LMFDB - Elliptic curves over $\Q$ of conductor 2760

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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
2760.a1	2760d3	2760.a	2760d	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ 2^{11} \cdot 3^{4} \cdot 5^{4} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$2760$	$48$	$0$	$1$	$1$		$1$	$1536$	$0.594230$	$63649751618/1164375$	$0.90665$	$4.10215$	$[0, -1, 0, -1056, 13356]$	$y^2=x^3-x^2-1056x+13356$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 92.12.0.?, 120.24.0.?, $\ldots$	$[]$
2760.a2	2760d2	2760.a	2760d	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ 2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 23^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$2760$	$48$	$0$	$1$	$1$		$3$	$768$	$0.247656$	$273671716/119025$	$0.86426$	$3.32689$	$[0, -1, 0, -136, -260]$	$y^2=x^3-x^2-136x-260$	2.6.0.a.1, 8.12.0-2.a.1.1, 60.12.0-2.a.1.1, 92.12.0.?, 120.24.0.?, $\ldots$	$[]$
2760.a3	2760d1	2760.a	2760d	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ 2^{8} \cdot 3 \cdot 5 \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$2760$	$48$	$0$	$1$	$1$		$1$	$384$	$-0.098917$	$680136784/345$	$1.01638$	$3.26682$	$[0, -1, 0, -116, -444]$	$y^2=x^3-x^2-116x-444$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 60.12.0-4.c.1.2, 92.12.0.?, $\ldots$	$[]$
2760.a4	2760d4	2760.a	2760d	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ - 2^{11} \cdot 3 \cdot 5 \cdot 23^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$2760$	$48$	$0$	$1$	$4$	$2$	$1$	$1536$	$0.594230$	$5382838942/4197615$	$0.91324$	$3.79038$	$[0, -1, 0, 464, -2420]$	$y^2=x^3-x^2+464x-2420$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 60.12.0-4.c.1.1, 120.24.0.?, $\ldots$	$[]$
2760.b1	2760e1	2760.b	2760e	$1$	$1$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ - 2^{8} \cdot 3^{16} \cdot 5 \cdot 23 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$230$	$2$	$0$	$1$	$1$		$0$	$3072$	$1.001423$	$-9619385344/4950372915$	$1.03730$	$4.45839$	$[0, -1, 0, -281, -54099]$	$y^2=x^3-x^2-281x-54099$	230.2.0.?	$[]$
2760.c1	2760b2	2760.c	2760b	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ 2^{11} \cdot 3^{2} \cdot 5^{6} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1$	$1$		$1$	$2688$	$0.622306$	$33909572018/3234375$	$0.90332$	$4.02267$	$[0, -1, 0, -856, 9100]$	$y^2=x^3-x^2-856x+9100$	2.3.0.a.1, 60.6.0.c.1, 184.6.0.?, 2760.12.0.?	$[]$
2760.c2	2760b1	2760.c	2760b	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ - 2^{10} \cdot 3 \cdot 5^{3} \cdot 23^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1$	$1$		$1$	$1344$	$0.275732$	$27871484/198375$	$0.87484$	$3.34461$	$[0, -1, 0, 64, 636]$	$y^2=x^3-x^2+64x+636$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[]$
2760.d1	2760a3	2760.d	2760a	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ 2^{10} \cdot 3^{4} \cdot 5 \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2760$	$48$	$0$	$1$	$1$		$1$	$1792$	$0.529248$	$1600610497636/9315$	$0.92763$	$4.42168$	$[0, -1, 0, -2456, 47676]$	$y^2=x^3-x^2-2456x+47676$	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 24.12.0-4.c.1.3, 92.12.0.?, $\ldots$	$[]$
2760.d2	2760a2	2760.d	2760a	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ 2^{8} \cdot 3^{2} \cdot 5^{2} \cdot 23^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$1380$	$48$	$0$	$1$	$1$		$3$	$896$	$0.182675$	$1650587344/119025$	$0.84461$	$3.37872$	$[0, -1, 0, -156, 756]$	$y^2=x^3-x^2-156x+756$	2.6.0.a.1, 12.12.0-2.a.1.1, 20.12.0-2.a.1.1, 60.24.0-60.b.1.2, 92.12.0.?, $\ldots$	$[]$
2760.d3	2760a1	2760.d	2760a	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ 2^{4} \cdot 3 \cdot 5^{4} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2760$	$48$	$0$	$1$	$1$		$1$	$448$	$-0.163899$	$212629504/43125$	$0.84937$	$2.77012$	$[0, -1, 0, -31, -44]$	$y^2=x^3-x^2-31x-44$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 40.12.0-4.c.1.5, 92.12.0.?, $\ldots$	$[]$
