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Results (12 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
512.1-c1 512.1-c \(\Q(\sqrt{3}) \) \( 2^{9} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $15.68304578$ 2.263652675 \( 128 \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -5 a + 9\) , \( 30 a - 52\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-5a+9\right){x}+30a-52$
512.1-d1 512.1-d \(\Q(\sqrt{3}) \) \( 2^{9} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $15.68304578$ 2.263652675 \( 128 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -69 a + 122\) , \( -1490 a + 2580\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-69a+122\right){x}-1490a+2580$
512.1-e1 512.1-e \(\Q(\sqrt{3}) \) \( 2^{9} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.363017536$ $15.68304578$ 1.643491233 \( 128 \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -5 a + 9\) , \( -30 a + 52\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-5a+9\right){x}-30a+52$
512.1-f1 512.1-f \(\Q(\sqrt{3}) \) \( 2^{9} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.363017536$ $15.68304578$ 1.643491233 \( 128 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -69 a + 122\) , \( 1490 a - 2580\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-69a+122\right){x}+1490a-2580$
1024.1-e1 1024.1-e \(\Q(\sqrt{3}) \) \( 2^{10} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $16.29302268$ 2.351695258 \( 128 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2 a + 6\) , \( -12 a + 20\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a+6\right){x}-12a+20$
1024.1-f1 1024.1-f \(\Q(\sqrt{3}) \) \( 2^{10} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.632943382$ $7.547952572$ 3.558030500 \( 128 \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -38 a + 66\) , \( 612 a - 1060\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-38a+66\right){x}+612a-1060$
1024.1-o1 1024.1-o \(\Q(\sqrt{3}) \) \( 2^{10} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.547952572$ 1.089453112 \( 128 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a + 6\) , \( 12 a - 20\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a+6\right){x}+12a-20$
1024.1-p1 1024.1-p \(\Q(\sqrt{3}) \) \( 2^{10} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.432331164$ $16.29302268$ 2.033422299 \( 128 \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -38 a + 66\) , \( -612 a + 1060\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-38a+66\right){x}-612a+1060$
4608.1-h1 4608.1-h \(\Q(\sqrt{3}) \) \( 2^{9} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.162877468$ 1.779069482 \( 128 \) \( \bigl[0\) , \( a\) , \( 0\) , \( -15 a + 27\) , \( 156 a - 270\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-15a+27\right){x}+156a-270$
4608.1-i1 4608.1-i \(\Q(\sqrt{3}) \) \( 2^{9} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.162877468$ 1.779069482 \( 128 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -209 a + 363\) , \( 7532 a - 13046\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-209a+363\right){x}+7532a-13046$
4608.1-v1 4608.1-v \(\Q(\sqrt{3}) \) \( 2^{9} \cdot 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.512963232$ $13.30319731$ 3.939867736 \( 128 \) \( \bigl[0\) , \( a\) , \( 0\) , \( -209 a + 363\) , \( -7532 a + 13046\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-209a+363\right){x}-7532a+13046$
4608.1-ba1 4608.1-ba \(\Q(\sqrt{3}) \) \( 2^{9} \cdot 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.512963232$ $13.30319731$ 3.939867736 \( 128 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -15 a + 27\) , \( -156 a + 270\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-15a+27\right){x}-156a+270$
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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.