LMFDB - Elliptic curves over $\Q$ of conductor 12615

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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 (21 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
12615.a1	12615g1	12615.a	12615g	$1$	$1$	$ 3 \cdot 5 \cdot 29^{2} $	$ - 3 \cdot 5^{2} \cdot 29^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$6$	$2$	$0$	$1$	$1$		$0$	$52200$	$1.293676$	$118784/75$	$0.81570$	$4.09032$	$[0, 1, 1, 8130, -82426]$	$y^2+y=x^3+x^2+8130x-82426$	6.2.0.a.1	$[]$
12615.b1	12615c3	12615.b	12615c	$4$	$4$	$ 3 \cdot 5 \cdot 29^{2} $	$ 3^{2} \cdot 5 \cdot 29^{10} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$1160$	$48$	$0$	$1$	$4$	$2$	$0$	$161280$	$1.921299$	$1888690601881/31827645$	$0.93261$	$5.13317$	$[1, 1, 1, -216575, -38314888]$	$y^2+xy+y=x^3+x^2-216575x-38314888$	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, $\ldots$	$[]$
12615.b2	12615c2	12615.b	12615c	$4$	$4$	$ 3 \cdot 5 \cdot 29^{2} $	$ 3^{4} \cdot 5^{2} \cdot 29^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$580$	$48$	$0$	$1$	$4$	$2$	$2$	$80640$	$1.574724$	$3803721481/1703025$	$0.90376$	$4.47576$	$[1, 1, 1, -27350, 816842]$	$y^2+xy+y=x^3+x^2-27350x+816842$	2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.b.1.3, 116.24.0.?, 580.48.0.?	$[]$
12615.b3	12615c1	12615.b	12615c	$4$	$4$	$ 3 \cdot 5 \cdot 29^{2} $	$ 3^{2} \cdot 5 \cdot 29^{7} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$1160$	$48$	$0$	$1$	$4$	$2$	$3$	$40320$	$1.228151$	$2305199161/1305$	$0.87163$	$4.42272$	$[1, 1, 1, -23145, 1344990]$	$y^2+xy+y=x^3+x^2-23145x+1344990$	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.z.1.13, 232.24.0.?, 290.6.0.?, $\ldots$	$[]$
12615.b4	12615c4	12615.b	12615c	$4$	$4$	$ 3 \cdot 5 \cdot 29^{2} $	$ - 3^{8} \cdot 5^{4} \cdot 29^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$1160$	$48$	$0$	$1$	$1$		$0$	$161280$	$1.921299$	$157376536199/118918125$	$0.94171$	$4.87000$	$[1, 1, 1, 94595, 6231200]$	$y^2+xy+y=x^3+x^2+94595x+6231200$	2.3.0.a.1, 4.12.0-4.c.1.2, 40.24.0-40.z.1.5, 116.24.0.?, 1160.48.0.?	$[]$
12615.c1	12615a1	12615.c	12615a	$2$	$3$	$ 3 \cdot 5 \cdot 29^{2} $	$ - 3^{3} \cdot 5 \cdot 29^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$870$	$16$	$0$	$0.899542109$	$1$		$4$	$16800$	$1.158476$	$-160989184/3915$	$0.86981$	$4.14522$	$[0, -1, 1, -9531, 368786]$	$y^2+y=x^3-x^2-9531x+368786$	3.4.0.a.1, 30.8.0-3.a.1.2, 87.8.0.?, 870.16.0.?	$[(-106, 420)]$
12615.c2	12615a2	12615.c	12615a	$2$	$3$	$ 3 \cdot 5 \cdot 29^{2} $	$ - 3 \cdot 5^{3} \cdot 29^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$870$	$16$	$0$	$2.698626327$	$1$		$0$	$50400$	$1.707781$	$12747309056/9145875$	$0.97110$	$4.60383$	$[0, -1, 1, 40929, 1547027]$	$y^2+y=x^3-x^2+40929x+1547027$	3.4.0.a.1, 30.8.0-3.a.1.1, 87.8.0.?, 870.16.0.?	$[(-649/5, 85299/5)]$
