LMFDB - Elliptic curve search results

Refine search

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

		Sort order	Select

Results (1-50 of 1404510 matches)

Next Download displayed columns for results to

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	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
11.a1	11a2	11.a	11a	$3$	$25$	$ 11 $	$ -11 $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$5$	25.120.0.3	5B.1.2	$550$	$1200$	$37$	$1$	$1$	$0$	$5$	$0.496709$	$-52893159101157376/11$	$1.09296$	$16.05869$	$[0, -1, 1, -7820, -263580]$	$y^2+y=x^3-x^2-7820x-263580$	5.24.0-5.a.2.2, 22.2.0.a.1, 25.120.0-25.a.2.2, 110.48.1.?, 275.600.12.?, $\ldots$	$[]$
11.a2	11a1	11.a	11a	$3$	$25$	$ 11 $	$ - 11^{5} $	$0$	$\Z/5\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$5$	5.120.0.1	5Cs.1.1	$550$	$1200$	$37$	$1$	$1$	$4$	$1$	$-0.308010$	$-122023936/161051$	$1.01300$	$8.26048$	$[0, -1, 1, -10, -20]$	$y^2+y=x^3-x^2-10x-20$	5.120.0-5.a.1.2, 22.2.0.a.1, 110.240.5.?, 275.600.12.?, 550.1200.37.?	$[]$
11.a3	11a3	11.a	11a	$3$	$25$	$ 11 $	$ -11 $	$0$	$\Z/5\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$5$	25.120.0.1	5B.1.1	$550$	$1200$	$37$	$1$	$1$	$4$	$5$	$-1.112728$	$-4096/11$	$0.82546$	$4.19024$	$[0, -1, 1, 0, 0]$	$y^2+y=x^3-x^2$	5.24.0-5.a.1.2, 22.2.0.a.1, 25.120.0-25.a.1.2, 110.48.1.?, 275.600.12.?, $\ldots$	$[]$
14.a1	14a5	14.a	14a	$6$	$18$	$ 2 \cdot 7 $	$ 2^{9} \cdot 7^{2} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.6, 9.24.0.3	2B, 3B.1.2	$504$	$864$	$21$	$1$	$1$	$0$	$6$	$0.413101$	$2251439055699625/25088$	$1.06489$	$13.39507$	$[1, 0, 1, -2731, -55146]$	$y^2+xy+y=x^3-2731x-55146$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 8.6.0.b.1, 9.24.0-9.a.1.1, $\ldots$	$[]$
14.a2	14a3	14.a	14a	$6$	$18$	$ 2 \cdot 7 $	$ - 2^{18} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.1, 9.24.0.3	2B, 3B.1.2	$504$	$864$	$21$	$1$	$1$	$1$	$3$	$0.066527$	$-548347731625/1835008$	$1.02933$	$10.24454$	$[1, 0, 1, -171, -874]$	$y^2+xy+y=x^3-171x-874$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 8.6.0.c.1, 9.24.0-9.a.1.1, $\ldots$	$[]$
14.a3	14a2	14.a	14a	$6$	$18$	$ 2 \cdot 7 $	$ 2^{3} \cdot 7^{6} $	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.6, 3.24.0.1	2B, 3Cs.1.1	$504$	$864$	$21$	$1$	$1$	$4$	$2$	$-0.136205$	$4956477625/941192$	$1.00821$	$8.45907$	$[1, 0, 1, -36, -70]$	$y^2+xy+y=x^3-36x-70$	2.3.0.a.1, 3.24.0-3.a.1.1, 6.72.0-6.a.1.1, 8.6.0.b.1, 24.144.1-24.h.1.1, $\ldots$	$[]$
