LMFDB - Elliptic curves over $\Q$ of conductor 2415

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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 (24 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	Semistable	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
2415.a1	2415a3	2415.a	2415a	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ 3^{3} \cdot 5 \cdot 7 \cdot 23^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.6.0.1	2B	$19320$	$48$	$0$	$1.914810088$	$1$	$4$	$1920$	$0.741029$	$14251520160844849/264449745$	$0.94216$	$4.77513$	$[1, 1, 1, -5051, 136064]$	$y^2+xy+y=x^3+x^2-5051x+136064$	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.1, 60.12.0-4.c.1.1, 184.12.0.?, $\ldots$	$[(41, -17)]$
2415.a2	2415a2	2415.a	2415a	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ 3^{6} \cdot 5^{2} \cdot 7^{2} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.6.0.1	2Cs	$9660$	$48$	$0$	$0.957405044$	$1$	$12$	$960$	$0.394455$	$3832302404449/472410225$	$0.89130$	$3.71971$	$[1, 1, 1, -326, 1874]$	$y^2+xy+y=x^3+x^2-326x+1874$	2.6.0.a.1, 28.12.0-2.a.1.1, 60.12.0-2.a.1.1, 92.12.0.?, 420.24.0.?, $\ldots$	$[(6, 10)]$
2415.a3	2415a1	2415.a	2415a	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ 3^{3} \cdot 5 \cdot 7^{4} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.6.0.1	2B	$19320$	$48$	$0$	$1.914810088$	$1$	$5$	$480$	$0.047881$	$58818484369/7455105$	$0.85439$	$3.18350$	$[1, 1, 1, -81, -282]$	$y^2+xy+y=x^3+x^2-81x-282$	2.3.0.a.1, 4.6.0.c.1, 56.12.0-4.c.1.5, 60.12.0-4.c.1.2, 92.12.0.?, $\ldots$	$[(-6, 8)]$
2415.a4	2415a4	2415.a	2415a	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ - 3^{12} \cdot 5^{4} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.6.0.1	2B	$19320$	$48$	$0$	$1.914810088$	$1$	$4$	$1920$	$0.741029$	$12152722588271/53476250625$	$0.93119$	$4.11020$	$[1, 1, 1, 479, 10568]$	$y^2+xy+y=x^3+x^2+479x+10568$	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.2, 92.12.0.?, 120.12.0.?, $\ldots$	$[(-9, 79)]$
2415.b1	2415f3	2415.b	2415f	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ 3 \cdot 5^{3} \cdot 7^{4} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.6.0.1	2B	$19320$	$48$	$0$	$1$	$1$	$0$	$4224$	$1.085478$	$10765299591712341649/20708625$	$0.97381$	$5.62592$	$[1, 0, 0, -46001, 3793680]$	$y^2+xy=x^3-46001x+3793680$	2.3.0.a.1, 4.6.0.c.1, 56.12.0-4.c.1.5, 60.12.0-4.c.1.1, 92.12.0.?, $\ldots$	$[]$
2415.b2	2415f2	2415.b	2415f	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ 3^{2} \cdot 5^{6} \cdot 7^{2} \cdot 23^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.6.0.1	2Cs	$9660$	$48$	$0$	$1$	$1$	$2$	$2112$	$0.738904$	$2630872462131649/3645140625$	$1.01084$	$4.55823$	$[1, 0, 0, -2876, 59055]$	$y^2+xy=x^3-2876x+59055$	2.6.0.a.1, 28.12.0-2.a.1.1, 60.12.0-2.a.1.1, 92.12.0.?, 420.24.0.?, $\ldots$	$[]$
2415.b3	2415f4	2415.b	2415f	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ - 3^{4} \cdot 5^{12} \cdot 7 \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.6.0.1	2B	$19320$	$48$	$0$	$1$	$1$	$0$	$4224$	$1.085478$	$-982374577874929/3183837890625$	$1.03288$	$4.67403$	$[1, 0, 0, -2071, 93026]$	$y^2+xy=x^3-2071x+93026$	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.1, 92.12.0.?, 120.12.0.?, $\ldots$	$[]$