2760.d4	2760a4	2760.d	2760a	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ - 2^{10} \cdot 3 \cdot 5 \cdot 23^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$2760$	$48$	$0$	$1$	$1$		$1$	$1792$	$0.529248$	$320251964/4197615$	$0.91734$	$3.73484$	$[0, -1, 0, 144, 3036]$	$y^2=x^3-x^2+144x+3036$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 20.12.0-4.c.1.1, 30.6.0.a.1, $\ldots$	$[]$
2760.e1	2760f5	2760.e	2760f	$6$	$8$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ 2^{11} \cdot 3^{6} \cdot 5^{2} \cdot 23^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.173	2B	$1104$	$192$	$1$	$9.330950852$	$1$		$1$	$43008$	$2.309658$	$35667215800077781442/1427217706746225$	$1.02042$	$6.64464$	$[0, -1, 0, -870880, -301514900]$	$y^2=x^3-x^2-870880x-301514900$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.r.1.6, 24.96.0-24.bf.1.4, 368.96.0.?, $\ldots$	$[(-25975/7, 1132230/7)]$
2760.e2	2760f3	2760.e	2760f	$6$	$8$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ 2^{10} \cdot 3^{12} \cdot 5^{4} \cdot 23^{4} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.30	2Cs	$552$	$192$	$1$	$4.665475426$	$1$		$5$	$21504$	$1.963083$	$308453964046598884/92949363050625$	$1.00808$	$5.95758$	$[0, -1, 0, -141880, 14287900]$	$y^2=x^3-x^2-141880x+14287900$	2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.c.1.2, 24.96.0-24.d.1.3, 184.96.0.?, $\ldots$	$[(65, 2310)]$
2760.e3	2760f2	2760.e	2760f	$6$	$8$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ 2^{8} \cdot 3^{6} \cdot 5^{8} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.29	2Cs	$552$	$192$	$1$	$2.332737713$	$1$		$15$	$10752$	$1.616510$	$935596404100595536/150641015625$	$0.99737$	$5.92266$	$[0, -1, 0, -129380, 17952900]$	$y^2=x^3-x^2-129380x+17952900$	2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.h.1.9, 24.96.0-24.x.1.5, 184.96.0.?, $\ldots$	$[(190, 440)]$
2760.e4	2760f1	2760.e	2760f	$6$	$8$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ 2^{4} \cdot 3^{3} \cdot 5^{4} \cdot 23 $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.29	2B	$1104$	$192$	$1$	$4.665475426$	$1$		$5$	$5376$	$1.269938$	$14967807005098080256/388125$	$1.03317$	$5.92264$	$[0, -1, 0, -129375, 17954352]$	$y^2=x^3-x^2-129375x+17954352$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.h.1.2, 24.48.0-24.by.2.3, $\ldots$	$[(649, 14385)]$
2760.e5	2760f4	2760.e	2760f	$6$	$8$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ - 2^{10} \cdot 3^{3} \cdot 5^{16} \cdot 23 $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.29	2B	$1104$	$192$	$1$	$4.665475426$	$1$		$3$	$21504$	$1.963083$	$-172798332611391364/94757080078125$	$1.00466$	$5.96858$	$[0, -1, 0, -116960, 21524892]$	$y^2=x^3-x^2-116960x+21524892$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.h.1.2, 24.48.0-24.by.1.3, $\ldots$	$[(1381/2, 37675/2)]$
2760.e6	2760f6	2760.e	2760f	$6$	$8$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ - 2^{11} \cdot 3^{24} \cdot 5^{2} \cdot 23^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.174	2B	$1104$	$192$	$1$	$9.330950852$	$1$		$1$	$43008$	$2.309658$	$3132776881711582558/3735130619961225$	$1.02747$	$6.34503$	$[0, -1, 0, 387120, 95330700]$	$y^2=x^3-x^2+387120x+95330700$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.k.1.6, 48.96.0-48.f.1.8, 184.96.0.?, $\ldots$	$[(21745/3, 3321010/3)]$
2760.f1	2760c1	2760.f	2760c	$1$	$1$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ - 2^{8} \cdot 3^{2} \cdot 5^{3} \cdot 23 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$230$	$2$	$0$	$0.071515739$	$1$		$12$	$384$	$-0.010740$	$1362944/25875$	$0.86000$	$2.91935$	$[0, -1, 0, 15, 117]$	$y^2=x^3-x^2+15x+117$	230.2.0.?	$[(9, 30)]$
2760.g1	2760g2	2760.g	2760g	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ 2^{11} \cdot 3^{3} \cdot 5^{4} \cdot 23^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$552$	$12$	$0$	$1$	$1$		$1$	$2304$	$0.687132$	$47825527682/8926875$	$0.91015$	$4.06607$	$[0, -1, 0, -960, -9108]$	$y^2=x^3-x^2-960x-9108$	2.3.0.a.1, 24.6.0.a.1, 92.6.0.?, 552.12.0.?	$[]$