14.a4	14a6	14.a	14a	$6$	$18$	$ 2 \cdot 7 $	$ 2 \cdot 7^{2} $	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.6, 9.24.0.1	2B, 3B.1.1	$504$	$864$	$21$	$1$	$1$	$4$	$6$	$-0.685512$	$128787625/98$	$0.96763$	$7.07589$	$[1, 0, 1, -11, 12]$	$y^2+xy+y=x^3-11x+12$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 8.6.0.b.1, 9.24.0-9.a.1.2, $\ldots$	$[]$
14.a5	14a4	14.a	14a	$6$	$18$	$ 2 \cdot 7 $	$ - 2^{2} \cdot 7 $	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.1, 9.24.0.1	2B, 3B.1.1	$504$	$864$	$21$	$1$	$1$	$5$	$3$	$-1.032085$	$-15625/28$	$1.01712$	$4.19346$	$[1, 0, 1, -1, 0]$	$y^2+xy+y=x^3-x$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 8.6.0.c.1, 9.24.0-9.a.1.2, $\ldots$	$[]$
14.a6	14a1	14.a	14a	$6$	$18$	$ 2 \cdot 7 $	$ - 2^{6} \cdot 7^{3} $	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.1, 3.24.0.1	2B, 3Cs.1.1	$504$	$864$	$21$	$1$	$1$	$5$	$1$	$-0.482779$	$9938375/21952$	$0.98695$	$6.49759$	$[1, 0, 1, 4, -6]$	$y^2+xy+y=x^3+4x-6$	2.3.0.a.1, 3.24.0-3.a.1.1, 6.72.0-6.a.1.1, 8.6.0.c.1, 14.6.0.b.1, $\ldots$	$[]$
15.a1	15a5	15.a	15a	$8$	$16$	$ 3 \cdot 5 $	$ 3^{4} \cdot 5 $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.96.0.148	2B	$480$	$768$	$13$	$1$	$1$	$0$	$4$	$0.290870$	$1114544804970241/405$	$1.07354$	$12.79416$	$[1, 1, 1, -2160, -39540]$	$y^2+xy+y=x^3+x^2-2160x-39540$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.bb.2.3, 10.6.0.a.1, 16.96.0-16.x.2.4, $\ldots$	$[]$
15.a2	15a2	15.a	15a	$8$	$16$	$ 3 \cdot 5 $	$ 3^{8} \cdot 5^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.96.0.58	2Cs	$240$	$768$	$13$	$1$	$1$	$2$	$2$	$-0.055704$	$272223782641/164025$	$1.03897$	$9.72282$	$[1, 1, 1, -135, -660]$	$y^2+xy+y=x^3+x^2-135x-660$	2.6.0.a.1, 4.24.0-4.b.1.1, 8.96.0-8.k.1.1, 20.48.0-20.c.1.2, 40.192.1-40.cc.2.4, $\ldots$	$[]$
15.a3	15a6	15.a	15a	$8$	$16$	$ 3 \cdot 5 $	$ - 3^{16} \cdot 5 $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.96.0.153	2B	$480$	$768$	$13$	$1$	$1$	$0$	$4$	$0.290870$	$-147281603041/215233605$	$1.05949$	$9.96125$	$[1, 1, 1, -110, -880]$	$y^2+xy+y=x^3+x^2-110x-880$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.ba.2.6, 16.96.0-16.u.2.3, 20.24.0-20.h.1.1, $\ldots$	$[]$
15.a4	15a7	15.a	15a	$8$	$16$	$ 3 \cdot 5 $	$ 3 \cdot 5 $	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	32.96.0.5	2B	$480$	$768$	$13$	$1$	$1$	$2$	$4$	$-0.402277$	$56667352321/15$	$1.03019$	$9.14328$	$[1, 1, 1, -80, 242]$	$y^2+xy+y=x^3+x^2-80x+242$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.g.1.2, 24.48.0-24.by.2.3, $\ldots$	$[]$