2415.b4	2415f1	2415.b	2415f	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ 3 \cdot 5^{3} \cdot 7 \cdot 23^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.6.0.1	2B	$19320$	$48$	$0$	$1$	$1$	$1$	$1056$	$0.392331$	$1363569097969/734582625$	$0.91819$	$3.58705$	$[1, 0, 0, -231, 336]$	$y^2+xy=x^3-231x+336$	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.2, 60.12.0-4.c.1.2, 184.12.0.?, $\ldots$	$[]$
2415.c1	2415h3	2415.c	2415h	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ 3^{16} \cdot 5 \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.12.0.6	2B	$6440$	$48$	$0$	$1.075860483$	$1$	$4$	$2048$	$0.883592$	$9614816895690721/34652610405$	$0.94008$	$4.72460$	$[1, 0, 0, -4430, -113505]$	$y^2+xy=x^3-4430x-113505$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 20.12.0-4.c.1.1, 40.24.0-40.ba.1.2, $\ldots$	$[(-38, 1)]$
2415.c2	2415h2	2415.c	2415h	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ 3^{8} \cdot 5^{2} \cdot 7^{2} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.12.0.1	2Cs	$3220$	$48$	$0$	$0.537930241$	$1$	$14$	$1024$	$0.537018$	$7347774183121/4251692025$	$1.12900$	$3.80327$	$[1, 0, 0, -405, 0]$	$y^2+xy=x^3-405x$	2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.a.1.2, 644.24.0.?, 3220.48.0.?	$[(27, 81)]$
2415.c3	2415h1	2415.c	2415h	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ 3^{4} \cdot 5^{4} \cdot 7 \cdot 23 $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.12.0.7	2B	$6440$	$48$	$0$	$1.075860483$	$1$	$9$	$512$	$0.190445$	$2428257525121/8150625$	$0.95548$	$3.66113$	$[1, 0, 0, -280, 1775]$	$y^2+xy=x^3-280x+1775$	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.ba.1.4, 322.6.0.?, 644.24.0.?, $\ldots$	$[(11, 2)]$
2415.c4	2415h4	2415.c	2415h	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ - 3^{4} \cdot 5 \cdot 7^{4} \cdot 23^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.12.0.8	2B	$6440$	$48$	$0$	$1.075860483$	$1$	$4$	$2048$	$0.883592$	$470166844956479/272118787605$	$1.05234$	$4.33716$	$[1, 0, 0, 1620, 405]$	$y^2+xy=x^3+1620x+405$	2.3.0.a.1, 4.12.0-4.c.1.2, 20.24.0-20.h.1.1, 1288.24.0.?, 6440.48.0.?	$[(12, 141)]$
2415.d1	2415i1	2415.d	2415i	$2$	$2$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ 3^{4} \cdot 5^{6} \cdot 7 \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$0.346604813$	$1$	$9$	$768$	$0.318350$	$1345938541921/203765625$	$0.88368$	$3.58537$	$[1, 0, 0, -230, -1173]$	$y^2+xy=x^3-230x-1173$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[(19, 28)]$
2415.d2	2415i2	2415.d	2415i	$2$	$2$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ - 3^{8} \cdot 5^{3} \cdot 7^{2} \cdot 23^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$0.173302406$	$1$	$14$	$1536$	$0.664924$	$6814692748079/21258460125$	$0.92281$	$3.98353$	$[1, 0, 0, 395, -6298]$	$y^2+xy=x^3+395x-6298$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(29, 158)]$
2415.e1	2415b1	2415.e	2415b	$1$	$1$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ - 3^{5} \cdot 5^{2} \cdot 7^{7} \cdot 23^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓				$966$	$2$	$0$	$0.086976853$	$1$	$8$	$14000$	$1.881489$	$-106177523183250079744/32201176731237675$	$1.01923$	$5.97385$	$[0, -1, 1, -98651, 14756141]$	$y^2+y=x^3-x^2-98651x+14756141$	966.2.0.?	$[(493, 9257)]$
2415.f1	2415c1	2415.f	2415c	$1$	$1$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ - 3^{13} \cdot 5^{6} \cdot 7^{5} \cdot 23 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓				$966$	$2$	$0$	$0.545339510$	$1$	$4$	$9360$	$1.749947$	$2744564518708084736/9629735831296875$	$1.02481$	$5.65869$	$[0, 1, 1, 29169, -4304725]$	$y^2+y=x^3+x^2+29169x-4304725$	966.2.0.?	$[(279, 5062)]$
