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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
32.1-a1 32.1-a \(\Q(\sqrt{6}) \) \( 2^{5} \) 0 $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $1$ $13.75037163$ 1.403391428 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2={x}^{3}+{x}$
32.1-a2 32.1-a \(\Q(\sqrt{6}) \) \( 2^{5} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $1$ $27.50074327$ 1.403391428 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -20 a - 49\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-20a-49\right){x}$
32.1-a3 32.1-a \(\Q(\sqrt{6}) \) \( 2^{5} \) 0 $\Z/2\Z$ $-16$ $N(\mathrm{U}(1))$ $1$ $13.75037163$ 1.403391428 \( 287496 \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -2\) , \( -3\bigr] \) ${y}^2+a{x}{y}={x}^{3}-2{x}-3$
32.1-a4 32.1-a \(\Q(\sqrt{6}) \) \( 2^{5} \) 0 $\Z/4\Z$ $-16$ $N(\mathrm{U}(1))$ $1$ $55.00148654$ 1.403391428 \( 287496 \) \( \bigl[a\) , \( 0\) , \( a\) , \( -5\) , \( -1\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-5{x}-1$
32.1-b1 32.1-b \(\Q(\sqrt{6}) \) \( 2^{5} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $0.888625874$ $27.50074327$ 1.247089935 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) ${y}^2={x}^{3}-{x}$
32.1-b2 32.1-b \(\Q(\sqrt{6}) \) \( 2^{5} \) $1$ $\Z/4\Z$ $-4$ $N(\mathrm{U}(1))$ $1.777251749$ $13.75037163$ 1.247089935 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 20 a + 49\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(20a+49\right){x}$
32.1-b3 32.1-b \(\Q(\sqrt{6}) \) \( 2^{5} \) $1$ $\Z/2\Z$ $-16$ $N(\mathrm{U}(1))$ $0.444312937$ $13.75037163$ 1.247089935 \( 287496 \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 55 a - 134\) , \( 374 a - 916\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(55a-134\right){x}+374a-916$
32.1-b4 32.1-b \(\Q(\sqrt{6}) \) \( 2^{5} \) $1$ $\Z/4\Z$ $-16$ $N(\mathrm{U}(1))$ $0.444312937$ $55.00148654$ 1.247089935 \( 287496 \) \( \bigl[a\) , \( 0\) , \( a\) , \( 55 a - 137\) , \( -319 a + 780\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(55a-137\right){x}-319a+780$
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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.