LMFDB - Elliptic curves over $\Q$ of conductor 5415

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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

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Results (28 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
5415.a1	5415d1	5415.a	5415d	$1$	$1$	$ 3 \cdot 5 \cdot 19^{2} $	$ 3^{2} \cdot 5 \cdot 19^{2} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$10$	$2$	$0$	$0.330320112$	$1$		$18$	$720$	$-0.502553$	$77824/45$	$1.11940$	$1.99502$	$[0, -1, 1, -6, 2]$	$y^2+y=x^3-x^2-6x+2$	10.2.0.a.1	$[(0, 1), (3, 1)]$
5415.b1	5415b1	5415.b	5415b	$1$	$1$	$ 3 \cdot 5 \cdot 19^{2} $	$ 3^{14} \cdot 5^{3} \cdot 19^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$10$	$2$	$0$	$1.252432105$	$1$		$4$	$21168$	$1.369852$	$1914902401024/597871125$	$1.06216$	$4.65962$	$[0, -1, 1, -13116, 396722]$	$y^2+y=x^3-x^2-13116x+396722$	10.2.0.a.1	$[(138, 1093)]$
5415.c1	5415h2	5415.c	5415h	$2$	$2$	$ 3 \cdot 5 \cdot 19^{2} $	$ 3^{2} \cdot 5^{6} \cdot 19^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$2.199062716$	$1$		$4$	$17280$	$1.482559$	$90458382169/2671875$	$1.09032$	$4.98955$	$[1, 0, 0, -33761, 2323110]$	$y^2+xy=x^3-33761x+2323110$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 1140.12.0.?	$[(123, 126)]$
5415.c2	5415h1	5415.c	5415h	$2$	$2$	$ 3 \cdot 5 \cdot 19^{2} $	$ - 3 \cdot 5^{3} \cdot 19^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$4.398125433$	$1$		$3$	$8640$	$1.135986$	$357911/135375$	$0.95197$	$4.29637$	$[1, 0, 0, 534, 121371]$	$y^2+xy=x^3+534x+121371$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(-37, 245)]$
5415.d1	5415f2	5415.d	5415f	$2$	$2$	$ 3 \cdot 5 \cdot 19^{2} $	$ 3^{4} \cdot 5^{2} \cdot 19^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$380$	$12$	$0$	$1$	$1$		$0$	$24320$	$1.556835$	$9393931/2025$	$0.89098$	$4.95009$	$[1, 0, 0, -30151, -1598794]$	$y^2+xy=x^3-30151x-1598794$	2.3.0.a.1, 20.6.0.e.1, 76.6.0.?, 380.12.0.?	$[]$
5415.d2	5415f1	5415.d	5415f	$2$	$2$	$ 3 \cdot 5 \cdot 19^{2} $	$ - 3^{2} \cdot 5 \cdot 19^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$380$	$12$	$0$	$1$	$4$	$2$	$1$	$12160$	$1.210262$	$24389/45$	$0.82301$	$4.34864$	$[1, 0, 0, 4144, -151545]$	$y^2+xy=x^3+4144x-151545$	2.3.0.a.1, 20.6.0.e.1, 76.6.0.?, 190.6.0.?, 380.12.0.?	$[]$
5415.e1	5415l4	5415.e	5415l	$4$	$4$	$ 3 \cdot 5 \cdot 19^{2} $	$ 3^{2} \cdot 5^{3} \cdot 19^{10} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$760$	$48$	$0$	$1$	$1$		$0$	$103680$	$2.226357$	$23977812996389881/146611125$	$1.09826$	$6.44213$	$[1, 0, 0, -2168715, 1229095692]$	$y^2+xy=x^3-2168715x+1229095692$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 10.6.0.a.1, 20.12.0.g.1, $\ldots$	$[]$
