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Results (8 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-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-a2 64.5-a \(\Q(\sqrt{17}) \) \( 2^{6} \) $0$ $\Z/2\Z$ $1$ $7.156385278$ 0.867839188 \( -\frac{1592342311}{2} a + \frac{4078872403}{2} \) \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -16 a - 25\) , \( -4 a - 9\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-16a-25\right){x}-4a-9$
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-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-b1 64.5-b \(\Q(\sqrt{17}) \) \( 2^{6} \) $0$ $\Z/4\Z$ $1$ $14.01972920$ 1.700141892 \( -\frac{217}{16} a - \frac{339}{16} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -2 a - 3\) , \( 2 a + 3\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-2a-3\right){x}+2a+3$
64.5-b2 64.5-b \(\Q(\sqrt{17}) \) \( 2^{6} \) $0$ $\Z/2\Z$ $1$ $7.009864600$ 1.700141892 \( -\frac{1592342311}{2} a + \frac{4078872403}{2} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 38 a - 95\) , \( 180 a - 461\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(38a-95\right){x}+180a-461$
64.5-b3 64.5-b \(\Q(\sqrt{17}) \) \( 2^{6} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $28.03945840$ 1.700141892 \( \frac{159495}{4} a + \frac{481229}{4} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 3 a - 5\) , \( 3 a - 7\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(3a-5\right){x}+3a-7$
64.5-b4 64.5-b \(\Q(\sqrt{17}) \) \( 2^{6} \) $0$ $\Z/2\Z$ $1$ $28.03945840$ 1.700141892 \( \frac{23841914775}{2} a + \frac{37230413581}{2} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 3 a - 15\) , \( -3 a + 11\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(3a-15\right){x}-3a+11$
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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.