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Results (6 matches)

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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-a3 64.5-a \(\Q(\sqrt{17}) \) \( 2^{6} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $14.31277055$ 0.867839188 \( \frac{159495}{4} a + \frac{481229}{4} \) \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -11 a - 15\) , \( -33 a - 51\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-11a-15\right){x}-33a-51$
64.5-b3 64.5-b \(\Q(\sqrt{17}) \) \( 2^{6} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $28.03945840$ 1.700141892 \( \frac{159495}{4} a + \frac{481229}{4} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 3 a - 5\) , \( 3 a - 7\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(3a-5\right){x}+3a-7$
128.5-a3 128.5-a \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $17.64735057$ 2.140055600 \( \frac{159495}{4} a + \frac{481229}{4} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 47 a - 126\) , \( -221 a + 563\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(47a-126\right){x}-221a+563$
128.5-d3 128.5-d \(\Q(\sqrt{17}) \) \( 2^{7} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.163938021$ $34.57207326$ 1.374613658 \( \frac{159495}{4} a + \frac{481229}{4} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -3 a - 7\) , \( a + 2\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-3a-7\right){x}+a+2$
512.2-e3 512.2-e \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $12.47856126$ 1.513247827 \( \frac{159495}{4} a + \frac{481229}{4} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -69 a - 108\) , \( -374 a - 584\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-69a-108\right){x}-374a-584$
512.2-f3 512.2-f \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.471661635$ $24.44614744$ 2.796510914 \( \frac{159495}{4} a + \frac{481229}{4} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 5 a - 15\) , \( -6 a + 22\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(5a-15\right){x}-6a+22$
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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.