15.a5	15a1	15.a	15a	$8$	$16$	$ 3 \cdot 5 $	$ 3^{4} \cdot 5^{4} $	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.96.0.3	2Cs	$240$	$768$	$13$	$1$	$1$	$6$	$1$	$-0.402277$	$111284641/50625$	$1.02534$	$6.84168$	$[1, 1, 1, -10, -10]$	$y^2+xy+y=x^3+x^2-10x-10$	2.6.0.a.1, 4.48.0-4.b.1.1, 8.96.0-8.b.2.9, 24.192.1-24.n.1.1, 40.192.1-40.s.1.5, $\ldots$	$[]$
15.a6	15a3	15.a	15a	$8$	$16$	$ 3 \cdot 5 $	$ 3^{2} \cdot 5^{2} $	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.96.0.7	2Cs	$240$	$768$	$13$	$1$	$1$	$6$	$2$	$-0.748851$	$13997521/225$	$0.96230$	$6.07610$	$[1, 1, 1, -5, 2]$	$y^2+xy+y=x^3+x^2-5x+2$	2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.i.1.10, 16.96.0-16.d.2.3, 24.96.0-24.bb.2.5, $\ldots$	$[]$
15.a7	15a8	15.a	15a	$8$	$16$	$ 3 \cdot 5 $	$ - 3 \cdot 5 $	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	32.96.0.5	2B	$480$	$768$	$13$	$1$	$1$	$3$	$4$	$-1.095425$	$-1/15$	$1.19808$	$3.75281$	$[1, 1, 1, 0, 0]$	$y^2+xy+y=x^3+x^2$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.g.1.2, 24.48.0-24.bz.1.3, $\ldots$	$[]$
15.a8	15a4	15.a	15a	$8$	$16$	$ 3 \cdot 5 $	$ - 3^{2} \cdot 5^{8} $	$0$	$\Z/8\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.96.0.99	2B	$480$	$768$	$13$	$1$	$1$	$6$	$2$	$-0.055704$	$4733169839/3515625$	$1.05585$	$8.22653$	$[1, 1, 1, 35, -28]$	$y^2+xy+y=x^3+x^2+35x-28$	2.3.0.a.1, 4.24.0-4.d.1.1, 8.96.0-8.n.2.5, 24.192.1-24.cv.2.2, 80.192.1.?, $\ldots$	$[]$
17.a1	17a3	17.a	17a	$4$	$4$	$ 17 $	$ 17 $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	32.96.0.18	2B	$1088$	$1536$	$53$	$1$	$1$	$0$	$4$	$-0.376636$	$82483294977/17$	$1.03131$	$8.87186$	$[1, -1, 1, -91, -310]$	$y^2+xy+y=x^3-x^2-91x-310$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.o.1.3, 16.48.0-16.j.1.3, 32.96.0-32.f.2.1, $\ldots$	$[]$
17.a2	17a2	17.a	17a	$4$	$4$	$ 17 $	$ 17^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.96.0.13	2Cs	$544$	$1536$	$53$	$1$	$1$	$2$	$2$	$-0.723209$	$20346417/289$	$1.02963$	$5.93969$	$[1, -1, 1, -6, -4]$	$y^2+xy+y=x^3-x^2-6x-4$	2.6.0.a.1, 4.24.0-4.a.1.1, 8.48.0-8.f.1.1, 16.96.0-16.c.2.2, 68.48.0-68.b.1.1, $\ldots$	$[]$
17.a3	17a1	17.a	17a	$4$	$4$	$ 17 $	$ - 17^{4} $	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.96.0.32	2B	$1088$	$1536$	$53$	$1$	$1$	$2$	$1$	$-0.376636$	$-35937/83521$	$1.18071$	$6.63128$	$[1, -1, 1, -1, -14]$	$y^2+xy+y=x^3-x^2-x-14$	2.3.0.a.1, 4.24.0-4.d.1.1, 8.48.0-8.t.1.2, 16.96.0-16.m.2.1, 136.96.1.?, $\ldots$	$[]$
17.a4	17a4	17.a	17a	$4$	$4$	$ 17 $	$ 17 $	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	32.96.0.10	2B	$1088$	$1536$	$53$	$1$	$1$	$3$	$4$	$-1.069784$	$35937/17$	$1.02432$	$3.70234$	$[1, -1, 1, -1, 0]$	$y^2+xy+y=x^3-x^2-x$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.o.1.1, 16.48.0-16.j.1.1, 32.96.0-32.f.2.2, $\ldots$	$[]$
