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
43.1-a1 43.1-a \(\Q(\zeta_{11})^+\) \( 43 \) 0 $\Z/7\Z$ $\mathrm{SU}(2)$ $1$ $5702.693977$ 0.961830659 \( -\frac{166996603}{43} a^{4} - \frac{153441602}{43} a^{3} + \frac{373478096}{43} a^{2} + \frac{215672423}{43} a - \frac{87008899}{43} \) \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 2 a - 2\) , \( a^{2} - 2\) , \( -a^{4} + 3 a^{2} - 2 a - 1\) , \( a^{4} - 3 a^{2} - a\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-2\right){x}^{2}+\left(-a^{4}+3a^{2}-2a-1\right){x}+a^{4}-3a^{2}-a$
  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.