Learn more

Refine search


Results (8 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
16.1-a2 16.1-a \(\Q(\sqrt{17}) \) \( 2^{4} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $13.66488855$ 0.828555571 \( -1552 a + 4288 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a + 3\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+3\right){x}$
64.2-a2 64.2-a \(\Q(\sqrt{17}) \) \( 2^{6} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $18.89585243$ 1.145729345 \( -1552 a + 4288 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 4 a - 8\) , \( -3 a + 7\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(4a-8\right){x}-3a+7$
64.3-a2 64.3-a \(\Q(\sqrt{17}) \) \( 2^{6} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $18.89585243$ 1.145729345 \( -1552 a + 4288 \) \( \bigl[0\) , \( a\) , \( 0\) , \( 4 a - 8\) , \( 3 a - 7\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(4a-8\right){x}+3a-7$
256.1-d2 256.1-d \(\Q(\sqrt{17}) \) \( 2^{8} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $26.12924634$ 1.584318273 \( -1552 a + 4288 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a + 3\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a+3\right){x}$
256.4-a2 256.4-a \(\Q(\sqrt{17}) \) \( 2^{8} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $13.36138539$ 1.620305978 \( -1552 a + 4288 \) \( \bigl[0\) , \( 1\) , \( 0\) , \( a - 1\) , \( a - 1\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(a-1\right){x}+a-1$
256.4-d2 256.4-d \(\Q(\sqrt{17}) \) \( 2^{8} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.163791520$ $18.47616728$ 2.201912694 \( -1552 a + 4288 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 20 a + 32\) , \( 128 a + 200\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(20a+32\right){x}+128a+200$
256.5-a2 256.5-a \(\Q(\sqrt{17}) \) \( 2^{8} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $13.36138539$ 1.620305978 \( -1552 a + 4288 \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 12 a + 19\) , \( -73 a - 114\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(12a+19\right){x}-73a-114$
256.5-d2 256.5-d \(\Q(\sqrt{17}) \) \( 2^{8} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.081895760$ $18.47616728$ 2.201912694 \( -1552 a + 4288 \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a - 1\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-1\right){x}$
  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.