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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
64.5-a4 64.5-a \(\Q(\sqrt{17}) \) \( 2^{6} \) $0$ $\Z/2\Z$ $1$ $7.156385278$ 0.867839188 \( \frac{23841914775}{2} a + \frac{37230413581}{2} \) \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -171 a - 265\) , \( -1835 a - 2865\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-171a-265\right){x}-1835a-2865$
64.5-b4 64.5-b \(\Q(\sqrt{17}) \) \( 2^{6} \) $0$ $\Z/2\Z$ $1$ $28.03945840$ 1.700141892 \( \frac{23841914775}{2} a + \frac{37230413581}{2} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 3 a - 15\) , \( -3 a + 11\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(3a-15\right){x}-3a+11$
128.5-a4 128.5-a \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z$ $1$ $4.411837643$ 2.140055600 \( \frac{23841914775}{2} a + \frac{37230413581}{2} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 97 a - 256\) , \( 459 a - 1181\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(97a-256\right){x}+459a-1181$
128.5-d4 128.5-d \(\Q(\sqrt{17}) \) \( 2^{7} \) $1$ $\Z/2\Z$ $0.327876043$ $17.28603663$ 1.374613658 \( \frac{23841914775}{2} a + \frac{37230413581}{2} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -33 a - 57\) , \( 141 a + 214\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-33a-57\right){x}+141a+214$
512.2-e4 512.2-e \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/2\Z$ $1$ $3.119640315$ 1.513247827 \( \frac{23841914775}{2} a + \frac{37230413581}{2} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 768 a - 1968\) , \( 7764 a - 19888\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(768a-1968\right){x}+7764a-19888$
512.2-f4 512.2-f \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/2\Z$ $0.943323270$ $12.22307372$ 2.796510914 \( \frac{23841914775}{2} a + \frac{37230413581}{2} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -5 a - 55\) , \( 90 a + 54\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-5a-55\right){x}+90a+54$
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  *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.