2760.g2	2760g1	2760.g	2760g	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ - 2^{10} \cdot 3^{6} \cdot 5^{2} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$552$	$12$	$0$	$1$	$1$		$1$	$1152$	$0.340558$	$185073116/419175$	$0.87304$	$3.41250$	$[0, -1, 0, 120, -900]$	$y^2=x^3-x^2+120x-900$	2.3.0.a.1, 24.6.0.d.1, 46.6.0.a.1, 552.12.0.?	$[]$
2760.h1	2760h3	2760.h	2760h	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ 2^{11} \cdot 3^{4} \cdot 5^{4} \cdot 23^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.58	2B	$184$	$48$	$0$	$7.296895918$	$1$		$3$	$24576$	$2.098572$	$544328872410114151778/14166950625$	$1.07423$	$6.98862$	$[0, 1, 0, -2160176, -1222750176]$	$y^2=x^3+x^2-2160176x-1222750176$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.k.1.1, 184.48.0.?	$[(2515, 96222)]$
2760.h2	2760h4	2760.h	2760h	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ 2^{11} \cdot 3^{4} \cdot 5^{16} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.103	2B	$184$	$48$	$0$	$7.296895918$	$1$		$1$	$24576$	$2.098572$	$497927680189263938/284271240234375$	$1.06072$	$6.10551$	$[0, 1, 0, -209696, 4219680]$	$y^2=x^3+x^2-209696x+4219680$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.p.1.7, 92.12.0.?, 184.48.0.?	$[(2629/2, 98223/2)]$
2760.h3	2760h2	2760.h	2760h	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ 2^{10} \cdot 3^{8} \cdot 5^{8} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.1	2Cs	$184$	$48$	$0$	$3.648447959$	$1$		$7$	$12288$	$1.751997$	$266763091319403556/1355769140625$	$0.99805$	$5.93925$	$[0, 1, 0, -135176, -19090176]$	$y^2=x^3+x^2-135176x-19090176$	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.2, 92.24.0.?, 184.48.0.?	$[(640, 12528)]$
2760.h4	2760h1	2760.h	2760h	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ - 2^{8} \cdot 3^{16} \cdot 5^{4} \cdot 23 $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.50	2B	$184$	$48$	$0$	$1.824223979$	$1$		$11$	$6144$	$1.405424$	$-26752376766544/618796614375$	$1.00033$	$5.07077$	$[0, 1, 0, -3956, -614400]$	$y^2=x^3+x^2-3956x-614400$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.p.1.1, 46.6.0.a.1, 92.24.0.?, $\ldots$	$[(112, 600)]$
2760.i1	2760i1	2760.i	2760i	$1$	$1$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ - 2^{8} \cdot 3^{4} \cdot 5 \cdot 23 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$230$	$2$	$0$	$0.181699752$	$1$		$6$	$768$	$0.098748$	$-3525581824/9315$	$0.87105$	$3.47508$	$[0, 1, 0, -201, 1035]$	$y^2=x^3+x^2-201x+1035$	230.2.0.?	$[(9, 6)]$
2760.j1	2760k1	2760.j	2760k	$1$	$1$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ - 2^{8} \cdot 3^{10} \cdot 5^{5} \cdot 23^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$230$	$2$	$0$	$0.032572446$	$1$		$16$	$9600$	$1.512997$	$190737654201344/2245153696875$	$1.02276$	$5.22395$	$[0, 1, 0, 7615, 1127283]$	$y^2=x^3+x^2+7615x+1127283$	230.2.0.?	$[(-59, 690)]$
2760.k1	2760j2	2760.k	2760j	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ 2^{11} \cdot 3^{10} \cdot 5^{2} \cdot 23^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1$	$1$		$1$	$21120$	$1.844418$	$7536914291382802562/17961229575$	$1.01404$	$6.44845$	$[0, 1, 0, -518720, 143623200]$	$y^2=x^3+x^2-518720x+143623200$	2.3.0.a.1, 60.6.0.c.1, 184.6.0.?, 2760.12.0.?	$[]$
2760.k2	2760j1	2760.k	2760j	$2$	$2$	$ 2^{3} \cdot 3 \cdot 5 \cdot 23 $	$ - 2^{10} \cdot 3^{5} \cdot 5 \cdot 23^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2760$	$12$	$0$	$1$	$1$		$1$	$10560$	$1.497843$	$-3552342505518244/179863605135$	$0.97850$	$5.40475$	$[0, 1, 0, -32040, 2291328]$	$y^2=x^3+x^2-32040x+2291328$	2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.?	$[]$

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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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