.14980$	$[0, 0, 0, -33043971, 59277654110]$	$y^2=x^3-33043971x+59277654110$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[ ]$
296208.eo1	296208eo2	296208.eo	296208eo	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 11^{2} \cdot 17 $	$ 2^{11} \cdot 3^{12} \cdot 11^{12} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$4$	$2$	$1$	$22118400$	$3.084347$	$110725946217794/21954955473$	$0.95362$	$4.83710$	$[0, 0, 0, -13835019, 16059140570]$	$y^2=x^3-13835019x+16059140570$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[ ]$
336600.dl1	336600dl2	336600.dl	336600dl	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 17 $	$ 2^{11} \cdot 3^{12} \cdot 5^{6} \cdot 11^{6} \cdot 17 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$2.669552678$	$1$		$3$	$11796480$	$2.690121$	$110725946217794/21954955473$	$0.95362$	$4.41679$	$[0, 0, 0, -2858475, 1508183750]$	$y^2=x^3-2858475x+1508183750$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[(1390, 14850)]$
394944.dy1	394944dy2	394944.dy	394944dy	$2$	$2$	$ 2^{6} \cdot 3 \cdot 11^{2} \cdot 17 $	$ 2^{17} \cdot 3^{6} \cdot 11^{12} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$4$	$2$	$1$	$22118400$	$2.881615$	$110725946217794/21954955473$	$0.95362$	$4.54033$	$[0, -1, 0, -6148897, 4760313505]$	$y^2=x^3-x^2-6148897x+4760313505$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[ ]$
394944.ie1	394944ie2	394944.ie	394944ie	$2$	$2$	$ 2^{6} \cdot 3 \cdot 11^{2} \cdot 17 $	$ 2^{17} \cdot 3^{6} \cdot 11^{12} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$22118400$	$2.881615$	$110725946217794/21954955473$	$0.95362$	$4.54033$	$[0, 1, 0, -6148897, -4760313505]$	$y^2=x^3+x^2-6148897x-4760313505$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[ ]$
439824.ga1	439824ga2	439824.ga	439824ga	$2$	$2$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 11 \cdot 17 $	$ 2^{11} \cdot 3^{6} \cdot 7^{6} \cdot 11^{6} \cdot 17 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1$	$1$		$1$	$8294400$	$2.309048$	$110725946217794/21954955473$	$0.95362$	$3.97396$	$[0, 1, 0, -622512, -153483660]$	$y^2=x^3+x^2-622512x-153483660$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[ ]$
457776.bb1	457776bb2	457776.bb	457776bb	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 11 \cdot 17^{2} $	$ 2^{11} \cdot 3^{12} \cdot 11^{6} \cdot 17^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4488$	$12$	$0$	$1.324682453$	$1$		$9$	$53084160$	$3.302006$	$110725946217794/21954955473$	$0.95362$	$4.87594$	$[0, 0, 0, -33043971, -59277654110]$	$y^2=x^3-33043971x-59277654110$	2.3.0.a.1, 132.6.0.?, 136.6.0.?, 4488.12.0.?	$[(-3307, 117612)]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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