19.a1	19a2	19.a	19a	$3$	$9$	$ 19 $	$ -19 $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	27.72.0.2	3B.1.2	$1026$	$1296$	$43$	$1$	$1$	$0$	$3$	$0.033439$	$-50357871050752/19$	$1.10495$	$10.71517$	$[0, 1, 1, -769, -8470]$	$y^2+y=x^3+x^2-769x-8470$	3.8.0-3.a.1.1, 9.24.0-9.a.1.1, 27.72.0-27.a.1.1, 38.2.0.a.1, 114.16.0.?, $\ldots$	$[]$
19.a2	19a1	19.a	19a	$3$	$9$	$ 19 $	$ - 19^{3} $	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.72.0.3	3Cs.1.1	$1026$	$1296$	$43$	$1$	$1$	$2$	$1$	$-0.515867$	$-89915392/6859$	$1.03310$	$6.26204$	$[0, 1, 1, -9, -15]$	$y^2+y=x^3+x^2-9x-15$	3.24.0-3.a.1.1, 9.72.0-9.b.1.1, 38.2.0.a.1, 114.48.1.?, 171.216.4.?, $\ldots$	$[]$
19.a3	19a3	19.a	19a	$3$	$9$	$ 19 $	$ -19 $	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	27.72.0.1	3B.1.1	$1026$	$1296$	$43$	$1$	$1$	$2$	$3$	$-1.065172$	$32768/19$	$1.31757$	$3.53113$	$[0, 1, 1, 1, 0]$	$y^2+y=x^3+x^2+x$	3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 27.72.0-27.a.1.2, 38.2.0.a.1, 114.16.0.?, $\ldots$	$[]$
20.a1	20a4	20.a	20a	$4$	$6$	$ 2^{2} \cdot 5 $	$ 2^{4} \cdot 5^{3} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.12.0.22, 3.8.0.2	2B, 3B.1.2	$120$	$384$	$9$	$1$	$1$	$1$	$6$	$-0.380644$	$488095744/125$	$1.07376$	$7.60369$	$[0, 1, 0, -41, -116]$	$y^2=x^3+x^2-41x-116$	2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.b.1, 6.24.0-6.a.1.2, 8.12.0-4.b.1.2, $\ldots$	$[]$
20.a2	20a3	20.a	20a	$4$	$6$	$ 2^{2} \cdot 5 $	$ - 2^{8} \cdot 5^{6} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.12.0.37, 3.8.0.2	2B, 3B.1.2	$120$	$384$	$9$	$1$	$1$	$1$	$3$	$-0.034070$	$-20720464/15625$	$0.95894$	$7.75305$	$[0, 1, 0, -36, -140]$	$y^2=x^3+x^2-36x-140$	2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.a.1, 6.24.0-6.a.1.2, 8.12.0-4.a.1.1, $\ldots$	$[]$
20.a3	20a2	20.a	20a	$4$	$6$	$ 2^{2} \cdot 5 $	$ 2^{4} \cdot 5 $	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.12.0.22, 3.8.0.1	2B, 3B.1.1	$120$	$384$	$9$	$1$	$1$	$5$	$2$	$-0.929950$	$16384/5$	$0.95621$	$4.16481$	$[0, 1, 0, -1, 0]$	$y^2=x^3+x^2-x$	2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.b.1, 6.24.0-6.a.1.4, 8.12.0-4.b.1.2, $\ldots$	$[]$
20.a4	20a1	20.a	20a	$4$	$6$	$ 2^{2} \cdot 5 $	$ - 2^{8} \cdot 5^{2} $	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.12.0.37, 3.8.0.1	2B, 3B.1.1	$120$	$384$	$9$	$1$	$1$	$5$	$1$	$-0.583377$	$21296/25$	$0.83964$	$5.18725$	$[0, 1, 0, 4, 4]$	$y^2=x^3+x^2+4x+4$	2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.a.1, 6.24.0-6.a.1.4, 8.12.0-4.a.1.1, $\ldots$	$[]$