5415.e2	5415l3	5415.e	5415l	$4$	$4$	$ 3 \cdot 5 \cdot 19^{2} $	$ 3^{2} \cdot 5^{12} \cdot 19^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$760$	$48$	$0$	$1$	$1$		$0$	$103680$	$2.226357$	$209595169258201/41748046875$	$0.98100$	$5.89081$	$[1, 0, 0, -446745, -93110850]$	$y^2+xy=x^3-446745x-93110850$	2.3.0.a.1, 4.12.0-4.c.1.2, 40.24.0-40.z.1.5, 76.24.0.?, 760.48.0.?	$[]$
5415.e3	5415l2	5415.e	5415l	$4$	$4$	$ 3 \cdot 5 \cdot 19^{2} $	$ 3^{4} \cdot 5^{6} \cdot 19^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$380$	$48$	$0$	$1$	$1$		$2$	$51840$	$1.879786$	$6189976379881/456890625$	$0.95560$	$5.48110$	$[1, 0, 0, -138090, 18437067]$	$y^2+xy=x^3-138090x+18437067$	2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.b.1.3, 76.24.0.?, 380.48.0.?	$[]$
5415.e4	5415l1	5415.e	5415l	$4$	$4$	$ 3 \cdot 5 \cdot 19^{2} $	$ - 3^{8} \cdot 5^{3} \cdot 19^{7} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$760$	$48$	$0$	$1$	$1$		$3$	$25920$	$1.533211$	$1256216039/15582375$	$0.94875$	$4.84304$	$[1, 0, 0, 8115, 1272600]$	$y^2+xy=x^3+8115x+1272600$	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.z.1.13, 152.24.0.?, 190.6.0.?, $\ldots$	$[]$
5415.f1	5415e2	5415.f	5415e	$2$	$3$	$ 3 \cdot 5 \cdot 19^{2} $	$ 3^{2} \cdot 5 \cdot 19^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$570$	$16$	$0$	$0.739243991$	$1$		$2$	$3888$	$0.768552$	$1590409933520896/45$	$1.29281$	$4.75654$	$[0, -1, 1, -17315, 882761]$	$y^2+y=x^3-x^2-17315x+882761$	3.4.0.a.1, 10.2.0.a.1, 30.8.0.a.1, 57.8.0-3.a.1.2, 570.16.0.?	$[(77, 10)]$
5415.f2	5415e1	5415.f	5415e	$2$	$3$	$ 3 \cdot 5 \cdot 19^{2} $	$ 3^{6} \cdot 5^{3} \cdot 19^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$570$	$16$	$0$	$0.246414663$	$1$		$6$	$1296$	$0.219246$	$3058794496/91125$	$0.98270$	$3.22559$	$[0, -1, 1, -215, 1256]$	$y^2+y=x^3-x^2-215x+1256$	3.4.0.a.1, 10.2.0.a.1, 30.8.0.a.1, 57.8.0-3.a.1.1, 570.16.0.?	$[(20, 67)]$
5415.g1	5415j2	5415.g	5415j	$2$	$3$	$ 3 \cdot 5 \cdot 19^{2} $	$ 3^{2} \cdot 5 \cdot 19^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$30$	$16$	$0$	$7.238802236$	$1$		$0$	$73872$	$2.240772$	$1590409933520896/45$	$1.29281$	$6.81154$	$[0, 1, 1, -6250835, -6017354656]$	$y^2+y=x^3+x^2-6250835x-6017354656$	3.8.0-3.a.1.1, 10.2.0.a.1, 30.16.0-30.a.1.1	$[(-282987/14, -1219/14)]$
5415.g2	5415j1	5415.g	5415j	$2$	$3$	$ 3 \cdot 5 \cdot 19^{2} $	$ 3^{6} \cdot 5^{3} \cdot 19^{8} $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$30$	$16$	$0$	$2.412934078$	$1$		$4$	$24624$	$1.691465$	$3058794496/91125$	$0.98270$	$5.28058$	$[0, 1, 1, -77735, -8150461]$	$y^2+y=x^3+x^2-77735x-8150461$	3.8.0-3.a.1.2, 10.2.0.a.1, 30.16.0-30.a.1.4	$[(-149, 382)]$
