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Results (8 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
64.1-a1 64.1-a \(\Q(\zeta_{7})^+\) \( 2^{6} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.746658170$ 0.561425840 \( -72061125694419920 a^{2} + 39990907711475312 a + 161919879656286672 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 1742 a^{2} - 971 a - 3929\) , \( 42399 a^{2} - 23535 a - 95292\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(1742a^{2}-971a-3929\right){x}+42399a^{2}-23535a-95292$
64.1-a2 64.1-a \(\Q(\zeta_{7})^+\) \( 2^{6} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.746658170$ 0.561425840 \( 32070217982944608 a^{2} - 72061125694419920 a + 25718317995977536 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 72 a^{2} + 4 a - 264\) , \( 500 a^{2} - 16 a - 1624\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(72a^{2}+4a-264\right){x}+500a^{2}-16a-1624$
64.1-a3 64.1-a \(\Q(\zeta_{7})^+\) \( 2^{6} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.986632680$ 0.561425840 \( 406749952 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 102 a^{2} - 61 a - 244\) , \( 640 a^{2} - 360 a - 1460\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(102a^{2}-61a-244\right){x}+640a^{2}-360a-1460$
64.1-a4 64.1-a \(\Q(\zeta_{7})^+\) \( 2^{6} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.746658170$ 0.561425840 \( 39990907711475312 a^{2} + 32070217982944608 a - 22193279444028480 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 17 a^{2} - 131 a - 199\) , \( -6 a^{2} - 855 a - 1073\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(17a^{2}-131a-199\right){x}-6a^{2}-855a-1073$
64.1-a5 64.1-a \(\Q(\zeta_{7})^+\) \( 2^{6} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $47.15977059$ 0.561425840 \( -208912 a^{2} + 65520 a + 561936 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 22 a^{2} - 11 a - 49\) , \( 55 a^{2} - 31 a - 124\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(22a^{2}-11a-49\right){x}+55a^{2}-31a-124$
64.1-a6 64.1-a \(\Q(\zeta_{7})^+\) \( 2^{6} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $47.15977059$ 0.561425840 \( 65520 a^{2} + 143392 a + 78592 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 17 a^{2} - 11 a - 39\) , \( -46 a^{2} + 25 a + 103\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(17a^{2}-11a-39\right){x}-46a^{2}+25a+103$
64.1-a7 64.1-a \(\Q(\zeta_{7})^+\) \( 2^{6} \) 0 $\Z/2\Z\oplus\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $188.6390823$ 0.561425840 \( 1792 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a^{2} - a - 4\) , \( 0\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(2a^{2}-a-4\right){x}$
64.1-a8 64.1-a \(\Q(\zeta_{7})^+\) \( 2^{6} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $47.15977059$ 0.561425840 \( 143392 a^{2} - 208912 a + 66240 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -8 a^{2} + 4 a + 16\) , \( 4 a^{2} - 8\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-8a^{2}+4a+16\right){x}+4a^{2}-8$
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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.