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
1.1-a1 1.1-a \(\Q(\sqrt{7}) \) \( 1 \) 0 $\Z/4\Z$ $-7$ $N(\mathrm{U}(1))$ $1$ $26.16385905$ 0.309031537 \( -3375 \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -15 a - 40\) , \( 67 a + 177\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-15a-40\right){x}+67a+177$
1.1-a2 1.1-a \(\Q(\sqrt{7}) \) \( 1 \) 0 $\Z/4\Z$ $-7$ $N(\mathrm{U}(1))$ $1$ $26.16385905$ 0.309031537 \( -3375 \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 15 a - 40\) , \( -67 a + 177\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(15a-40\right){x}-67a+177$
1.1-a3 1.1-a \(\Q(\sqrt{7}) \) \( 1 \) 0 $\Z/2\Z$ $-112$ $N(\mathrm{U}(1))$ $1$ $6.540964764$ 0.309031537 \( -51954490735875 a + 137458661985000 \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -270 a - 715\) , \( 3223 a + 8527\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-270a-715\right){x}+3223a+8527$
1.1-a4 1.1-a \(\Q(\sqrt{7}) \) \( 1 \) 0 $\Z/4\Z$ $-112$ $N(\mathrm{U}(1))$ $1$ $26.16385905$ 0.309031537 \( -51954490735875 a + 137458661985000 \) \( \bigl[a\) , \( -1\) , \( a\) , \( -270 a - 718\) , \( -3223 a - 8529\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-270a-718\right){x}-3223a-8529$
1.1-a5 1.1-a \(\Q(\sqrt{7}) \) \( 1 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $-28$ $N(\mathrm{U}(1))$ $1$ $26.16385905$ 0.309031537 \( 16581375 \) \( \bigl[a\) , \( -1\) , \( a\) , \( -255 a - 678\) , \( -3669 a - 9709\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-255a-678\right){x}-3669a-9709$
1.1-a6 1.1-a \(\Q(\sqrt{7}) \) \( 1 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $-28$ $N(\mathrm{U}(1))$ $1$ $26.16385905$ 0.309031537 \( 16581375 \) \( \bigl[a\) , \( -1\) , \( a\) , \( 255 a - 678\) , \( 3669 a - 9709\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(255a-678\right){x}+3669a-9709$
1.1-a7 1.1-a \(\Q(\sqrt{7}) \) \( 1 \) 0 $\Z/2\Z$ $-112$ $N(\mathrm{U}(1))$ $1$ $6.540964764$ 0.309031537 \( 51954490735875 a + 137458661985000 \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 270 a - 715\) , \( -3223 a + 8527\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(270a-715\right){x}-3223a+8527$
1.1-a8 1.1-a \(\Q(\sqrt{7}) \) \( 1 \) 0 $\Z/4\Z$ $-112$ $N(\mathrm{U}(1))$ $1$ $26.16385905$ 0.309031537 \( 51954490735875 a + 137458661985000 \) \( \bigl[a\) , \( -1\) , \( a\) , \( 270 a - 718\) , \( 3223 a - 8529\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(270a-718\right){x}+3223a-8529$
  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.