Learn more

Refine search


Results (8 matches)

  displayed columns for results
Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
29.2-a1 29.2-a 6.6.434581.1 \( 29 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.481331625$ 1.40442 \( \frac{23990737415377332964630580910385}{20511149} a^{5} - \frac{83448470178538726713593050182342}{20511149} a^{4} + \frac{27404100394439215638449912012936}{20511149} a^{3} + \frac{79440505494694377085636578668150}{20511149} a^{2} - \frac{21478877574700214871390186433119}{20511149} a - \frac{16227917704608257854366710709033}{20511149} \) \( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} + a\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a + 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a - 2\) , \( 105 a^{5} - 194 a^{4} - 403 a^{3} + 388 a^{2} + 317 a - 39\) , \( 274 a^{5} - 510 a^{4} - 1086 a^{3} + 1108 a^{2} + 922 a - 292\bigr] \) ${y}^2+\left(a^{5}-2a^{4}-3a^{3}+4a^{2}+a\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+4a-2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+3a+1\right){x}^{2}+\left(105a^{5}-194a^{4}-403a^{3}+388a^{2}+317a-39\right){x}+274a^{5}-510a^{4}-1086a^{3}+1108a^{2}+922a-292$
29.2-a2 29.2-a 6.6.434581.1 \( 29 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.481331625$ 1.40442 \( \frac{49517926748131685406029400211528}{8629188747598184440949} a^{5} - \frac{118018847388936022519470695147732}{8629188747598184440949} a^{4} - \frac{152677702645431525968546689515834}{8629188747598184440949} a^{3} + \frac{305537605996119022369549489960117}{8629188747598184440949} a^{2} + \frac{81336262405475238261621776760232}{8629188747598184440949} a - \frac{129867942024508507713764721191699}{8629188747598184440949} \) \( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a + 1\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 8 a^{2} - a + 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} - 1\) , \( 130 a^{5} - 309 a^{4} - 397 a^{3} + 796 a^{2} + 211 a - 347\) , \( 980 a^{5} - 2356 a^{4} - 3009 a^{3} + 6089 a^{2} + 1599 a - 2603\bigr] \) ${y}^2+\left(a^{5}-a^{4}-5a^{3}+5a+1\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+4a^{2}-1\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+2a^{3}-8a^{2}-a+3\right){x}^{2}+\left(130a^{5}-309a^{4}-397a^{3}+796a^{2}+211a-347\right){x}+980a^{5}-2356a^{4}-3009a^{3}+6089a^{2}+1599a-2603$
29.2-a3 29.2-a 6.6.434581.1 \( 29 \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $23145.80664$ 1.40442 \( -\frac{144127121}{29} a^{5} + \frac{191914084}{29} a^{4} + \frac{703418442}{29} a^{3} - \frac{248156687}{29} a^{2} - \frac{735776072}{29} a - \frac{210483929}{29} \) \( \bigl[2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} + 2 a - 3\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 3 a - 3\) , \( 3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 4\) , \( -4 a^{5} + 8 a^{4} + 14 a^{3} - 15 a^{2} - 9 a - 1\) , \( 2 a^{5} - a^{4} - 13 a^{3} - 2 a^{2} + 15 a + 4\bigr] \) ${y}^2+\left(2a^{5}-5a^{4}-5a^{3}+11a^{2}+2a-3\right){x}{y}+\left(3a^{5}-7a^{4}-8a^{3}+15a^{2}+a-4\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+3a-3\right){x}^{2}+\left(-4a^{5}+8a^{4}+14a^{3}-15a^{2}-9a-1\right){x}+2a^{5}-a^{4}-13a^{3}-2a^{2}+15a+4$
29.2-a4 29.2-a 6.6.434581.1 \( 29 \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $23145.80664$ 1.40442 \( -\frac{5183334}{24389} a^{5} - \frac{23483887}{24389} a^{4} + \frac{12947976}{24389} a^{3} + \frac{55965587}{24389} a^{2} - \frac{18648968}{24389} a - \frac{11368635}{24389} \) \( \bigl[3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + 2 a - 4\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 3 a - 1\) , \( 3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 3\) , \( 0\) , \( 0\bigr] \) ${y}^2+\left(3a^{5}-7a^{4}-8a^{3}+15a^{2}+2a-4\right){x}{y}+\left(3a^{5}-7a^{4}-8a^{3}+15a^{2}+a-3\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-3a-1\right){x}^{2}$
