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
49.1-b2 49.1-b 6.6.434581.1 \( 7^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.005414256$ $47699.10907$ 2.35052 \( \frac{160286323352}{7} a^{5} - 30307293282 a^{4} - \frac{784649541341}{7} a^{3} + \frac{270675690984}{7} a^{2} + \frac{824237004320}{7} a + \frac{236961171817}{7} \) \( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a + 1\) , \( 2 a^{5} - 3 a^{4} - 8 a^{3} + 4 a^{2} + 5 a - 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2}\) , \( 3 a^{5} - 8 a^{4} - 8 a^{3} + 21 a^{2} + 5 a - 7\) , \( -5 a^{5} + 13 a^{4} + 14 a^{3} - 36 a^{2} - 6 a + 15\bigr] \) ${y}^2+\left(a^{5}-a^{4}-5a^{3}+5a+1\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+4a^{2}\right){y}={x}^{3}+\left(2a^{5}-3a^{4}-8a^{3}+4a^{2}+5a-1\right){x}^{2}+\left(3a^{5}-8a^{4}-8a^{3}+21a^{2}+5a-7\right){x}-5a^{5}+13a^{4}+14a^{3}-36a^{2}-6a+15$
  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.