LMFDB - Elliptic curve search results

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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 (26 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	Semistable	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
1290.a2	1290a1	1290.a	1290a	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 43 $	$ - 2^{10} \cdot 3^{2} \cdot 5 \cdot 43 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$5160$	$12$	$0$	$1$	$1$		$1$	$240$	$-0.094250$	$-2305199161/1981440$	$0.87827$	$3.13705$	$[1, 1, 0, -27, -99]$	$y^2+xy=x^3+x^2-27x-99$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[]$
3870.r2	3870p1	3870.r	3870p	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 43 $	$ - 2^{10} \cdot 3^{8} \cdot 5 \cdot 43 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$0.354720051$	$1$		$11$	$1920$	$0.455056$	$-2305199161/1981440$	$0.87827$	$3.51779$	$[1, -1, 1, -248, 2427]$	$y^2+xy+y=x^3-x^2-248x+2427$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[(5, 33)]$
6450.bj2	6450bg1	6450.bj	6450bg	$2$	$2$	$ 2 \cdot 3 \cdot 5^{2} \cdot 43 $	$ - 2^{10} \cdot 3^{2} \cdot 5^{7} \cdot 43 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$1$	$1$		$1$	$5760$	$0.710469$	$-2305199161/1981440$	$0.87827$	$3.66234$	$[1, 0, 0, -688, -11008]$	$y^2+xy=x^3-688x-11008$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[]$
10320.bi2	10320be1	10320.bi	10320be	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 43 $	$ - 2^{22} \cdot 3^{2} \cdot 5 \cdot 43 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$2.328725664$	$1$		$3$	$5760$	$0.598897$	$-2305199161/1981440$	$0.87827$	$3.33122$	$[0, 1, 0, -440, 5460]$	$y^2=x^3+x^2-440x+5460$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[(28, 126)]$
19350.t2	19350t1	19350.t	19350t	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 43 $	$ - 2^{10} \cdot 3^{8} \cdot 5^{7} \cdot 43 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$0.824595277$	$1$		$9$	$46080$	$1.259775$	$-2305199161/1981440$	$0.87827$	$3.92253$	$[1, -1, 0, -6192, 297216]$	$y^2+xy=x^3-x^2-6192x+297216$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[(39, 318)]$
30960.k2	30960bj1	30960.k	30960bj	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 43 $	$ - 2^{22} \cdot 3^{8} \cdot 5 \cdot 43 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$1$	$1$		$1$	$46080$	$1.148203$	$-2305199161/1981440$	$0.87827$	$3.61476$	$[0, 0, 0, -3963, -151382]$	$y^2=x^3-3963x-151382$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[]$
41280.m2	41280bw1	41280.m	41280bw	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 43 $	$ - 2^{28} \cdot 3^{2} \cdot 5 \cdot 43 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$1$	$1$		$1$	$46080$	$0.945471$	$-2305199161/1981440$	$0.87827$	$3.28802$	$[0, -1, 0, -1761, 45441]$	$y^2=x^3-x^2-1761x+45441$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[]$
41280.cf2	41280bb1	41280.cf	41280bb	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5 \cdot 43 $	$ - 2^{28} \cdot 3^{2} \cdot 5 \cdot 43 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$9.983459163$	$1$		$1$	$46080$	$0.945471$	$-2305199161/1981440$	$0.87827$	$3.28802$	$[0, 1, 0, -1761, -45441]$	$y^2=x^3+x^2-1761x-45441$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[(60729/23, 13757400/23)]$
51600.bc2	51600bl1	51600.bc	51600bl	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 43 $	$ - 2^{22} \cdot 3^{2} \cdot 5^{7} \cdot 43 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$1$	$1$		$1$	$138240$	$1.403616$	$-2305199161/1981440$	$0.87827$	$3.72705$	$[0, -1, 0, -11008, 704512]$	$y^2=x^3-x^2-11008x+704512$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[]$
