Elliptic curve search results

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

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Results (1-50 of 37334 matches)

 

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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
5077.a1	5077a1	5077.a	5077a	$1$	$1$	\( 5077 \)	\( 5077 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.417143558$	$1$		$36$	$1984$	$-0.561390$	$37933056/5077$	$[0, 0, 1, -7, 6]$	\(y^2+y=x^3-7x+6\)
11197.a1	11197a1	11197.a	11197a	$1$	$1$	\( 11197 \)	\( 11197 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.868421953$	$1$		$24$	$2080$	$-0.532441$	$20346417/11197$	$[1, -1, 1, -6, 0]$	\(y^2+xy+y=x^3-x^2-6x\)
11642.a1	11642a1	11642.a	11642a	$1$	$1$	\( 2 \cdot 5821 \)	\( 2^{2} \cdot 5821 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.421965530$	$1$		$38$	$4624$	$-0.403039$	$469097433/23284$	$[1, -1, 0, -16, 28]$	\(y^2+xy=x^3-x^2-16x+28\)
12279.a1	12279a1	12279.a	12279a	$1$	$1$	\( 3 \cdot 4093 \)	\( 3^{2} \cdot 4093 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.430420237$	$1$		$36$	$4320$	$-0.418653$	$122023936/36837$	$[0, -1, 1, -10, 12]$	\(y^2+y=x^3-x^2-10x+12\)
13766.a1	13766a1	13766.a	13766a	$1$	$1$	\( 2 \cdot 6883 \)	\( - 2^{4} \cdot 6883 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.554302953$	$1$		$34$	$4896$	$-0.288401$	$-1263214441/110128$	$[1, 0, 1, -23, 42]$	\(y^2+xy+y=x^3-23x+42\)
16811.a1	16811a1	16811.a	16811a	$1$	$1$	\( 16811 \)	\( -16811 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.847002239$	$1$		$30$	$4160$	$-0.509805$	$-110592/16811$	$[0, 0, 1, -1, 6]$	\(y^2+y=x^3-x+6\)
18097.a1	18097b1	18097.a	18097b	$1$	$1$	\( 18097 \)	\( 18097 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1.107557875$	$1$		$22$	$2160$	$-0.461119$	$111284641/18097$	$[1, 1, 1, -10, 6]$	\(y^2+xy+y=x^3+x^2-10x+6\)
18562.a1	18562c1	18562.a	18562c	$1$	$1$	\( 2 \cdot 9281 \)	\( 2^{2} \cdot 9281 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.566748574$	$1$		$30$	$4720$	$-0.360919$	$822656953/37124$	$[1, 0, 1, -20, 30]$	\(y^2+xy+y=x^3-20x+30\)
18745.a1	18745a1	18745.a	18745a	$1$	$1$	\( 5 \cdot 23 \cdot 163 \)	\( - 5^{2} \cdot 23^{2} \cdot 163 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.309889177$	$1$		$38$	$10976$	$0.053575$	$-346540109824/2155675$	$[0, 1, 1, -146, 636]$	\(y^2+y=x^3+x^2-146x+636\)
20888.a1	20888a1	20888.a	20888a	$1$	$1$	\( 2^{3} \cdot 7 \cdot 373 \)	\( 2^{8} \cdot 7^{2} \cdot 373 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.273664702$	$1$		$52$	$18176$	$-0.014875$	$60742656/18277$	$[0, 0, 0, -52, 100]$	\(y^2=x^3-52x+100\)
21443.a1	21443a1	21443.a	21443a	$1$	$1$	\( 41 \cdot 523 \)	\( - 41 \cdot 523 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1.245101124$	$1$		$20$	$2912$	$-0.477383$	$-13997521/21443$	$[1, 1, 1, -5, 6]$	\(y^2+xy+y=x^3+x^2-5x+6\)
21858.a1	21858a1	21858.a	21858a	$1$	$1$	\( 2 \cdot 3 \cdot 3643 \)	\( - 2^{2} \cdot 3^{2} \cdot 3643 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.360627681$	$1$		$44$	$9984$	$-0.244728$	$-3803721481/131148$	$[1, 1, 0, -32, 60]$	\(y^2+xy=x^3+x^2-32x+60\)
