Elliptic curves over $\Q$ of conductor 7752

The results below are complete, since the LMFDB contains all elliptic curves with conductor at most 500000

Results (26 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
7752.a1	7752g4	7752.a	7752g	$4$	$4$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( 2^{10} \cdot 3^{2} \cdot 17^{4} \cdot 19 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$2584$	$48$	$0$	$1.899799686$	$1$		$9$	$7168$	$0.827495$	$5669532745348/14282091$	$0.90597$	$4.05301$	$1$	$[0, -1, 0, -3744, 89244]$	\(y^2=x^3-x^2-3744x+89244\)	2.3.0.a.1, 4.12.0-4.c.1.1, 76.24.0.?, 136.24.0.?, 2584.48.0.?	$[(38, 20)]$	$1$
7752.a2	7752g3	7752.a	7752g	$4$	$4$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( 2^{10} \cdot 3^{2} \cdot 17 \cdot 19^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$2584$	$48$	$0$	$1.899799686$	$1$		$5$	$7168$	$0.827495$	$4186423406308/19939113$	$0.90360$	$4.01915$	$2$	$[0, -1, 0, -3384, -74340]$	\(y^2=x^3-x^2-3384x-74340\)	2.3.0.a.1, 4.12.0-4.c.1.2, 34.6.0.a.1, 68.24.0-68.g.1.1, 152.24.0.?, $\ldots$	$[(-34, 16)]$	$1$
7752.a3	7752g2	7752.a	7752g	$4$	$4$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( 2^{8} \cdot 3^{4} \cdot 17^{2} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1292$	$48$	$0$	$0.949899843$	$1$		$13$	$3584$	$0.480921$	$14738677072/8450649$	$0.92035$	$3.23357$	$1$	$[0, -1, 0, -324, 324]$	\(y^2=x^3-x^2-324x+324\)	2.6.0.a.1, 4.12.0-2.a.1.1, 68.24.0-68.b.1.2, 76.24.0.?, 1292.48.0.?	$[(0, 18)]$	$1$
7752.a4	7752g1	7752.a	7752g	$4$	$4$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( - 2^{4} \cdot 3^{8} \cdot 17 \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$2584$	$48$	$0$	$1.899799686$	$1$		$5$	$1792$	$0.134347$	$3628156928/2119203$	$1.07889$	$2.76746$	$2$	$[0, -1, 0, 81, 0]$	\(y^2=x^3-x^2+81x\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 68.12.0-4.c.1.2, 76.12.0.?, $\ldots$	$[(1, 9)]$	$1$
7752.b1	7752e2	7752.b	7752e	$2$	$2$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( 2^{10} \cdot 3^{8} \cdot 17^{2} \cdot 19 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1292$	$12$	$0$	$2.288591108$	$1$		$13$	$5120$	$0.719665$	$69737687428/36026451$	$0.90335$	$3.56192$	$1$	$[0, -1, 0, -864, -2916]$	\(y^2=x^3-x^2-864x-2916\)	2.3.0.a.1, 68.6.0.c.1, 76.6.0.?, 1292.12.0.?	$[(-10, 68), (-26, 36)]$	$1$
7752.b2	7752e1	7752.b	7752e	$2$	$2$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( 2^{8} \cdot 3^{4} \cdot 17 \cdot 19^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1292$	$12$	$0$	$0.572147777$	$1$		$25$	$2560$	$0.373091$	$49081386832/497097$	$0.84785$	$3.36790$	$1$	$[0, -1, 0, -484, 4228]$	\(y^2=x^3-x^2-484x+4228\)	2.3.0.a.1, 34.6.0.a.1, 76.6.0.?, 1292.12.0.?	$[(16, 18), (12, 2)]$	$1$
7752.c1	7752c2	7752.c	7752c	$2$	$2$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( 2^{10} \cdot 3^{4} \cdot 17^{6} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1292$	$12$	$0$	$1$	$1$		$1$	$16896$	$1.342453$	$375123468790948/37147718691$	$0.93835$	$4.52111$	$1$	$[0, -1, 0, -15144, -648036]$	\(y^2=x^3-x^2-15144x-648036\)	2.3.0.a.1, 68.6.0.c.1, 76.6.0.?, 1292.12.0.?	$[ ]$	$1$
7752.c2	7752c1	7752.c	7752c	$2$	$2$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( 2^{8} \cdot 3^{2} \cdot 17^{3} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1292$	$12$	$0$	$1$	$1$		$1$	$8448$	$0.995879$	$1390353619548112/15962337$	$0.93530$	$4.51260$	$1$	$[0, -1, 0, -14764, -685580]$	\(y^2=x^3-x^2-14764x-685580\)	2.3.0.a.1, 34.6.0.a.1, 76.6.0.?, 1292.12.0.?	$[ ]$	$1$