21.a1	21a5	21.a	21a	$6$	$8$	$ 3 \cdot 7 $	$ 3 \cdot 7^{2} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.48.0.48	2B	$336$	$192$	$1$	$1$	$1$	$0$	$4$	$0.074205$	$53297461115137/147$	$1.05087$	$10.38157$	$[1, 0, 0, -784, -8515]$	$y^2+xy=x^3-784x-8515$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 12.24.0-12.h.1.1, 16.48.0-16.e.2.5, $\ldots$	$[]$
21.a2	21a2	21.a	21a	$6$	$8$	$ 3 \cdot 7 $	$ 3^{2} \cdot 7^{4} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.48.0.34	2Cs	$168$	$192$	$1$	$1$	$1$	$2$	$2$	$-0.272368$	$13027640977/21609$	$1.08149$	$7.64992$	$[1, 0, 0, -49, -136]$	$y^2+xy=x^3-49x-136$	2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.e.1.1, 12.48.0-12.c.1.3, 24.96.0-24.j.2.5, $\ldots$	$[]$
21.a3	21a3	21.a	21a	$6$	$8$	$ 3 \cdot 7 $	$ 3^{8} \cdot 7 $	$0$	$\Z/8\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.48.0.159	2B	$336$	$192$	$1$	$1$	$1$	$6$	$2$	$-0.272368$	$6570725617/45927$	$1.00160$	$7.42510$	$[1, 0, 0, -39, 90]$	$y^2+xy=x^3-39x+90$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.1.1, 28.24.0-28.h.1.2, 48.96.0-48.bf.1.3, $\ldots$	$[]$
21.a4	21a6	21.a	21a	$6$	$8$	$ 3 \cdot 7 $	$ - 3 \cdot 7^{8} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.48.0.177	2B	$336$	$192$	$1$	$1$	$1$	$0$	$4$	$0.074205$	$-4354703137/17294403$	$1.04266$	$7.96731$	$[1, 0, 0, -34, -217]$	$y^2+xy=x^3-34x-217$	2.3.0.a.1, 4.12.0-4.c.1.2, 6.6.0.a.1, 8.48.0-8.bb.2.3, 12.24.0-12.g.1.1, $\ldots$	$[]$
21.a5	21a1	21.a	21a	$6$	$8$	$ 3 \cdot 7 $	$ 3^{4} \cdot 7^{2} $	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.48.0.24	2Cs	$168$	$192$	$1$	$1$	$1$	$6$	$1$	$-0.618942$	$7189057/3969$	$1.14862$	$5.18573$	$[1, 0, 0, -4, -1]$	$y^2+xy=x^3-4x-1$	2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.e.2.2, 24.96.0-24.w.2.6, 28.48.0-28.c.1.1, $\ldots$	$[]$
21.a6	21a4	21.a	21a	$6$	$8$	$ 3 \cdot 7 $	$ - 3^{2} \cdot 7 $	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.48.0.27	2B	$336$	$192$	$1$	$1$	$1$	$3$	$2$	$-0.965515$	$103823/63$	$0.97868$	$3.79384$	$[1, 0, 0, 1, 0]$	$y^2+xy=x^3+x$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 14.6.0.b.1, 16.48.0-16.e.1.2, $\ldots$	$[]$
24.a1	24a5	24.a	24a	$6$	$8$	$ 2^{3} \cdot 3 $	$ 2^{11} \cdot 3^{2} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.135	2B	$48$	$192$	$1$	$1$	$1$	$1$	$4$	$0.047795$	$3065617154/9$	$1.21059$	$9.27238$	$[0, -1, 0, -384, -2772]$	$y^2=x^3-x^2-384x-2772$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.r.1.6, 16.96.0-16.l.1.6, 24.96.0-24.bf.1.4, $\ldots$	$[]$