55470.be2	55470bf1	55470.be	55470bf	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 43^{2} $	$ - 2^{10} \cdot 3^{2} \cdot 5 \cdot 43^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$1$	$1$		$1$	$443520$	$1.786350$	$-2305199161/1981440$	$0.87827$	$4.12282$	$[1, 0, 0, -50886, 6960996]$	$y^2+xy=x^3-50886x+6960996$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[]$
63210.v2	63210u1	63210.v	63210u	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 43 $	$ - 2^{10} \cdot 3^{2} \cdot 5 \cdot 7^{6} \cdot 43 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$1.577879635$	$1$		$5$	$92160$	$0.878705$	$-2305199161/1981440$	$0.87827$	$3.08880$	$[1, 0, 1, -1349, 29936]$	$y^2+xy+y=x^3-1349x+29936$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[(-24, 232)]$
123840.fb2	123840cw1	123840.fb	123840cw	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 43 $	$ - 2^{28} \cdot 3^{8} \cdot 5 \cdot 43 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$1$	$1$		$1$	$368640$	$1.494778$	$-2305199161/1981440$	$0.87827$	$3.54209$	$[0, 0, 0, -15852, 1211056]$	$y^2=x^3-15852x+1211056$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[]$
123840.fc2	123840fs1	123840.fc	123840fs	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 43 $	$ - 2^{28} \cdot 3^{8} \cdot 5 \cdot 43 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$1$	$4$	$2$	$1$	$368640$	$1.494778$	$-2305199161/1981440$	$0.87827$	$3.54209$	$[0, 0, 0, -15852, -1211056]$	$y^2=x^3-15852x-1211056$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[]$
154800.dl2	154800cm1	154800.dl	154800cm	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 43 $	$ - 2^{22} \cdot 3^{8} \cdot 5^{7} \cdot 43 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$3.441450619$	$1$		$5$	$1105920$	$1.952923$	$-2305199161/1981440$	$0.87827$	$3.93601$	$[0, 0, 0, -99075, -18922750]$	$y^2=x^3-99075x-18922750$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[(610, 12150)]$
156090.bg2	156090w1	156090.bg	156090w	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 11^{2} \cdot 43 $	$ - 2^{10} \cdot 3^{2} \cdot 5 \cdot 11^{6} \cdot 43 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$0.766160743$	$1$		$7$	$345600$	$1.104698$	$-2305199161/1981440$	$0.87827$	$3.08209$	$[1, 1, 1, -3330, 115215]$	$y^2+xy+y=x^3+x^2-3330x+115215$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[(-5, 365)]$
166410.z2	166410bp1	166410.z	166410bp	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 43^{2} $	$ - 2^{10} \cdot 3^{8} \cdot 5 \cdot 43^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$1$	$1$		$1$	$3548160$	$2.335655$	$-2305199161/1981440$	$0.87827$	$4.29436$	$[1, -1, 0, -457974, -187946892]$	$y^2+xy=x^3-x^2-457974x-187946892$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[]$
189630.eo2	189630n1	189630.eo	189630n	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 43 $	$ - 2^{10} \cdot 3^{8} \cdot 5 \cdot 7^{6} \cdot 43 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$1.513661247$	$1$		$5$	$737280$	$1.428011$	$-2305199161/1981440$	$0.87827$	$3.35197$	$[1, -1, 1, -12137, -808279]$	$y^2+xy+y=x^3-x^2-12137x-808279$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[(219, 2536)]$
206400.co2	206400js1	206400.co	206400js	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 43 $	$ - 2^{28} \cdot 3^{2} \cdot 5^{7} \cdot 43 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$3.447195178$	$1$		$5$	$1105920$	$1.750191$	$-2305199161/1981440$	$0.87827$	$3.64469$	$[0, -1, 0, -44033, -5592063]$	$y^2=x^3-x^2-44033x-5592063$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[(272, 1575)]$