29.2-b1 29.2-b 6.6.434581.1 \( 29 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $644.7601049$ 0.978054 \( \frac{163462751293821202}{17249876309} a^{5} - \frac{111681935365476176}{17249876309} a^{4} - \frac{801547698431869756}{17249876309} a^{3} - \frac{236802257690773383}{17249876309} a^{2} + \frac{343172721161084264}{17249876309} a + \frac{124367830204079372}{17249876309} \) \( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 4 a - 2\) , \( a^{3} - 2 a^{2} - a + 1\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} - 4\) , \( -a^{5} + 3 a^{4} + a^{3} - 6 a^{2} + a + 1\) , \( 2 a^{5} - 5 a^{4} - 4 a^{3} + 12 a^{2} - a - 4\bigr] \) ${y}^2+\left(2a^{5}-4a^{4}-7a^{3}+9a^{2}+4a-2\right){x}{y}+\left(2a^{5}-5a^{4}-5a^{3}+12a^{2}-4\right){y}={x}^{3}+\left(a^{3}-2a^{2}-a+1\right){x}^{2}+\left(-a^{5}+3a^{4}+a^{3}-6a^{2}+a+1\right){x}+2a^{5}-5a^{4}-4a^{3}+12a^{2}-a-4$
29.2-c1 29.2-c 6.6.434581.1 \( 29 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $790.5898677$ 1.19927 \( -\frac{328404104530776}{29} a^{5} + \frac{906495307821765}{29} a^{4} + \frac{624404013794482}{29} a^{3} - \frac{2116757679534948}{29} a^{2} + \frac{295763857235945}{29} a + \frac{431937635205700}{29} \) \( \bigl[a^{5} - a^{4} - 5 a^{3} + a^{2} + 3 a + 1\) , \( -2 a^{5} + 5 a^{4} + 4 a^{3} - 10 a^{2} + a + 1\) , \( 2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 3 a - 3\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 2 a^{2} + 11 a + 4\) , \( 6 a^{5} - 8 a^{4} - 29 a^{3} + 11 a^{2} + 28 a + 6\bigr] \) ${y}^2+\left(a^{5}-a^{4}-5a^{3}+a^{2}+3a+1\right){x}{y}+\left(2a^{5}-4a^{4}-7a^{3}+9a^{2}+3a-3\right){y}={x}^{3}+\left(-2a^{5}+5a^{4}+4a^{3}-10a^{2}+a+1\right){x}^{2}+\left(2a^{5}-2a^{4}-11a^{3}+2a^{2}+11a+4\right){x}+6a^{5}-8a^{4}-29a^{3}+11a^{2}+28a+6$
29.2-d1 29.2-d 6.6.434581.1 \( 29 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.000776528$ $95834.38159$ 2.03196 \( \frac{2227643651}{24389} a^{5} - \frac{6600751439}{24389} a^{4} - \frac{5119963945}{24389} a^{3} + \frac{20357393301}{24389} a^{2} + \frac{411157352}{24389} a - \frac{13119189482}{24389} \) \( \bigl[a^{5} - a^{4} - 5 a^{3} + a^{2} + 3 a\) , \( -2 a^{5} + 4 a^{4} + 7 a^{3} - 8 a^{2} - 5 a + 2\) , \( 3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 2\) , \( -a^{5} + 5 a^{3} + 6 a^{2} - 2 a - 3\) , \( -4 a^{5} + 4 a^{4} + 18 a^{3} + a^{2} - 8 a - 3\bigr] \) ${y}^2+\left(a^{5}-a^{4}-5a^{3}+a^{2}+3a\right){x}{y}+\left(3a^{5}-6a^{4}-10a^{3}+12a^{2}+5a-2\right){y}={x}^{3}+\left(-2a^{5}+4a^{4}+7a^{3}-8a^{2}-5a+2\right){x}^{2}+\left(-a^{5}+5a^{3}+6a^{2}-2a-3\right){x}-4a^{5}+4a^{4}+18a^{3}+a^{2}-8a-3$
29.2-d2 29.2-d 6.6.434581.1 \( 29 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.002329586$ $95834.38159$ 2.03196 \( -\frac{48945886}{29} a^{5} + \frac{138712716}{29} a^{4} - \frac{41434329}{29} a^{3} - \frac{133295612}{29} a^{2} + \frac{35939234}{29} a + \frac{27409508}{29} \) \( \bigl[a^{5} - a^{4} - 5 a^{3} + a^{2} + 3 a + 1\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 4 a^{2} - 5 a + 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 2\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 3 a + 5\) , \( a^{5} - 8 a^{3} - a^{2} + 9 a + 5\bigr] \) ${y}^2+\left(a^{5}-a^{4}-5a^{3}+a^{2}+3a+1\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-4a^{2}-5a+2\right){x}^{2}+\left(a^{4}-3a^{3}-2a^{2}+3a+5\right){x}+a^{5}-8a^{3}-a^{2}+9a+5$
  displayed columns for results

  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.