Learn more

Refine search


Results (12 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
33.1-a1 33.1-a \(\Q(\sqrt{33}) \) \( 3 \cdot 11 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $5.915402008$ $4.468126413$ 2.300502718 \( -\frac{181064514814}{99} a + \frac{610600481027}{99} \) \( \bigl[1\) , \( -a\) , \( a + 1\) , \( 943 a - 3179\) , \( 27552 a - 92919\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(943a-3179\right){x}+27552a-92919$
33.1-a2 33.1-a \(\Q(\sqrt{33}) \) \( 3 \cdot 11 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.957701004$ $2.234063206$ 2.300502718 \( \frac{9090072503}{5845851} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 44\) , \( 55\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+44{x}+55$
33.1-a3 33.1-a \(\Q(\sqrt{33}) \) \( 3 \cdot 11 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.478850502$ $8.936252827$ 2.300502718 \( \frac{169112377}{88209} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -11\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-11{x}$
33.1-a4 33.1-a \(\Q(\sqrt{33}) \) \( 3 \cdot 11 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $2.957701004$ $8.936252827$ 2.300502718 \( \frac{30664297}{297} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -6\) , \( -9\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-6{x}-9$
33.1-a5 33.1-a \(\Q(\sqrt{33}) \) \( 3 \cdot 11 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.739425251$ $8.936252827$ 2.300502718 \( \frac{347873904937}{395307} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -146\) , \( 621\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-146{x}+621$
33.1-a6 33.1-a \(\Q(\sqrt{33}) \) \( 3 \cdot 11 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $5.915402008$ $4.468126413$ 2.300502718 \( \frac{181064514814}{99} a + \frac{429535966213}{99} \) \( \bigl[1\) , \( a - 1\) , \( a\) , \( -944 a - 2235\) , \( -27553 a - 65366\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-944a-2235\right){x}-27553a-65366$
33.1-b1 33.1-b \(\Q(\sqrt{33}) \) \( 3 \cdot 11 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $30.13204906$ 0.327832279 \( -\frac{181064514814}{99} a + \frac{610600481027}{99} \) \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -a - 1\) , \( 9 a + 24\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-1\right){x}+9a+24$
33.1-b2 33.1-b \(\Q(\sqrt{33}) \) \( 3 \cdot 11 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.883253066$ 0.327832279 \( \frac{9090072503}{5845851} \) \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -16001 a + 53960\) , \( 639500 a - 2156578\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-16001a+53960\right){x}+639500a-2156578$
33.1-b3 33.1-b \(\Q(\sqrt{33}) \) \( 3 \cdot 11 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.533012266$ 0.327832279 \( \frac{169112377}{88209} \) \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 4239 a - 14295\) , \( 75585 a - 254898\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4239a-14295\right){x}+75585a-254898$
33.1-b4 33.1-b \(\Q(\sqrt{33}) \) \( 3 \cdot 11 \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $30.13204906$ 0.327832279 \( \frac{30664297}{297} \) \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 2399 a - 8090\) , \( -110030 a + 371048\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2399a-8090\right){x}-110030a+371048$
33.1-b5 33.1-b \(\Q(\sqrt{33}) \) \( 3 \cdot 11 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.883253066$ 0.327832279 \( \frac{347873904937}{395307} \) \( \bigl[1\) , \( -a\) , \( a\) , \( -53920 a - 127910\) , \( -11482951 a - 27240791\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-53920a-127910\right){x}-11482951a-27240791$
33.1-b6 33.1-b \(\Q(\sqrt{33}) \) \( 3 \cdot 11 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $30.13204906$ 0.327832279 \( \frac{181064514814}{99} a + \frac{429535966213}{99} \) \( \bigl[1\) , \( -a\) , \( a\) , \( -1\) , \( -10 a + 34\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}-{x}-10a+34$
  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.