22481.b1	22481a1	22481.b	22481a	$1$	$1$	\( 22481 \)	\( -22481 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$2.021307690$	$1$		$20$	$2152$	$-0.477118$	$27818127/22481$	$[1, -1, 1, 6, 2]$	\(y^2+xy+y=x^3-x^2+6x+2\)
22696.a1	22696a1	22696.a	22696a	$1$	$1$	\( 2^{3} \cdot 2837 \)	\( 2^{8} \cdot 2837 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.483007207$	$1$		$40$	$8768$	$-0.033181$	$504871936/2837$	$[0, 1, 0, -105, 379]$	\(y^2=x^3+x^2-105x+379\)
24301.a1	24301a1	24301.a	24301a	$1$	$1$	\( 19 \cdot 1279 \)	\( - 19 \cdot 1279 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1.088564602$	$1$		$22$	$3584$	$-0.282316$	$-9434056897/24301$	$[1, 0, 0, -44, 109]$	\(y^2+xy=x^3-44x+109\)
24546.a1	24546a1	24546.a	24546a	$1$	$1$	\( 2 \cdot 3 \cdot 4091 \)	\( - 2^{2} \cdot 3^{2} \cdot 4091 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.388822663$	$1$		$38$	$9984$	$-0.218565$	$-6826561273/147276$	$[1, 1, 0, -39, 81]$	\(y^2+xy=x^3+x^2-39x+81\)
24646.a1	24646b1	24646.a	24646b	$1$	$1$	\( 2 \cdot 12323 \)	\( 2^{2} \cdot 12323 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.661670817$	$1$		$34$	$5392$	$-0.386887$	$217081801/49292$	$[1, 0, 1, -13, 12]$	\(y^2+xy+y=x^3-13x+12\)
25071.a1	25071a1	25071.a	25071a	$1$	$1$	\( 3 \cdot 61 \cdot 137 \)	\( 3^{4} \cdot 61 \cdot 137 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.880641968$	$1$		$32$	$8960$	$-0.184552$	$1593413632/676917$	$[0, -1, 1, -24, -16]$	\(y^2+y=x^3-x^2-24x-16\)
25383.a1	25383a1	25383.a	25383a	$1$	$1$	\( 3 \cdot 8461 \)	\( 3^{2} \cdot 8461 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.550031411$	$1$		$34$	$7680$	$-0.272481$	$3738308608/76149$	$[0, -1, 1, -32, 80]$	\(y^2+y=x^3-x^2-32x+80\)
25451.c1	25451a1	25451.c	25451a	$1$	$1$	\( 31 \cdot 821 \)	\( - 31^{2} \cdot 821 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.850609947$	$1$		$24$	$4160$	$-0.104242$	$-17434421857/788981$	$[1, 1, 1, -54, 136]$	\(y^2+xy+y=x^3+x^2-54x+136\)
25751.a1	25751a1	25751.a	25751a	$1$	$1$	\( 11 \cdot 2341 \)	\( - 11^{2} \cdot 2341 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.705951665$	$1$		$26$	$3456$	$-0.188021$	$-6570725617/283261$	$[1, 0, 0, -39, 94]$	\(y^2+xy=x^3-39x+94\)
26171.a1	26171a1	26171.a	26171a	$1$	$1$	\( 26171 \)	\( -26171 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.767411060$	$1$		$30$	$8752$	$-0.265061$	$-13011038208/26171$	$[0, 0, 1, -49, 132]$	\(y^2+y=x^3-49x+132\)
26198.a1	26198a1	26198.a	26198a	$1$	$1$	\( 2 \cdot 13099 \)	\( 2^{4} \cdot 13099 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.698734427$	$1$		$34$	$12704$	$-0.283459$	$469097433/209584$	$[1, -1, 0, -16, 16]$	\(y^2+xy=x^3-x^2-16x+16\)
26284.a1	26284a1	26284.a	26284a	$1$	$1$	\( 2^{2} \cdot 6571 \)	\( - 2^{4} \cdot 6571 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.666468303$	$1$		$32$	$5256$	$-0.342361$	$-5619712/6571$	$[0, 1, 0, -9, 16]$	\(y^2=x^3+x^2-9x+16\)
26743.a1	26743a1	26743.a	26743a	$1$	$1$	\( 47 \cdot 569 \)	\( - 47 \cdot 569 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$2.082972164$	$1$		$22$	$2480$	$-0.464068$	$23639903/26743$	$[1, 0, 0, 6, -5]$	\(y^2+xy=x^3+6x-5\)
