Learn more

Refine search


Results (4 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
41.1-a1 41.1-a \(\Q(\zeta_{7})^+\) \( 41 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.357827366$ 0.484938345 \( \frac{182915726357803972950650}{13422659310152401} a^{2} - \frac{357571850055303381213985}{13422659310152401} a + \frac{50482569444763032743584}{13422659310152401} \) \( \bigl[1\) , \( -a^{2} + 3\) , \( 1\) , \( 99 a^{2} - 10 a - 348\) , \( 952 a^{2} - 216 a - 2798\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(99a^{2}-10a-348\right){x}+952a^{2}-216a-2798$
41.1-a2 41.1-a \(\Q(\zeta_{7})^+\) \( 41 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.715654732$ 0.484938345 \( -\frac{1469483101129546552831}{115856201} a^{2} + \frac{815501597212588028076}{115856201} a + \frac{3301898555789100922576}{115856201} \) \( \bigl[1\) , \( -a^{2} + 3\) , \( 1\) , \( 144 a^{2} - 75 a - 328\) , \( 1172 a^{2} - 646 a - 2650\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(144a^{2}-75a-328\right){x}+1172a^{2}-646a-2650$
41.1-a3 41.1-a \(\Q(\zeta_{7})^+\) \( 41 \) 0 $\Z/10\Z$ $\mathrm{SU}(2)$ $1$ $339.4568415$ 0.484938345 \( -\frac{968480}{41} a^{2} - \frac{734681}{41} a + \frac{589810}{41} \) \( \bigl[1\) , \( -a^{2} + 3\) , \( 1\) , \( -a^{2} + 2\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-a^{2}+2\right){x}$
41.1-a4 41.1-a \(\Q(\zeta_{7})^+\) \( 41 \) 0 $\Z/10\Z$ $\mathrm{SU}(2)$ $1$ $169.7284207$ 0.484938345 \( \frac{3693705667625}{1681} a^{2} + \frac{2962060985575}{1681} a - \frac{2049821964241}{1681} \) \( \bigl[1\) , \( -a^{2} + 3\) , \( 1\) , \( -6 a^{2} + 7\) , \( 2 a^{2} + 4 a + 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-6a^{2}+7\right){x}+2a^{2}+4a+2$
  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.