24.a2	24a3	24.a	24a	$6$	$8$	$ 2^{3} \cdot 3 $	$ 2^{10} \cdot 3 $	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.106	2B	$48$	$192$	$1$	$1$	$1$	$3$	$2$	$-0.298779$	$28756228/3$	$1.05617$	$7.58509$	$[0, -1, 0, -64, 220]$	$y^2=x^3-x^2-64x+220$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.2.4, 12.24.0-12.h.1.2, 16.96.0-16.bb.2.4, $\ldots$	$[]$
24.a3	24a2	24.a	24a	$6$	$8$	$ 2^{3} \cdot 3 $	$ 2^{10} \cdot 3^{4} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.96.0.49	2Cs	$24$	$192$	$1$	$1$	$1$	$3$	$2$	$-0.298779$	$1556068/81$	$1.03212$	$6.66733$	$[0, -1, 0, -24, -36]$	$y^2=x^3-x^2-24x-36$	2.6.0.a.1, 4.24.0-4.b.1.1, 8.96.0-8.e.2.2, 24.192.1-24.bl.2.4	$[]$
24.a4	24a1	24.a	24a	$6$	$8$	$ 2^{3} \cdot 3 $	$ 2^{8} \cdot 3^{2} $	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.96.0.42	2Cs	$24$	$192$	$1$	$1$	$1$	$7$	$1$	$-0.645352$	$35152/9$	$0.97255$	$5.03850$	$[0, -1, 0, -4, 4]$	$y^2=x^3-x^2-4x+4$	2.6.0.a.1, 4.24.0-4.b.1.3, 8.96.0-8.h.1.6, 12.48.0-12.c.1.1, 24.192.1-24.bu.1.7	$[]$
24.a5	24a4	24.a	24a	$6$	$8$	$ 2^{3} \cdot 3 $	$ - 2^{4} \cdot 3 $	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.110	2B	$48$	$192$	$1$	$1$	$1$	$3$	$2$	$-0.991926$	$2048/3$	$1.17572$	$3.40564$	$[0, -1, 0, 1, 0]$	$y^2=x^3-x^2+x$	2.3.0.a.1, 4.12.0-4.c.1.1, 6.6.0.a.1, 8.48.0-8.ba.1.2, 12.24.0-12.g.1.2, $\ldots$	$[]$
24.a6	24a6	24.a	24a	$6$	$8$	$ 2^{3} \cdot 3 $	$ - 2^{11} \cdot 3^{8} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.96.0.166	2B	$48$	$192$	$1$	$1$	$1$	$1$	$4$	$0.047795$	$207646/6561$	$1.15980$	$7.50451$	$[0, -1, 0, 16, -180]$	$y^2=x^3-x^2+16x-180$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.96.0-8.m.1.2, 48.192.1-48.w.2.4	$[]$
26.a1	26a2	26.a	26a	$3$	$9$	$ 2 \cdot 13 $	$ - 2^{9} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.24.0.3	3B.1.2	$936$	$144$	$3$	$1$	$1$	$0$	$6$	$0.054386$	$-10730978619193/6656$	$1.02193$	$9.20911$	$[1, 0, 1, -460, -3830]$	$y^2+xy+y=x^3-460x-3830$	3.8.0-3.a.1.1, 9.24.0-9.a.1.1, 104.2.0.?, 117.72.0.?, 312.16.0.?, $\ldots$	$[]$
26.a2	26a1	26.a	26a	$3$	$9$	$ 2 \cdot 13 $	$ - 2^{3} \cdot 13^{3} $	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.24.0.1	3Cs.1.1	$936$	$144$	$3$	$1$	$1$	$2$	$2$	$-0.494920$	$-10218313/17576$	$0.94717$	$5.37707$	$[1, 0, 1, -5, -8]$	$y^2+xy+y=x^3-5x-8$	3.24.0-3.a.1.1, 104.2.0.?, 117.72.0.?, 312.48.1.?, 936.144.3.?	$[]$