27262.a1	27262c1	27262.a	27262c	$1$	$1$	\( 2 \cdot 43 \cdot 317 \)	\( 2^{13} \cdot 43 \cdot 317 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.297872072$	$1$		$50$	$65312$	$0.289154$	$1466390638881/111665152$	$[1, -1, 1, -237, 1365]$	\(y^2+xy+y=x^3-x^2-237x+1365\)
27382.a1	27382a1	27382.a	27382a	$1$	$1$	\( 2 \cdot 13691 \)	\( 2^{2} \cdot 13691 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.781504154$	$1$		$28$	$5664$	$-0.401107$	$95443993/54764$	$[1, 0, 1, -10, 0]$	\(y^2+xy+y=x^3-10x\)
27448.a1	27448d1	27448.a	27448d	$1$	$1$	\( 2^{3} \cdot 47 \cdot 73 \)	\( - 2^{8} \cdot 47 \cdot 73 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.480174625$	$1$		$38$	$14080$	$-0.058945$	$-212992848/3431$	$[0, 0, 0, -79, 274]$	\(y^2=x^3-79x+274\)
27584.a1	27584bd1	27584.a	27584bd	$1$	$1$	\( 2^{6} \cdot 431 \)	\( - 2^{12} \cdot 431 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.625203696$	$1$		$38$	$12032$	$-0.122108$	$-1728/431$	$[0, 0, 0, -4, 64]$	\(y^2=x^3-4x+64\)
27746.a1	27746a1	27746.a	27746a	$1$	$1$	\( 2 \cdot 13873 \)	\( - 2^{4} \cdot 13873 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.849672446$	$1$		$30$	$5824$	$-0.281223$	$-169112377/221968$	$[1, 0, 1, -12, 26]$	\(y^2+xy+y=x^3-12x+26\)
27747.a1	27747c1	27747.a	27747c	$1$	$1$	\( 3^{2} \cdot 3083 \)	\( - 3^{8} \cdot 3083 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.494966291$	$1$		$38$	$27776$	$0.247391$	$-5304438784/27747$	$[0, 0, 1, -327, 2286]$	\(y^2+y=x^3-327x+2286\)
27773.a1	27773a1	27773.a	27773a	$1$	$1$	\( 27773 \)	\( -27773 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1.006755713$	$1$		$24$	$5536$	$-0.367348$	$-979146657/27773$	$[1, -1, 1, -21, 42]$	\(y^2+xy+y=x^3-x^2-21x+42\)
27808.a1	27808a1	27808.a	27808a	$1$	$1$	\( 2^{5} \cdot 11 \cdot 79 \)	\( 2^{12} \cdot 11^{2} \cdot 79 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.326366893$	$1$		$46$	$34560$	$0.287956$	$1302170688/9559$	$[0, 0, 0, -364, 2656]$	\(y^2=x^3-364x+2656\)
28042.a1	28042b1	28042.a	28042b	$1$	$1$	\( 2 \cdot 7 \cdot 2003 \)	\( - 2^{2} \cdot 7^{2} \cdot 2003 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.370852369$	$1$		$42$	$16416$	$-0.221667$	$-781229961/392588$	$[1, -1, 0, -19, 49]$	\(y^2+xy=x^3-x^2-19x+49\)
28498.a1	28498a1	28498.a	28498a	$1$	$1$	\( 2 \cdot 14249 \)	\( - 2^{2} \cdot 14249 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.663906286$	$1$		$30$	$8512$	$-0.367279$	$-253636137/56996$	$[1, -1, 0, -13, 25]$	\(y^2+xy=x^3-x^2-13x+25\)
28571.a1	28571a1	28571.a	28571a	$1$	$1$	\( 28571 \)	\( -28571 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1.223126117$	$1$		$24$	$4240$	$-0.458493$	$-8998912/28571$	$[0, -1, 1, -4, 10]$	\(y^2+y=x^3-x^2-4x+10\)
29157.a1	29157b1	29157.a	29157b	$1$	$1$	\( 3 \cdot 9719 \)	\( 3^{9} \cdot 9719 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.310792976$	$1$		$50$	$54864$	$0.318799$	$1535202758656/191299077$	$[0, 1, 1, -240, 1190]$	\(y^2+y=x^3+x^2-240x+1190\)
