LMFDB - Elliptic curves over $\Q$ of conductor 15075

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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	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
15075.a1	15075k1	15075.a	15075k	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ - 3^{8} \cdot 5^{6} \cdot 67 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$134$	$2$	$0$	$0.797314291$	$1$	$4$	$13824$	$0.573792$	$512000/603$	$0.80036$	$3.05889$	$[0, 0, 1, 375, -2844]$	$y^2+y=x^3+375x-2844$	134.2.0.?	$[(20, 112)]$
15075.b1	15075b1	15075.b	15075b	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ 3^{3} \cdot 5^{6} \cdot 67 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$804$	$12$	$0$	$0.737649543$	$1$	$9$	$3584$	$0.122347$	$132651/67$	$0.90998$	$2.57234$	$[1, -1, 1, -80, -78]$	$y^2+xy+y=x^3-x^2-80x-78$	2.3.0.a.1, 12.6.0.c.1, 268.6.0.?, 402.6.0.?, 804.12.0.?	$[(-6, 15)]$
15075.b2	15075b2	15075.b	15075b	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ - 3^{3} \cdot 5^{6} \cdot 67^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$804$	$12$	$0$	$1.475299086$	$1$	$4$	$7168$	$0.468920$	$6751269/4489$	$0.95178$	$2.98080$	$[1, -1, 1, 295, -828]$	$y^2+xy+y=x^3-x^2+295x-828$	2.3.0.a.1, 6.6.0.a.1, 268.6.0.?, 804.12.0.?	$[(9, 45)]$
15075.c1	15075m2	15075.c	15075m	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ 3^{7} \cdot 5^{9} \cdot 67^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4020$	$12$	$0$	$1.196219425$	$1$	$4$	$42240$	$1.315926$	$344472101/13467$	$0.91269$	$4.23397$	$[1, -1, 1, -16430, 786822]$	$y^2+xy+y=x^3-x^2-16430x+786822$	2.3.0.a.1, 60.6.0.a.1, 804.6.0.?, 1340.6.0.?, 4020.12.0.?	$[(113, 546)]$
15075.c2	15075m1	15075.c	15075m	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ - 3^{8} \cdot 5^{9} \cdot 67 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4020$	$12$	$0$	$2.392438850$	$1$	$3$	$21120$	$0.969352$	$6859/603$	$0.92002$	$3.63033$	$[1, -1, 1, 445, 44322]$	$y^2+xy+y=x^3-x^2+445x+44322$	2.3.0.a.1, 60.6.0.b.1, 670.6.0.?, 804.6.0.?, 4020.12.0.?	$[(5, 213)]$
15075.d1	15075f1	15075.d	15075f	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ - 3^{9} \cdot 5^{6} \cdot 67 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$804$	$2$	$0$	$1$	$1$	$0$	$13440$	$0.660432$	$-117649/1809$	$0.97109$	$3.24719$	$[1, -1, 1, -230, -6978]$	$y^2+xy+y=x^3-x^2-230x-6978$	804.2.0.?	$[ ]$
15075.e1	15075l1	15075.e	15075l	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ - 3^{8} \cdot 5^{4} \cdot 67 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$134$	$2$	$0$	$0.513768041$	$1$	$4$	$4224$	$0.307556$	$819200/603$	$0.83004$	$2.76958$	$[0, 0, 1, 150, -369]$	$y^2+y=x^3+150x-369$	134.2.0.?	$[(5, 22)]$
15075.f1	15075d1	15075.f	15075d	$2$	$3$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ - 3^{6} \cdot 5^{2} \cdot 67 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2010$	$16$	$0$	$1$	$1$	$0$	$2016$	$0.005100$	$-10485760/67$	$0.88269$	$2.70113$	$[0, 0, 1, -120, -509]$	$y^2+y=x^3-120x-509$	3.4.0.a.1, 15.8.0-3.a.1.1, 134.2.0.?, 402.8.0.?, 2010.16.0.?	$[ ]$
15075.f2	15075d2	15075.f	15075d	$2$	$3$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ - 3^{6} \cdot 5^{2} \cdot 67^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2010$	$16$	$0$	$1$	$1$	$0$	$6048$	$0.554406$	$218071040/300763$	$0.89954$	$3.04916$	$[0, 0, 1, 330, -2714]$	$y^2+y=x^3+330x-2714$	3.4.0.a.1, 15.8.0-3.a.1.2, 134.2.0.?, 402.8.0.?, 2010.16.0.?	$[ ]$
15075.g1	15075e2	15075.g	15075e	$2$	$3$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ - 3^{10} \cdot 5^{12} \cdot 67^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2010$	$16$	$0$	$1$	$1$	$0$	$276480$	$2.309925$	$-2989967081734144/380653171875$	$1.01643$	$5.41340$	$[0, 0, 1, -675300, 235923781]$	$y^2+y=x^3-675300x+235923781$	3.4.0.a.1, 15.8.0-3.a.1.2, 134.2.0.?, 402.8.0.?, 2010.16.0.?	$[ ]$
15075.g2	15075e1	15075.g	15075e	$2$	$3$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ - 3^{18} \cdot 5^{8} \cdot 67 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2010$	$16$	$0$	$1$	$1$	$0$	$92160$	$1.760616$	$1503484706816/890163675$	$1.04611$	$4.60327$	$[0, 0, 1, 53700, -727844]$	$y^2+y=x^3+53700x-727844$	3.4.0.a.1, 15.8.0-3.a.1.1, 134.2.0.?, 402.8.0.?, 2010.16.0.?	$[ ]$
