Learn more

Refine search


Results (displaying both 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
171.1-f1 171.1-f \(\Q(\sqrt{19}) \) \( 3^{2} \cdot 19 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $5.203787826$ $0.565538563$ 0.675157357 \( -\frac{80836867580206264835}{124659} a + \frac{18545249299658286056}{6561} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 175 a - 860\) , \( 3178 a - 14456\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(175a-860\right){x}+3178a-14456$
171.1-i1 171.1-i \(\Q(\sqrt{19}) \) \( 3^{2} \cdot 19 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $9.423048177$ 1.080897756 \( -\frac{80836867580206264835}{124659} a + \frac{18545249299658286056}{6561} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 175 a - 862\) , \( -2828 a + 12735\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(175a-862\right){x}-2828a+12735$
  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.