30064.a1	30064c1	30064.a	30064c	$1$	$1$	\( 2^{4} \cdot 1879 \)	\( - 2^{10} \cdot 1879 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.593367916$	$1$		$36$	$10752$	$0.053912$	$-381775972/1879$	$[0, 1, 0, -152, 676]$	\(y^2=x^3+x^2-152x+676\)
30148.a1	30148b1	30148.a	30148b	$1$	$1$	\( 2^{2} \cdot 7537 \)	\( 2^{4} \cdot 7537 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.541379483$	$1$		$34$	$13848$	$-0.236238$	$350113536/7537$	$[0, 0, 0, -37, 85]$	\(y^2=x^3-37x+85\)
30376.a1	30376a1	30376.a	30376a	$1$	$1$	\( 2^{3} \cdot 3797 \)	\( 2^{8} \cdot 3797 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.682098529$	$1$		$36$	$9152$	$-0.160055$	$7023616/3797$	$[0, 1, 0, -25, -21]$	\(y^2=x^3+x^2-25x-21\)
30446.c1	30446a1	30446.c	30446a	$1$	$1$	\( 2 \cdot 13 \cdot 1171 \)	\( 2^{4} \cdot 13^{2} \cdot 1171 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.673965740$	$1$		$34$	$9856$	$-0.058079$	$6826561273/3166384$	$[1, 1, 0, -39, -59]$	\(y^2+xy=x^3+x^2-39x-59\)
30487.b1	30487a1	30487.b	30487a	$1$	$1$	\( 43 \cdot 709 \)	\( 43^{2} \cdot 709 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1.198104879$	$1$		$18$	$8576$	$-0.135103$	$2427715584/1310941$	$[0, 0, 1, -28, -15]$	\(y^2+y=x^3-28x-15\)
30767.a1	30767d1	30767.a	30767d	$1$	$1$	\( 11 \cdot 2797 \)	\( 11^{2} \cdot 2797 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.565500783$	$1$		$34$	$13632$	$-0.203469$	$3294646272/338437$	$[0, 0, 1, -31, 60]$	\(y^2+y=x^3-31x+60\)
30815.a1	30815a1	30815.a	30815a	$1$	$1$	\( 5 \cdot 6163 \)	\( - 5^{2} \cdot 6163 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.608306637$	$1$		$32$	$8096$	$-0.291671$	$-481890304/154075$	$[0, 1, 1, -16, 26]$	\(y^2+y=x^3+x^2-16x+26\)
31478.a1	31478b1	31478.a	31478b	$1$	$1$	\( 2 \cdot 15739 \)	\( - 2^{2} \cdot 15739 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.812053962$	$1$		$32$	$5536$	$-0.395512$	$-10218313/62956$	$[1, 0, 1, -5, 12]$	\(y^2+xy+y=x^3-5x+12\)
31737.a1	31737a1	31737.a	31737a	$1$	$1$	\( 3 \cdot 71 \cdot 149 \)	\( - 3^{2} \cdot 71 \cdot 149 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.624153583$	$1$		$32$	$9408$	$-0.254405$	$-4475809792/95211$	$[0, -1, 1, -34, 90]$	\(y^2+y=x^3-x^2-34x+90\)
31814.a1	31814a1	31814.a	31814a	$1$	$1$	\( 2 \cdot 15907 \)	\( - 2^{2} \cdot 15907 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.883060198$	$1$		$30$	$5808$	$-0.398380$	$1685159/63628$	$[1, 0, 1, 2, 12]$	\(y^2+xy+y=x^3+2x+12\)
32192.a1	32192e1	32192.a	32192e	$1$	$1$	\( 2^{6} \cdot 503 \)	\( - 2^{12} \cdot 503 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.544958568$	$1$		$38$	$18688$	$-0.055702$	$-3796416/503$	$[0, 0, 0, -52, 160]$	\(y^2=x^3-52x+160\)
32244.a1	32244c1	32244.a	32244c	$1$	$1$	\( 2^{2} \cdot 3 \cdot 2687 \)	\( - 2^{4} \cdot 3^{2} \cdot 2687 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.394959406$	$1$		$40$	$13344$	$-0.193628$	$-192914176/24183$	$[0, -1, 0, -30, 81]$	\(y^2=x^3-x^2-30x+81\)
32276.a1	32276b1	32276.a	32276b	$1$	$1$	\( 2^{2} \cdot 8069 \)	\( 2^{4} \cdot 8069 \)	$3$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.679926753$	$1$		$32$	$5136$	$-0.306302$	$35995648/8069$	$[0, 1, 0, -17, 16]$	\(y^2=x^3+x^2-17x+16\)