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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
23808.1-a1 23808.1-a \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3 \cdot 31 \) $0$ $\Z/2\Z$ $1$ $5.017906947$ 1.448544963 \( \frac{2998016}{93} a - \frac{425728}{93} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -2 a - 2\) , \( a + 1\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-2a-2\right){x}+a+1$
23808.1-a2 23808.1-a \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3 \cdot 31 \) $0$ $\Z/4\Z$ $1$ $1.254476736$ 1.448544963 \( \frac{2499774004}{2770563} a + \frac{1516133908}{2770563} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 18 a + 13\) , \( a - 50\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(18a+13\right){x}+a-50$
23808.1-a3 23808.1-a \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3 \cdot 31 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $2.508953473$ 1.448544963 \( -\frac{4637360}{2883} a + \frac{2720576}{961} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -2 a - 7\) , \( -3 a - 6\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-2a-7\right){x}-3a-6$
23808.1-a4 23808.1-a \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3 \cdot 31 \) $0$ $\Z/2\Z$ $1$ $1.254476736$ 1.448544963 \( -\frac{1160560100}{279} a + \frac{385205612}{279} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -22 a - 107\) , \( -183 a - 410\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-22a-107\right){x}-183a-410$
23808.1-b1 23808.1-b \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3 \cdot 31 \) $1$ $\Z/2\Z$ $1.240179320$ $5.017906947$ 3.592911016 \( \frac{2998016}{93} a - \frac{425728}{93} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 4 a - 2\) , \( -a - 1\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(4a-2\right){x}-a-1$
23808.1-b2 23808.1-b \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3 \cdot 31 \) $1$ $\Z/2\Z$ $1.240179320$ $1.254476736$ 3.592911016 \( \frac{2499774004}{2770563} a + \frac{1516133908}{2770563} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -31 a + 18\) , \( -a + 50\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-31a+18\right){x}-a+50$
23808.1-b3 23808.1-b \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3 \cdot 31 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.620089660$ $2.508953473$ 3.592911016 \( -\frac{4637360}{2883} a + \frac{2720576}{961} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 9 a - 2\) , \( 3 a + 6\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(9a-2\right){x}+3a+6$
23808.1-b4 23808.1-b \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3 \cdot 31 \) $1$ $\Z/4\Z$ $1.240179320$ $1.254476736$ 3.592911016 \( -\frac{1160560100}{279} a + \frac{385205612}{279} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 129 a - 22\) , \( 183 a + 410\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(129a-22\right){x}+183a+410$
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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.