5415.h1	5415c2	5415.h	5415c	$2$	$2$	$ 3 \cdot 5 \cdot 19^{2} $	$ 3^{10} \cdot 5^{2} \cdot 19^{7} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$2.885550076$	$1$		$10$	$28800$	$1.590862$	$48587168449/28048275$	$1.03180$	$4.91725$	$[1, 1, 0, -27443, 75438]$	$y^2+xy=x^3+x^2-27443x+75438$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 1140.12.0.?	$[(-2, 362), (-369/2, 11199/2)]$
5415.h2	5415c1	5415.h	5415c	$2$	$2$	$ 3 \cdot 5 \cdot 19^{2} $	$ - 3^{5} \cdot 5 \cdot 19^{8} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1140$	$12$	$0$	$11.54220030$	$1$		$5$	$14400$	$1.244289$	$756058031/438615$	$1.00322$	$4.43301$	$[1, 1, 0, 6852, 13707]$	$y^2+xy=x^3+x^2+6852x+13707$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(1442, 54151), (1198/3, 47299/3)]$
5415.i1	5415a2	5415.i	5415a	$2$	$2$	$ 3 \cdot 5 \cdot 19^{2} $	$ 3^{4} \cdot 5^{2} \cdot 19^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$380$	$12$	$0$	$0.877265500$	$1$		$4$	$1280$	$0.084616$	$9393931/2025$	$0.89098$	$2.89509$	$[1, 1, 0, -83, 198]$	$y^2+xy=x^3+x^2-83x+198$	2.3.0.a.1, 20.6.0.e.1, 76.6.0.?, 380.12.0.?	$[(-2, 20)]$
5415.i2	5415a1	5415.i	5415a	$2$	$2$	$ 3 \cdot 5 \cdot 19^{2} $	$ - 3^{2} \cdot 5 \cdot 19^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$380$	$12$	$0$	$1.754531001$	$1$		$3$	$640$	$-0.261958$	$24389/45$	$0.82301$	$2.29365$	$[1, 1, 0, 12, 27]$	$y^2+xy=x^3+x^2+12x+27$	2.3.0.a.1, 20.6.0.e.1, 76.6.0.?, 190.6.0.?, 380.12.0.?	$[(2, 7)]$
5415.j1	5415k7	5415.j	5415k	$8$	$16$	$ 3 \cdot 5 \cdot 19^{2} $	$ 3^{4} \cdot 5 \cdot 19^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.121	2B	$9120$	$768$	$13$	$1$	$1$		$0$	$27648$	$1.763088$	$1114544804970241/405$	$1.07354$	$6.08518$	$[1, 0, 1, -779768, 264965501]$	$y^2+xy+y=x^3-779768x+264965501$	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 10.6.0.a.1, 16.48.0.x.2, $\ldots$	$[]$
5415.j2	5415k5	5415.j	5415k	$8$	$16$	$ 3 \cdot 5 \cdot 19^{2} $	$ 3^{8} \cdot 5^{2} \cdot 19^{6} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.123	2Cs	$4560$	$768$	$13$	$1$	$1$		$2$	$13824$	$1.416515$	$272223782641/164025$	$1.03897$	$5.11770$	$[1, 0, 1, -48743, 4135781]$	$y^2+xy+y=x^3-48743x+4135781$	2.6.0.a.1, 4.12.0.b.1, 8.48.0.k.1, 20.24.0.c.1, 40.96.1.cc.2, $\ldots$	$[]$
5415.j3	5415k8	5415.j	5415k	$8$	$16$	$ 3 \cdot 5 \cdot 19^{2} $	$ - 3^{16} \cdot 5 \cdot 19^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.134	2B	$9120$	$768$	$13$	$1$	$1$		$0$	$27648$	$1.763088$	$-147281603041/215233605$	$1.05949$	$5.19281$	$[1, 0, 1, -39718, 5716961]$	$y^2+xy+y=x^3-39718x+5716961$	2.3.0.a.1, 4.6.0.c.1, 8.24.0.ba.2, 16.48.0.u.2, 20.12.0.h.1, $\ldots$	$[]$