7752.d1	7752a1	7752.d	7752a	$2$	$2$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( 2^{10} \cdot 3^{6} \cdot 17 \cdot 19^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$136$	$12$	$0$	$2.346804683$	$1$		$5$	$9216$	$1.038769$	$3434917850500/1615068153$	$0.92735$	$3.99706$	$1$	$[0, -1, 0, -3168, 30780]$	\(y^2=x^3-x^2-3168x+30780\)	2.3.0.a.1, 8.6.0.d.1, 34.6.0.a.1, 136.12.0.?	$[(9, 54)]$	$1$
7752.d2	7752a2	7752.d	7752a	$2$	$2$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( - 2^{11} \cdot 3^{12} \cdot 17^{2} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$136$	$12$	$0$	$4.693609367$	$1$		$3$	$18432$	$1.385342$	$77331809236750/55444708089$	$0.95672$	$4.42218$	$1$	$[0, -1, 0, 11272, 221388]$	\(y^2=x^3-x^2+11272x+221388\)	2.3.0.a.1, 8.6.0.a.1, 68.6.0.c.1, 136.12.0.?	$[(2897, 156006)]$	$1$
7752.e1	7752d1	7752.e	7752d	$1$	$1$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( - 2^{10} \cdot 3^{7} \cdot 17^{3} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3876$	$2$	$0$	$1.002077412$	$1$		$2$	$6720$	$0.859111$	$205749375836/204149889$	$0.90157$	$3.68272$	$1$	$[0, -1, 0, 1240, 13788]$	\(y^2=x^3-x^2+1240x+13788\)	3876.2.0.?	$[(18, 204)]$	$1$
7752.f1	7752h3	7752.f	7752h	$4$	$4$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( 2^{11} \cdot 3^{2} \cdot 17 \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$2584$	$48$	$0$	$1$	$16$	$2$	$1$	$14336$	$1.260742$	$103038256490713346/2907$	$0.97084$	$5.22555$	$2$	$[0, -1, 0, -124032, -16771860]$	\(y^2=x^3-x^2-124032x-16771860\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 68.12.0-4.c.1.1, 136.24.0.?, $\ldots$	$[ ]$	$1$
7752.f2	7752h2	7752.f	7752h	$4$	$4$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( 2^{10} \cdot 3^{4} \cdot 17^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$2584$	$48$	$0$	$1$	$4$	$2$	$3$	$7168$	$0.914169$	$50317733422372/8450649$	$0.92227$	$4.29680$	$1$	$[0, -1, 0, -7752, -260100]$	\(y^2=x^3-x^2-7752x-260100\)	2.6.0.a.1, 4.12.0-2.a.1.1, 68.24.0-68.b.1.1, 152.24.0.?, 2584.48.0.?	$[ ]$	$1$
7752.f3	7752h4	7752.f	7752h	$4$	$4$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( - 2^{11} \cdot 3^{8} \cdot 17^{4} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$2584$	$48$	$0$	$1$	$4$	$2$	$1$	$14336$	$1.260742$	$-18461208629666/10411644339$	$0.99002$	$4.33820$	$2$	$[0, -1, 0, -6992, -313908]$	\(y^2=x^3-x^2-6992x-313908\)	2.3.0.a.1, 4.12.0-4.c.1.2, 136.24.0.?, 152.24.0.?, 2584.48.0.?	$[ ]$	$1$
7752.f4	7752h1	7752.f	7752h	$4$	$4$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( 2^{8} \cdot 3^{2} \cdot 17 \cdot 19^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$2584$	$48$	$0$	$1$	$1$		$3$	$3584$	$0.567595$	$65168050768/19939113$	$0.86325$	$3.39955$	$1$	$[0, -1, 0, -532, -3068]$	\(y^2=x^3-x^2-532x-3068\)	2.3.0.a.1, 4.12.0-4.c.1.1, 34.6.0.a.1, 68.24.0-68.g.1.2, 152.24.0.?, $\ldots$	$[ ]$	$1$
7752.g1	7752b1	7752.g	7752b	$1$	$1$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( - 2^{10} \cdot 3^{15} \cdot 17 \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3876$	$2$	$0$	$40.82846592$	$1$		$0$	$106560$	$2.188148$	$-7515726102379506456868/4634696961$	$1.01229$	$6.39846$	$1$	$[0, -1, 0, -4113224, -3209491428]$	\(y^2=x^3-x^2-4113224x-3209491428\)	3876.2.0.?	$[(1499947182546120946/4578177, 1836261532572254015126782796/4578177)]$	$1$
7752.h1	7752f1	7752.h	7752f	$1$	$1$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( - 2^{10} \cdot 3^{3} \cdot 17 \cdot 19^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3876$	$2$	$0$	$1$	$1$		$0$	$6336$	$0.699409$	$-1188566172868/3148281$	$0.89305$	$3.87907$	$1$	$[0, -1, 0, -2224, 41212]$	\(y^2=x^3-x^2-2224x+41212\)	3876.2.0.?	$[ ]$	$1$