12615.d1	12615e1	12615.d	12615e	$1$	$1$	$ 3 \cdot 5 \cdot 29^{2} $	$ - 3^{5} \cdot 5^{7} \cdot 29^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$870$	$2$	$0$	$1$	$1$		$0$	$117600$	$2.041943$	$53838872576/550546875$	$1.03969$	$5.05438$	$[0, 1, 1, 66159, -26720260]$	$y^2+y=x^3+x^2+66159x-26720260$	870.2.0.?	$[]$
12615.e1	12615b3	12615.e	12615b	$4$	$4$	$ 3 \cdot 5 \cdot 29^{2} $	$ 3^{2} \cdot 5 \cdot 29^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.10	2B	$6960$	$192$	$3$	$1$	$4$	$2$	$0$	$268800$	$2.227768$	$37286818682653441/1305$	$1.23338$	$6.18060$	$[1, 1, 0, -5853377, -5453209656]$	$y^2+xy=x^3+x^2-5853377x-5453209656$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 20.12.0-4.c.1.1, 40.24.0-8.o.1.6, $\ldots$	$[]$
12615.e2	12615b2	12615.e	12615b	$4$	$4$	$ 3 \cdot 5 \cdot 29^{2} $	$ 3^{4} \cdot 5^{2} \cdot 29^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.4	2Cs	$3480$	$192$	$3$	$1$	$4$	$2$	$2$	$134400$	$1.881193$	$9104453457841/1703025$	$1.03605$	$5.29974$	$[1, 1, 0, -365852, -85312701]$	$y^2+xy=x^3+x^2-365852x-85312701$	2.6.0.a.1, 4.12.0.a.1, 20.24.0-4.a.1.2, 24.24.0.j.1, 116.24.0.?, $\ldots$	$[]$
12615.e3	12615b4	12615.e	12615b	$4$	$4$	$ 3 \cdot 5 \cdot 29^{2} $	$ - 3^{2} \cdot 5^{4} \cdot 29^{10} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.9	2B	$6960$	$192$	$3$	$1$	$1$		$0$	$268800$	$2.227768$	$-6561258219361/3978455625$	$0.95298$	$5.34096$	$[1, 1, 0, -328007, -103606974]$	$y^2+xy=x^3+x^2-328007x-103606974$	2.3.0.a.1, 4.12.0.d.1, 24.24.0.z.1, 40.24.0-4.d.1.3, 116.24.0.?, $\ldots$	$[]$
12615.e4	12615b1	12615.e	12615b	$4$	$4$	$ 3 \cdot 5 \cdot 29^{2} $	$ 3^{8} \cdot 5 \cdot 29^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.10	2B	$6960$	$192$	$3$	$1$	$1$		$1$	$67200$	$1.534620$	$2992209121/951345$	$0.88867$	$4.45035$	$[1, 1, 0, -25247, -1047024]$	$y^2+xy=x^3+x^2-25247x-1047024$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 20.12.0-4.c.1.2, 40.24.0-8.o.1.8, $\ldots$	$[]$
12615.f1	12615f7	12615.f	12615f	$8$	$16$	$ 3 \cdot 5 \cdot 29^{2} $	$ 3^{4} \cdot 5 \cdot 29^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.121	2B	$13920$	$768$	$13$	$13.91329384$	$1$		$0$	$100352$	$1.974518$	$1114544804970241/405$	$1.07354$	$5.80886$	$[1, 0, 1, -1816578, -942537797]$	$y^2+xy+y=x^3-1816578x-942537797$	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, $\ldots$	$[(29538433/56, 157970670523/56)]$
12615.f2	12615f5	12615.f	12615f	$8$	$16$	$ 3 \cdot 5 \cdot 29^{2} $	$ 3^{8} \cdot 5^{2} \cdot 29^{6} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.123	2Cs	$6960$	$768$	$13$	$6.956646921$	$1$		$2$	$50176$	$1.627943$	$272223782641/164025$	$1.03897$	$4.92803$	$[1, 0, 1, -113553, -14729777]$	$y^2+xy+y=x^3-113553x-14729777$	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, $\ldots$	$[(-7121/6, 30355/6)]$