26.a3	26a3	26.a	26a	$3$	$9$	$ 2 \cdot 13 $	$ - 2 \cdot 13 $	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	9.24.0.1	3B.1.1	$936$	$144$	$3$	$1$	$1$	$2$	$6$	$-1.044226$	$12167/26$	$0.84415$	$3.19113$	$[1, 0, 1, 0, 0]$	$y^2+xy+y=x^3$	3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 104.2.0.?, 117.72.0.?, 312.16.0.?, $\ldots$	$[]$
26.b1	26b2	26.b	26b	$2$	$7$	$ 2 \cdot 13 $	$ - 2 \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.5	7B.1.3	$728$	$96$	$2$	$1$	$1$	$0$	$14$	$0.289794$	$-1064019559329/125497034$	$1.06269$	$8.55670$	$[1, -1, 1, -213, -1257]$	$y^2+xy+y=x^3-x^2-213x-1257$	7.48.0-7.a.2.2, 104.2.0.?, 728.96.2.?	$[]$
26.b2	26b1	26.b	26b	$2$	$7$	$ 2 \cdot 13 $	$ - 2^{7} \cdot 13 $	$0$	$\Z/7\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.1	7B.1.1	$728$	$96$	$2$	$1$	$1$	$6$	$2$	$-0.683161$	$-2146689/1664$	$0.96784$	$4.73570$	$[1, -1, 1, -3, 3]$	$y^2+xy+y=x^3-x^2-3x+3$	7.48.0-7.a.1.2, 104.2.0.?, 728.96.2.?	$[]$
27.a1	27a2	27.a	27a	$4$	$27$	$ 3^{3} $	$ - 3^{11} $	$0$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-27$	$N(\mathrm{U}(1))$		✓	$3$	27.648.13.34	3B.1.2				$1$	$1$	$0$	$3$	$0.052148$	$-12288000$	$1.23864$	$8.61966$	$[0, 0, 1, -270, -1708]$	$y^2+y=x^3-270x-1708$		$[]$
27.a2	27a4	27.a	27a	$4$	$27$	$ 3^{3} $	$ - 3^{5} $	$0$	$\Z/3\Z$	$\Q(\sqrt{-3})$	$-27$	$N(\mathrm{U}(1))$		✓	$3$	27.648.13.25	3B.1.1				$1$	$1$	$2$	$9$	$-0.497158$	$-12288000$	$1.23864$	$6.61966$	$[0, 0, 1, -30, 63]$	$y^2+y=x^3-30x+63$		$[]$
27.a3	27a1	27.a	27a	$4$	$27$	$ 3^{3} $	$ - 3^{9} $	$0$	$\Z/3\Z$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$3$	27.1944.55.37	3Cs.1.1				$1$	$1$	$2$	$1$	$-0.497158$	$0$		$5.26186$	$[0, 0, 1, 0, -7]$	$y^2+y=x^3-7$		$[]$
27.a4	27a3	27.a	27a	$4$	$27$	$ 3^{3} $	$ - 3^{3} $	$0$	$\Z/3\Z$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$3$	27.1944.55.31	3Cs.1.1				$1$	$1$	$2$	$3$	$-1.046465$	$0$		$3.26186$	$[0, 0, 1, 0, 0]$	$y^2+y=x^3$		$[]$
30.a1	30a7	30.a	30a	$8$	$12$	$ 2 \cdot 3 \cdot 5 $	$ 2^{3} \cdot 3^{4} \cdot 5^{3} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.12.0.7, 3.8.0.2	2B, 3B.1.2	$120$	$384$	$5$	$1$	$1$	$0$	$24$	$0.564166$	$16778985534208729/81000$	$1.08181$	$10.98404$	$[1, 0, 1, -5334, -150368]$	$y^2+xy+y=x^3-5334x-150368$	2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.c.1, 6.24.0-6.a.1.2, 8.12.0-4.c.1.3, $\ldots$	$[]$

Next Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 1404510 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Learn more

Refine search Advanced search options

Results (1-50 of 1404510 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Refine search