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Results (28 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
6400.1-a1 6400.1-a \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.305697557$ $2.070728854$ 1.461889572 \( \frac{1293836}{25} a - \frac{1028876}{25} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -21 a - 2\) , \( -39 a + 13\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-21a-2\right){x}-39a+13$
6400.1-a2 6400.1-a \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.152848778$ $4.141457709$ 1.461889572 \( -\frac{5776}{5} a + 1728 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -a - 2\) , \( a + 1\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-a-2\right){x}+a+1$
6400.1-b1 6400.1-b \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.305697557$ $2.070728854$ 1.461889572 \( -\frac{1293836}{25} a + \frac{52992}{5} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 21 a - 23\) , \( 39 a - 26\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(21a-23\right){x}+39a-26$
6400.1-b2 6400.1-b \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.152848778$ $4.141457709$ 1.461889572 \( \frac{5776}{5} a + \frac{2864}{5} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( a - 3\) , \( -a + 2\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(a-3\right){x}-a+2$
6400.1-c1 6400.1-c \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.261119886$ $3.375263347$ 2.035386900 \( -\frac{108}{5} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( a - 1\) , \( 4 a - 2\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}+4a-2$
6400.1-c2 6400.1-c \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.522239772$ $1.687631673$ 2.035386900 \( \frac{3721734}{25} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 41 a - 41\) , \( 116 a - 58\bigr] \) ${y}^2={x}^{3}+\left(41a-41\right){x}+116a-58$
6400.1-d1 6400.1-d \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.221079403$ 1.409981044 \( -\frac{1860867}{320} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 42 a - 41\) , \( -119 a + 39\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(42a-41\right){x}-119a+39$
6400.1-d2 6400.1-d \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.221079403$ 1.409981044 \( \frac{804357}{500} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 32 a\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+32a{x}$
6400.1-d3 6400.1-d \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.610539701$ 1.409981044 \( \frac{57960603}{31250} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -128 a\) , \( -256 a + 128\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}-128a{x}-256a+128$
6400.1-d4 6400.1-d \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.610539701$ 1.409981044 \( \frac{8527173507}{200} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 682 a - 681\) , \( -7671 a + 3495\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(682a-681\right){x}-7671a+3495$
6400.1-e1 6400.1-e \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.261119886$ $3.375263347$ 2.035386900 \( -\frac{108}{5} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -a\) , \( -4 a + 2\bigr] \) ${y}^2={x}^{3}-a{x}-4a+2$
6400.1-e2 6400.1-e \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.522239772$ $1.687631673$ 2.035386900 \( \frac{3721734}{25} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -41 a\) , \( -116 a + 58\bigr] \) ${y}^2={x}^{3}-41a{x}-116a+58$
6400.1-f1 6400.1-f \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.221079403$ 1.409981044 \( -\frac{1860867}{320} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -40 a\) , \( 160 a - 80\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-40a{x}+160a-80$
6400.1-f2 6400.1-f \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.221079403$ 1.409981044 \( \frac{804357}{500} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a - 31\) , \( 31 a\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-31\right){x}+31a$
6400.1-f3 6400.1-f \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.610539701$ 1.409981044 \( \frac{57960603}{31250} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 129\) , \( 127 a - 128\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+129\right){x}+127a-128$
6400.1-f4 6400.1-f \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.610539701$ 1.409981044 \( \frac{8527173507}{200} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -680 a\) , \( 8352 a - 4176\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-680a{x}+8352a-4176$
6400.1-g1 6400.1-g \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $1.498444490$ 1.730254660 \( \frac{237276}{625} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( 34\bigr] \) ${y}^2={x}^{3}+13{x}+34$
6400.1-g2 6400.1-g \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.996888981$ 1.730254660 \( \frac{148176}{25} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) ${y}^2={x}^{3}-7{x}+6$
6400.1-g3 6400.1-g \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.993777963$ 1.730254660 \( \frac{55296}{5} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( -1\bigr] \) ${y}^2={x}^{3}-2{x}-1$
6400.1-g4 6400.1-g \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $1.498444490$ 1.730254660 \( \frac{132304644}{5} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -107\) , \( 426\bigr] \) ${y}^2={x}^{3}-107{x}+426$
6400.1-h1 6400.1-h \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.070515942$ 1.854188003 \( -\frac{20720464}{15625} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -36\) , \( 140\bigr] \) ${y}^2={x}^{3}-{x}^{2}-36{x}+140$
6400.1-h2 6400.1-h \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.211547828$ 1.854188003 \( \frac{21296}{25} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 4 a - 4\) , \( -4\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(4a-4\right){x}-4$
6400.1-h3 6400.1-h \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.423095656$ 1.854188003 \( \frac{16384}{5} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -a + 1\) , \( 0\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-a+1\right){x}$
6400.1-h4 6400.1-h \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.141031885$ 1.854188003 \( \frac{488095744}{125} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -41\) , \( 116\bigr] \) ${y}^2={x}^{3}-{x}^{2}-41{x}+116$
6400.1-i1 6400.1-i \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.070728854$ 2.391071723 \( \frac{1293836}{25} a - \frac{1028876}{25} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -21 a - 2\) , \( 39 a - 13\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-21a-2\right){x}+39a-13$
6400.1-i2 6400.1-i \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.141457709$ 2.391071723 \( -\frac{5776}{5} a + 1728 \) \( \bigl[0\) , \( a\) , \( 0\) , \( -a - 2\) , \( -a - 1\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-a-2\right){x}-a-1$
6400.1-j1 6400.1-j \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.070728854$ 2.391071723 \( -\frac{1293836}{25} a + \frac{52992}{5} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 21 a - 23\) , \( -39 a + 26\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(21a-23\right){x}-39a+26$
6400.1-j2 6400.1-j \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.141457709$ 2.391071723 \( \frac{5776}{5} a + \frac{2864}{5} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a - 3\) , \( a - 2\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-3\right){x}+a-2$
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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.