Learn more

Refine search


Results (6 matches)

  Download to        
Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
64.5-a1 64.5-a \(\Q(\sqrt{17}) \) \( 2^{6} \) $0$ $\Z/2\Z$ $1$ $7.156385278$ 0.867839188 \( -\frac{217}{16} a - \frac{339}{16} \) \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( a + 2\) , \( 3 a - 4\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(a+2\right){x}+3a-4$
64.5-b1 64.5-b \(\Q(\sqrt{17}) \) \( 2^{6} \) $0$ $\Z/4\Z$ $1$ $14.01972920$ 1.700141892 \( -\frac{217}{16} a - \frac{339}{16} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -2 a - 3\) , \( 2 a + 3\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-2a-3\right){x}+2a+3$
128.5-a1 128.5-a \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/4\Z$ $1$ $8.823675287$ 2.140055600 \( -\frac{217}{16} a - \frac{339}{16} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 2 a + 3\) , \( a + 3\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+3\right){x}+a+3$
128.5-d1 128.5-d \(\Q(\sqrt{17}) \) \( 2^{7} \) $1$ $\Z/2\Z$ $0.081969010$ $17.28603663$ 1.374613658 \( -\frac{217}{16} a - \frac{339}{16} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( a - 1\) , \( -197 a + 505\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(a-1\right){x}-197a+505$
512.2-e1 512.2-e \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/2\Z$ $1$ $6.239280630$ 1.513247827 \( -\frac{217}{16} a - \frac{339}{16} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 0\) , \( -8 a + 20\bigr] \) ${y}^2={x}^{3}+{x}^{2}-8a+20$
512.2-f1 512.2-f \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/2\Z$ $0.235830817$ $12.22307372$ 2.796510914 \( -\frac{217}{16} a - \frac{339}{16} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -5 a - 7\) , \( 50 a + 78\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-5a-7\right){x}+50a+78$
  Download to        

  *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.