12615.f3	12615f8	12615.f	12615f	$8$	$16$	$ 3 \cdot 5 \cdot 29^{2} $	$ - 3^{16} \cdot 5 \cdot 29^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.134	2B	$13920$	$768$	$13$	$3.478323460$	$1$		$2$	$100352$	$1.974518$	$-147281603041/215233605$	$1.05949$	$4.99641$	$[1, 0, 1, -92528, -20347657]$	$y^2+xy+y=x^3-92528x-20347657$	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, $\ldots$	$[(737, 17292)]$
12615.f4	12615f4	12615.f	12615f	$8$	$16$	$ 3 \cdot 5 \cdot 29^{2} $	$ 3 \cdot 5 \cdot 29^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	32.48.0.1	2B	$13920$	$768$	$13$	$13.91329384$	$1$		$0$	$25088$	$1.281370$	$56667352321/15$	$1.03019$	$4.76183$	$[1, 0, 1, -67298, 6714041]$	$y^2+xy+y=x^3-67298x+6714041$	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, $\ldots$	$[(1137503/22, 1193639367/22)]$
12615.f5	12615f3	12615.f	12615f	$8$	$16$	$ 3 \cdot 5 \cdot 29^{2} $	$ 3^{4} \cdot 5^{4} \cdot 29^{6} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.44	2Cs	$6960$	$768$	$13$	$3.478323460$	$1$		$6$	$25088$	$1.281370$	$111284641/50625$	$1.02534$	$4.10175$	$[1, 0, 1, -8428, -138427]$	$y^2+xy+y=x^3-8428x-138427$	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, $\ldots$	$[(-81, 160)]$
12615.f6	12615f2	12615.f	12615f	$8$	$16$	$ 3 \cdot 5 \cdot 29^{2} $	$ 3^{2} \cdot 5^{2} \cdot 29^{6} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.3	2Cs	$6960$	$768$	$13$	$6.956646921$	$1$		$4$	$12544$	$0.934796$	$13997521/225$	$0.96230$	$3.88219$	$[1, 0, 1, -4223, 103781]$	$y^2+xy+y=x^3-4223x+103781$	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, $\ldots$	$[(2345, 112347)]$
12615.f7	12615f1	12615.f	12615f	$8$	$16$	$ 3 \cdot 5 \cdot 29^{2} $	$ - 3 \cdot 5 \cdot 29^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	32.48.0.1	2B	$13920$	$768$	$13$	$13.91329384$	$1$		$1$	$6272$	$0.588223$	$-1/15$	$1.19808$	$3.21590$	$[1, 0, 1, -18, 4543]$	$y^2+xy+y=x^3-18x+4543$	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, $\ldots$	$[(1083703/43, 1105031480/43)]$
12615.f8	12615f6	12615.f	12615f	$8$	$16$	$ 3 \cdot 5 \cdot 29^{2} $	$ - 3^{2} \cdot 5^{8} \cdot 29^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.197	2B	$13920$	$768$	$13$	$1.739161730$	$1$		$0$	$50176$	$1.627943$	$4733169839/3515625$	$1.05585$	$4.49891$	$[1, 0, 1, 29417, -1031569]$	$y^2+xy+y=x^3+29417x-1031569$	2.3.0.a.1, 4.12.0.d.1, 8.48.0.n.2, 24.96.1.cv.2, 80.96.1.?, $\ldots$	$[(715/2, 24511/2)]$
12615.g1	12615d1	12615.g	12615d	$1$	$1$	$ 3 \cdot 5 \cdot 29^{2} $	$ - 3 \cdot 5^{2} \cdot 29^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$6$	$2$	$0$	$1$	$1$		$0$	$1800$	$-0.389971$	$118784/75$	$0.81570$	$1.95069$	$[0, -1, 1, 10, -7]$	$y^2+y=x^3-x^2+10x-7$	6.2.0.a.1	$[]$

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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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