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Results (11 matches)

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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
171.1-a1 171.1-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $2.713137527$ 0.522143560 \( \frac{29840721}{6859} a - \frac{35267232}{6859} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -5 a - 5\) , \( 9 a + 3\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-5a-5\right){x}+9a+3$
3249.1-a1 3249.1-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.078091533$ 1.244872874 \( \frac{29840721}{6859} a - \frac{35267232}{6859} \) \( \bigl[1\) , \( a\) , \( 1\) , \( -17 a + 56\) , \( -156 a + 42\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-17a+56\right){x}-156a+42$
8379.1-a1 8379.1-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 7^{2} \cdot 19 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.190951457$ $1.776165441$ 2.349778965 \( \frac{29840721}{6859} a - \frac{35267232}{6859} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( -17 a + 19\) , \( 11 a + 34\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-17a+19\right){x}+11a+34$
8379.5-d1 8379.5-d \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 7^{2} \cdot 19 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.776165441$ 2.050939191 \( \frac{29840721}{6859} a - \frac{35267232}{6859} \) \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 19 a - 17\) , \( 46 a - 16\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(19a-17\right){x}+46a-16$
28899.1-d1 28899.1-d \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 13^{2} \cdot 19 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.870555393$ $0.752488959$ 3.025700258 \( \frac{29840721}{6859} a - \frac{35267232}{6859} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -6 a + 106\) , \( 525 a - 306\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-6a+106\right){x}+525a-306$
28899.5-c1 28899.5-c \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 13^{2} \cdot 19 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.752488959$ 2.606698220 \( \frac{29840721}{6859} a - \frac{35267232}{6859} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -3 a - 102\) , \( 54 a + 409\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-3a-102\right){x}+54a+409$
43776.1-b1 43776.1-b \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 19 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.178921751$ $1.174823011$ 2.912635915 \( \frac{29840721}{6859} a - \frac{35267232}{6859} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -48 a + 24\) , \( 112 a - 160\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-48a+24\right){x}+112a-160$
43776.1-o1 43776.1-o \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 19 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.195060975$ $0.678284381$ 3.743960357 \( \frac{29840721}{6859} a - \frac{35267232}{6859} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -75 a + 147\) , \( -552 a - 118\bigr] \) ${y}^2={x}^{3}+\left(-75a+147\right){x}-552a-118$
43776.1-q1 43776.1-q \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 19 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.174823011$ 2.713137527 \( \frac{29840721}{6859} a - \frac{35267232}{6859} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 25 a + 25\) , \( -63 a + 136\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(25a+25\right){x}-63a+136$
61731.3-c1 61731.3-c \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.078091533$ 1.244872874 \( \frac{29840721}{6859} a - \frac{35267232}{6859} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -16 a - 40\) , \( -81 a - 75\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-16a-40\right){x}-81a-75$
106875.1-a1 106875.1-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 5^{4} \cdot 19 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.542627505$ 1.879716818 \( \frac{29840721}{6859} a - \frac{35267232}{6859} \) \( \bigl[1\) , \( -1\) , \( a\) , \( -113 a - 117\) , \( 1106 a + 260\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-113a-117\right){x}+1106a+260$
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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.