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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
64.1-a3 64.1-a \(\Q(\sqrt{2}) \) \( 2^{6} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $-8$ $N(\mathrm{U}(1))$ $1$ $17.94635162$ 0.793124183 \( 8000 \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a - 4\) , \( -4 a - 6\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-4\right){x}-4a-6$
64.1-a4 64.1-a \(\Q(\sqrt{2}) \) \( 2^{6} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $-8$ $N(\mathrm{U}(1))$ $1$ $35.89270325$ 0.793124183 \( 8000 \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a - 4\) , \( 4 a + 6\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a-4\right){x}+4a+6$
256.1-c3 256.1-c \(\Q(\sqrt{2}) \) \( 2^{8} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $-8$ $N(\mathrm{U}(1))$ $1$ $25.37997386$ 1.121646976 \( 8000 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -1\) , \( a\bigr] \) ${y}^2={x}^{3}-a{x}^{2}-{x}+a$
256.1-c4 256.1-c \(\Q(\sqrt{2}) \) \( 2^{8} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $-8$ $N(\mathrm{U}(1))$ $1$ $25.37997386$ 1.121646976 \( 8000 \) \( \bigl[0\) , \( a\) , \( 0\) , \( -1\) , \( -a\bigr] \) ${y}^2={x}^{3}+a{x}^{2}-{x}-a$
1024.1-d3 1024.1-d \(\Q(\sqrt{2}) \) \( 2^{10} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-8$ $N(\mathrm{U}(1))$ $0.960251595$ $12.68998693$ 2.154126597 \( 8000 \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -3\) , \( -1\bigr] \) ${y}^2={x}^{3}-{x}^{2}-3{x}-1$
1024.1-d4 1024.1-d \(\Q(\sqrt{2}) \) \( 2^{10} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-8$ $N(\mathrm{U}(1))$ $0.480125797$ $25.37997386$ 2.154126597 \( 8000 \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -3\) , \( 1\bigr] \) ${y}^2={x}^{3}+{x}^{2}-3{x}+1$
1024.1-m3 1024.1-m \(\Q(\sqrt{2}) \) \( 2^{10} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $-8$ $N(\mathrm{U}(1))$ $1$ $17.94635162$ 1.586248366 \( 8000 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6 a - 9\) , \( -5 a - 7\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a-9\right){x}-5a-7$
1024.1-m4 1024.1-m \(\Q(\sqrt{2}) \) \( 2^{10} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $-8$ $N(\mathrm{U}(1))$ $1$ $17.94635162$ 1.586248366 \( 8000 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a - 9\) , \( 5 a + 7\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a-9\right){x}+5a+7$
3136.2-a3 3136.2-a \(\Q(\sqrt{2}) \) \( 2^{6} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-8$ $N(\mathrm{U}(1))$ $0.868344182$ $9.592728448$ 2.945025478 \( 8000 \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -10 a - 18\) , \( -20 a - 24\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-10a-18\right){x}-20a-24$
3136.2-a4 3136.2-a \(\Q(\sqrt{2}) \) \( 2^{6} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-8$ $N(\mathrm{U}(1))$ $0.434172091$ $9.592728448$ 2.945025478 \( 8000 \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -10 a - 18\) , \( 20 a + 24\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-10a-18\right){x}+20a+24$
3136.3-a3 3136.3-a \(\Q(\sqrt{2}) \) \( 2^{6} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-8$ $N(\mathrm{U}(1))$ $0.868344182$ $9.592728448$ 2.945025478 \( 8000 \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 10 a - 18\) , \( 20 a - 24\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(10a-18\right){x}+20a-24$
3136.3-a4 3136.3-a \(\Q(\sqrt{2}) \) \( 2^{6} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-8$ $N(\mathrm{U}(1))$ $0.434172091$ $9.592728448$ 2.945025478 \( 8000 \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 10 a - 18\) , \( -20 a + 24\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(10a-18\right){x}-20a+24$
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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.