206400.ia2	206400bu1	206400.ia	206400bu	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 43 $	$ - 2^{28} \cdot 3^{2} \cdot 5^{7} \cdot 43 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$1$	$1$		$1$	$1105920$	$1.750191$	$-2305199161/1981440$	$0.87827$	$3.64469$	$[0, 1, 0, -44033, 5592063]$	$y^2=x^3+x^2-44033x+5592063$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[]$
218010.bn2	218010bc1	218010.bn	218010bc	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 13^{2} \cdot 43 $	$ - 2^{10} \cdot 3^{2} \cdot 5 \cdot 13^{6} \cdot 43 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$1$	$1$		$1$	$518400$	$1.188225$	$-2305199161/1981440$	$0.87827$	$3.07986$	$[1, 1, 1, -4651, -194407]$	$y^2+xy+y=x^3+x^2-4651x-194407$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[]$
277350.o2	277350o1	277350.o	277350o	$2$	$2$	$ 2 \cdot 3 \cdot 5^{2} \cdot 43^{2} $	$ - 2^{10} \cdot 3^{2} \cdot 5^{7} \cdot 43^{7} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$3.739143295$	$1$		$11$	$10644480$	$2.591068$	$-2305199161/1981440$	$0.87827$	$4.36388$	$[1, 1, 0, -1272150, 870124500]$	$y^2+xy=x^3+x^2-1272150x+870124500$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[(-4, 29586), (72095/2, 19249955/2)]$
316050.fz2	316050fz1	316050.fz	316050fz	$2$	$2$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 43 $	$ - 2^{10} \cdot 3^{2} \cdot 5^{7} \cdot 7^{6} \cdot 43 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$0.588533859$	$1$		$29$	$2211840$	$1.683424$	$-2305199161/1981440$	$0.87827$	$3.45879$	$[1, 1, 1, -33713, 3742031]$	$y^2+xy+y=x^3+x^2-33713x+3742031$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[(-85, 2492), (111, 1120)]$
372810.bi2	372810bi1	372810.bi	372810bi	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 17^{2} \cdot 43 $	$ - 2^{10} \cdot 3^{2} \cdot 5 \cdot 17^{6} \cdot 43 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$1$	$1$		$1$	$1244160$	$1.322357$	$-2305199161/1981440$	$0.87827$	$3.07652$	$[1, 0, 1, -7954, -431068]$	$y^2+xy+y=x^3-7954x-431068$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[]$
443760.i2	443760i1	443760.i	443760i	$2$	$2$	$ 2^{4} \cdot 3 \cdot 5 \cdot 43^{2} $	$ - 2^{22} \cdot 3^{2} \cdot 5 \cdot 43^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$8.286743601$	$1$		$1$	$10644480$	$2.479496$	$-2305199161/1981440$	$0.87827$	$4.10318$	$[0, -1, 0, -814176, -445503744]$	$y^2=x^3-x^2-814176x-445503744$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[(720945/8, 610053513/8)]$
465690.cm2	465690cm1	465690.cm	465690cm	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 19^{2} \cdot 43 $	$ - 2^{10} \cdot 3^{2} \cdot 5 \cdot 19^{6} \cdot 43 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$3.907420773$	$1$		$3$	$1658880$	$1.377970$	$-2305199161/1981440$	$0.87827$	$3.07521$	$[1, 0, 0, -9935, 600057]$	$y^2+xy=x^3-9935x+600057$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[(-68, 1015)]$
468270.n2	468270n1	468270.n	468270n	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 43 $	$ - 2^{10} \cdot 3^{8} \cdot 5 \cdot 11^{6} \cdot 43 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$5160$	$12$	$0$	$1$	$1$		$1$	$2764800$	$1.654003$	$-2305199161/1981440$	$0.87827$	$3.32761$	$[1, -1, 0, -29970, -3140780]$	$y^2+xy=x^3-x^2-29970x-3140780$	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[]$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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Abelian varieties over $\F_{q}$

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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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