2415.g1	2415d1	2415.g	2415d	$2$	$3$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ - 3^{3} \cdot 5^{2} \cdot 7^{3} \cdot 23 $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.8.0.1	3B.1.1	$966$	$16$	$0$	$0.732417504$	$1$	$8$	$432$	$-0.024906$	$-1073741824/5325075$	$1.05379$	$2.95952$	$[0, 1, 1, -21, 110]$	$y^2+y=x^3+x^2-21x+110$	3.8.0-3.a.1.2, 966.16.0.?	$[(-6, 7)]$
2415.g2	2415d2	2415.g	2415d	$2$	$3$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ - 3 \cdot 5^{6} \cdot 7 \cdot 23^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.8.0.2	3B.1.2	$966$	$16$	$0$	$2.197252513$	$1$	$0$	$1296$	$0.524401$	$742692847616/3992296875$	$0.94885$	$3.78055$	$[0, 1, 1, 189, -2809]$	$y^2+y=x^3+x^2+189x-2809$	3.8.0-3.a.1.1, 966.16.0.?	$[(53/2, 371/2)]$
2415.h1	2415e3	2415.h	2415e	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ 3^{4} \cdot 5 \cdot 7 \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.6.0.1	2B	$19320$	$48$	$0$	$1$	$1$	$0$	$1408$	$0.518334$	$8753151307882969/65205$	$0.93948$	$4.71255$	$[1, 0, 1, -4294, 107927]$	$y^2+xy+y=x^3-4294x+107927$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 28.12.0-4.c.1.1, 168.24.0.?, $\ldots$	$[]$
2415.h2	2415e2	2415.h	2415e	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 23^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.6.0.1	2Cs	$9660$	$48$	$0$	$1$	$1$	$2$	$704$	$0.171761$	$2141202151369/5832225$	$0.88338$	$3.64498$	$[1, 0, 1, -269, 1667]$	$y^2+xy+y=x^3-269x+1667$	2.6.0.a.1, 12.12.0-2.a.1.1, 28.12.0-2.a.1.1, 84.24.0.?, 460.12.0.?, $\ldots$	$[]$
2415.h3	2415e4	2415.h	2415e	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ - 3 \cdot 5^{4} \cdot 7 \cdot 23^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.6.0.1	2B	$19320$	$48$	$0$	$1$	$1$	$0$	$1408$	$0.518334$	$-483551781049/3672913125$	$0.91701$	$3.79390$	$[1, 0, 1, -164, 3011]$	$y^2+xy+y=x^3-164x+3011$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 28.12.0-4.c.1.2, 84.24.0.?, $\ldots$	$[]$
2415.h4	2415e1	2415.h	2415e	$4$	$4$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ 3 \cdot 5 \cdot 7^{4} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.6.0.1	2B	$19320$	$48$	$0$	$1$	$1$	$1$	$352$	$-0.174813$	$1439069689/828345$	$0.89965$	$2.70716$	$[1, 0, 1, -24, 1]$	$y^2+xy+y=x^3-24x+1$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 56.12.0-4.c.1.5, 168.24.0.?, $\ldots$	$[]$
2415.i1	2415g1	2415.i	2415g	$2$	$2$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ 3^{2} \cdot 5^{6} \cdot 7^{3} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1.919504905$	$1$	$3$	$1152$	$0.599636$	$328523283207001/1109390625$	$0.91995$	$4.29114$	$[1, 0, 1, -1438, -21037]$	$y^2+xy+y=x^3-1438x-21037$	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[(79, 560)]$
2415.i2	2415g2	2415.i	2415g	$2$	$2$	$ 3 \cdot 5 \cdot 7 \cdot 23 $	$ - 3^{4} \cdot 5^{3} \cdot 7^{6} \cdot 23^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$3220$	$12$	$0$	$0.959752452$	$1$	$4$	$2304$	$0.946210$	$-59323563117001/630142750125$	$0.95286$	$4.45179$	$[1, 0, 1, -813, -39287]$	$y^2+xy+y=x^3-813x-39287$	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(59, 315)]$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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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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