15075.h1	15075h1	15075.h	15075h	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ - 3^{8} \cdot 5^{10} \cdot 67 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$134$	$2$	$0$	$5.139164932$	$1$	$0$	$21120$	$1.112276$	$819200/603$	$0.83004$	$3.77330$	$[0, 0, 1, 3750, -46094]$	$y^2+y=x^3+3750x-46094$	134.2.0.?	$[(361/2, 8105/2)]$
15075.i1	15075n1	15075.i	15075n	$2$	$3$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ - 3^{6} \cdot 5^{8} \cdot 67 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$402$	$16$	$0$	$1$	$1$	$0$	$10080$	$0.809818$	$-10485760/67$	$0.88269$	$3.70486$	$[0, 0, 1, -3000, -63594]$	$y^2+y=x^3-3000x-63594$	3.8.0-3.a.1.1, 134.2.0.?, 402.16.0.?	$[ ]$
15075.i2	15075n2	15075.i	15075n	$2$	$3$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ - 3^{6} \cdot 5^{8} \cdot 67^{3} $	$0$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$402$	$16$	$0$	$1$	$1$	$2$	$30240$	$1.359125$	$218071040/300763$	$0.89954$	$4.05288$	$[0, 0, 1, 8250, -339219]$	$y^2+y=x^3+8250x-339219$	3.8.0-3.a.1.2, 134.2.0.?, 402.16.0.?	$[ ]$
15075.j1	15075c1	15075.j	15075c	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ - 3^{6} \cdot 5^{8} \cdot 67 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$134$	$2$	$0$	$1$	$1$	$0$	$6144$	$0.662465$	$-884736/1675$	$1.01110$	$3.26307$	$[0, 0, 1, -450, -7594]$	$y^2+y=x^3-450x-7594$	134.2.0.?	$[ ]$
15075.k1	15075a1	15075.k	15075a	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ 3^{9} \cdot 5^{6} \cdot 67 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$804$	$12$	$0$	$1.972112565$	$1$	$3$	$10752$	$0.671653$	$132651/67$	$0.90998$	$3.25749$	$[1, -1, 0, -717, 2816]$	$y^2+xy=x^3-x^2-717x+2816$	2.3.0.a.1, 12.6.0.c.1, 268.6.0.?, 402.6.0.?, 804.12.0.?	$[(-16, 108)]$
15075.k2	15075a2	15075.k	15075a	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ - 3^{9} \cdot 5^{6} \cdot 67^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$804$	$12$	$0$	$3.944225131$	$1$	$0$	$21504$	$1.018227$	$6751269/4489$	$0.95178$	$3.66595$	$[1, -1, 0, 2658, 19691]$	$y^2+xy=x^3-x^2+2658x+19691$	2.3.0.a.1, 6.6.0.a.1, 268.6.0.?, 804.12.0.?	$[(71/2, 2079/2)]$
15075.l1	15075i1	15075.l	15075i	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ 3^{11} \cdot 5^{12} \cdot 67 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4020$	$12$	$0$	$3.050602406$	$1$	$1$	$69120$	$1.707445$	$2912566550041/254390625$	$0.91283$	$4.67200$	$[1, -1, 0, -66942, 6159591]$	$y^2+xy=x^3-x^2-66942x+6159591$	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[(1191/2, 27159/2)]$
15075.l2	15075i2	15075.l	15075i	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ - 3^{16} \cdot 5^{9} \cdot 67^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4020$	$12$	$0$	$6.101204813$	$1$	$0$	$138240$	$2.054020$	$3883959939959/33133870125$	$0.95785$	$4.97429$	$[1, -1, 0, 73683, 28518966]$	$y^2+xy=x^3-x^2+73683x+28518966$	2.3.0.a.1, 20.6.0.a.1, 804.6.0.?, 4020.12.0.?	$[(6213/4, 675597/4)]$
15075.m1	15075o2	15075.m	15075o	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ 3^{7} \cdot 5^{3} \cdot 67^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4020$	$12$	$0$	$1$	$1$	$0$	$8448$	$0.511207$	$344472101/13467$	$0.91269$	$3.23024$	$[1, -1, 0, -657, 6426]$	$y^2+xy=x^3-x^2-657x+6426$	2.3.0.a.1, 60.6.0.a.1, 804.6.0.?, 1340.6.0.?, 4020.12.0.?	$[ ]$
15075.m2	15075o1	15075.m	15075o	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ - 3^{8} \cdot 5^{3} \cdot 67 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4020$	$12$	$0$	$1$	$1$	$1$	$4224$	$0.164633$	$6859/603$	$0.92002$	$2.62660$	$[1, -1, 0, 18, 351]$	$y^2+xy=x^3-x^2+18x+351$	2.3.0.a.1, 60.6.0.b.1, 670.6.0.?, 804.6.0.?, 4020.12.0.?	$[ ]$
15075.n1	15075j1	15075.n	15075j	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ - 3^{11} \cdot 5^{6} \cdot 67 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$804$	$2$	$0$	$26.11485481$	$1$	$0$	$51840$	$1.527960$	$-55467626237353/16281$	$1.06184$	$4.97829$	$[1, -1, 0, -178767, -29047734]$	$y^2+xy=x^3-x^2-178767x-29047734$	804.2.0.?	$[(531810542442/22807, 341047594232219262/22807)]$
15075.o1	15075g1	15075.o	15075g	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 67 $	$ - 3^{6} \cdot 5^{6} \cdot 67 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$134$	$2$	$0$	$1$	$1$	$0$	$15360$	$0.678759$	$-207474688/67$	$0.87656$	$3.67947$	$[0, 0, 1, -2775, 56281]$	$y^2+y=x^3-2775x+56281$	134.2.0.?	$[ ]$

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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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