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
37.1-a1 37.1-a 6.6.1397493.1 \( 37 \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.072226456$ $56104.43117$ 2.28521 \( \frac{262024065}{37} a^{5} - \frac{632903382}{37} a^{4} - \frac{1156055733}{37} a^{3} + \frac{1944483489}{37} a^{2} + \frac{1922787234}{37} a - \frac{448205859}{37} \) \( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 3 a - 1\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -4 a^{4} + 8 a^{3} + 9 a^{2} - 12 a + 2\) , \( -2 a^{4} + 3 a^{3} + 6 a^{2} - 4 a\bigr] \) ${y}^2+\left(a^{4}-2a^{3}-2a^{2}+3a-1\right){x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-3a+2\right){x}^{2}+\left(-4a^{4}+8a^{3}+9a^{2}-12a+2\right){x}-2a^{4}+3a^{3}+6a^{2}-4a$
37.1-b1 37.1-b 6.6.1397493.1 \( 37 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.058535038$ $7750.584670$ 2.30264 \( \frac{262024065}{37} a^{5} - \frac{632903382}{37} a^{4} - \frac{1156055733}{37} a^{3} + \frac{1944483489}{37} a^{2} + \frac{1922787234}{37} a - \frac{448205859}{37} \) \( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 4 a - 2\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 5 a^{2} + 8 a - 1\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 4 a - 2\) , \( 2 a^{5} - 5 a^{4} - 9 a^{3} + 17 a^{2} + 18 a - 6\) , \( 2 a^{5} - 5 a^{4} - 7 a^{3} + 12 a^{2} + 11 a - 3\bigr] \) ${y}^2+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+4a-2\right){x}{y}+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+4a-2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-5a^{3}+5a^{2}+8a-1\right){x}^{2}+\left(2a^{5}-5a^{4}-9a^{3}+17a^{2}+18a-6\right){x}+2a^{5}-5a^{4}-7a^{3}+12a^{2}+11a-3$
  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.