7752.i1	7752k4	7752.i	7752k	$6$	$8$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( 2^{10} \cdot 3^{4} \cdot 17 \cdot 19 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.29	2B	$5168$	$192$	$1$	$1$	$4$	$2$	$3$	$30720$	$1.590738$	$18778604488699762948/26163$	$0.99069$	$5.72939$	$2$	$[0, 1, 0, -558144, 160311312]$	\(y^2=x^3+x^2-558144x+160311312\)	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, 136.48.0.?, $\ldots$	$[ ]$	$1$
7752.i2	7752k5	7752.i	7752k	$6$	$8$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( 2^{11} \cdot 3^{2} \cdot 17^{8} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.173	2B	$5168$	$192$	$1$	$1$	$1$		$1$	$61440$	$1.937311$	$249090604899702914/22664235925809$	$0.97708$	$5.32412$	$2$	$[0, 1, 0, -166464, -24054048]$	\(y^2=x^3+x^2-166464x-24054048\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.r.1.6, 152.96.0.?, 272.96.0.?, $\ldots$	$[ ]$	$1$
7752.i3	7752k3	7752.i	7752k	$6$	$8$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( 2^{10} \cdot 3^{4} \cdot 17^{4} \cdot 19^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.30	2Cs	$2584$	$192$	$1$	$1$	$1$		$3$	$30720$	$1.590738$	$5253600201074788/881647759521$	$1.00038$	$4.81583$	$2$	$[0, 1, 0, -36504, 2249856]$	\(y^2=x^3+x^2-36504x+2249856\)	2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.c.1.2, 136.96.0.?, 152.96.0.?, $\ldots$	$[ ]$	$1$
7752.i4	7752k2	7752.i	7752k	$6$	$8$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( 2^{8} \cdot 3^{8} \cdot 17^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.29	2Cs	$2584$	$192$	$1$	$1$	$1$		$7$	$15360$	$1.244164$	$18338973792849232/684502569$	$0.99481$	$4.80062$	$1$	$[0, 1, 0, -34884, 2496096]$	\(y^2=x^3+x^2-34884x+2496096\)	2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.h.1.9, 136.96.0.?, 152.96.0.?, $\ldots$	$[ ]$	$1$
7752.i5	7752k1	7752.i	7752k	$6$	$8$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( - 2^{4} \cdot 3^{16} \cdot 17 \cdot 19 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.29	2B	$5168$	$192$	$1$	$1$	$1$		$3$	$7680$	$0.897591$	$-62140690757632/13904090883$	$0.94420$	$3.89248$	$2$	$[0, 1, 0, -2079, 42282]$	\(y^2=x^3+x^2-2079x+42282\)	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, 136.48.0.?, $\ldots$	$[ ]$	$1$
7752.i6	7752k6	7752.i	7752k	$6$	$8$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( - 2^{11} \cdot 3^{2} \cdot 17^{2} \cdot 19^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.174	2B	$5168$	$192$	$1$	$1$	$4$	$2$	$1$	$61440$	$1.937311$	$16633871175485086/44174247469641$	$1.07188$	$5.16461$	$2$	$[0, 1, 0, 67536, 12820320]$	\(y^2=x^3+x^2+67536x+12820320\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.k.1.6, 136.96.0.?, 304.96.0.?, $\ldots$	$[ ]$	$1$
7752.j1	7752j1	7752.j	7752j	$1$	$1$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( - 2^{10} \cdot 3 \cdot 17 \cdot 19 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3876$	$2$	$0$	$1$	$1$		$0$	$960$	$-0.170469$	$-4/969$	$0.92187$	$2.37418$	$1$	$[0, 1, 0, 0, -48]$	\(y^2=x^3+x^2-48\)	3876.2.0.?	$[ ]$	$1$
7752.k1	7752i1	7752.k	7752i	$2$	$2$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( 2^{10} \cdot 3^{3} \cdot 17^{2} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$456$	$12$	$0$	$1$	$1$		$1$	$19968$	$1.137459$	$13032727327528996/148257$	$0.95672$	$4.91728$	$1$	$[0, 1, 0, -49416, 4211712]$	\(y^2=x^3+x^2-49416x+4211712\)	2.3.0.a.1, 8.6.0.d.1, 114.6.0.?, 456.12.0.?	$[ ]$	$1$
7752.k2	7752i2	7752.k	7752i	$2$	$2$	\( 2^{3} \cdot 3 \cdot 17 \cdot 19 \)	\( - 2^{11} \cdot 3^{6} \cdot 17^{4} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$456$	$12$	$0$	$1$	$1$		$1$	$39936$	$1.484032$	$-6500552477501378/21980138049$	$0.95678$	$4.91766$	$1$	$[0, 1, 0, -49376, 4218912]$	\(y^2=x^3+x^2-49376x+4218912\)	2.3.0.a.1, 8.6.0.a.1, 228.6.0.?, 456.12.0.?	$[ ]$	$1$

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