5415.j4	5415k3	5415.j	5415k	$8$	$16$	$ 3 \cdot 5 \cdot 19^{2} $	$ 3 \cdot 5 \cdot 19^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	32.48.0.1	2B	$9120$	$768$	$13$	$1$	$16$	$2$	$0$	$6912$	$1.069942$	$56667352321/15$	$1.03019$	$4.93515$	$[1, 0, 1, -28888, -1892197]$	$y^2+xy+y=x^3-28888x-1892197$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 24.24.0.by.2, $\ldots$	$[]$
5415.j5	5415k4	5415.j	5415k	$8$	$16$	$ 3 \cdot 5 \cdot 19^{2} $	$ 3^{4} \cdot 5^{4} \cdot 19^{6} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.44	2Cs	$4560$	$768$	$13$	$1$	$1$		$2$	$6912$	$1.069942$	$111284641/50625$	$1.02534$	$4.21014$	$[1, 0, 1, -3618, 38431]$	$y^2+xy+y=x^3-3618x+38431$	2.6.0.a.1, 4.24.0.b.1, 8.48.0.b.2, 24.96.1.n.1, 40.96.1.s.1, $\ldots$	$[]$
5415.j6	5415k2	5415.j	5415k	$8$	$16$	$ 3 \cdot 5 \cdot 19^{2} $	$ 3^{2} \cdot 5^{2} \cdot 19^{6} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.3	2Cs	$4560$	$768$	$13$	$1$	$4$	$2$	$2$	$3456$	$0.723369$	$13997521/225$	$0.96230$	$3.96898$	$[1, 0, 1, -1813, -29437]$	$y^2+xy+y=x^3-1813x-29437$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.i.1, 16.48.0.d.2, 24.48.0.bb.2, $\ldots$	$[]$
5415.j7	5415k1	5415.j	5415k	$8$	$16$	$ 3 \cdot 5 \cdot 19^{2} $	$ - 3 \cdot 5 \cdot 19^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	32.48.0.1	2B	$9120$	$768$	$13$	$1$	$4$	$2$	$1$	$1728$	$0.376795$	$-1/15$	$1.19808$	$3.23714$	$[1, 0, 1, -8, -1279]$	$y^2+xy+y=x^3-8x-1279$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 24.24.0.bz.1, $\ldots$	$[]$
5415.j8	5415k6	5415.j	5415k	$8$	$16$	$ 3 \cdot 5 \cdot 19^{2} $	$ - 3^{2} \cdot 5^{8} \cdot 19^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.197	2B	$9120$	$768$	$13$	$1$	$1$		$0$	$13824$	$1.416515$	$4733169839/3515625$	$1.05585$	$4.64637$	$[1, 0, 1, 12627, 291853]$	$y^2+xy+y=x^3+12627x+291853$	2.3.0.a.1, 4.12.0.d.1, 8.48.0.n.2, 24.96.1.cv.2, 76.24.0.?, $\ldots$	$[]$
5415.k1	5415g1	5415.k	5415g	$1$	$1$	$ 3 \cdot 5 \cdot 19^{2} $	$ 3^{2} \cdot 5 \cdot 19^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$10$	$2$	$0$	$1$	$1$		$0$	$13680$	$0.969666$	$77824/45$	$1.11940$	$4.05002$	$[0, 1, 1, -2286, -1969]$	$y^2+y=x^3+x^2-2286x-1969$	10.2.0.a.1	$[]$
5415.l1	5415i1	5415.l	5415i	$1$	$1$	$ 3 \cdot 5 \cdot 19^{2} $	$ 3^{14} \cdot 5^{3} \cdot 19^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$10$	$2$	$0$	$5.318672127$	$1$		$0$	$402192$	$2.842072$	$1914902401024/597871125$	$1.06216$	$6.71462$	$[0, 1, 1, -4734996, -2692708189]$	$y^2+y=x^3+x^2-4734996x-2692708189$	10.2.0.a.1	$[(-6819/2, 165479/2)]$

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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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