Learn more

Refine search


Results (unique match)

  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
64.1-a6 64.1-a \(\Q(\zeta_{13})^+\) \( 2^{6} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.490374880$ 1.52868 \( \frac{1250637664527933}{32} a^{4} - \frac{1250637664527933}{32} a^{3} - \frac{1250637664527933}{8} a^{2} + \frac{1250637664527933}{16} a + \frac{871975048120043}{32} \) \( \bigl[1\) , \( 1\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 2\) , \( 28 a^{4} - 29 a^{3} - 112 a^{2} + 58 a + 58\) , \( 51 a^{4} - 52 a^{3} - 205 a^{2} + 104 a - 3\bigr] \) ${y}^2+{x}{y}+\left(a^{4}+a^{3}-4a^{2}-2a+2\right){y}={x}^{3}+{x}^{2}+\left(28a^{4}-29a^{3}-112a^{2}+58a+58\right){x}+51a^{4}-52a^{3}-205a^{2}+104a-3$
  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.