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Results (20 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
16.1-a5 16.1-a \(\Q(\sqrt{3}) \) \( 2^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $1$ $35.39006381$ 0.638514464 \( 54000 \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 3\) , \( -1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-3\right){x}-1$
16.1-a6 16.1-a \(\Q(\sqrt{3}) \) \( 2^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $1$ $35.39006381$ 0.638514464 \( 54000 \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -a - 3\) , \( -a - 1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-a-3\right){x}-a-1$
36.1-a5 36.1-a \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $1$ $11.79668793$ 0.851352619 \( 54000 \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 14 a - 26\) , \( 28 a - 50\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(14a-26\right){x}+28a-50$
36.1-a6 36.1-a \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/2\Z\oplus\Z/6\Z$ $-12$ $N(\mathrm{U}(1))$ $1$ $35.39006381$ 0.851352619 \( 54000 \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 15 a - 24\) , \( -54 a + 94\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(15a-24\right){x}-54a+94$
256.1-c5 256.1-c \(\Q(\sqrt{3}) \) \( 2^{8} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $1$ $17.69503190$ 1.277028929 \( 54000 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -4\) , \( 4 a\bigr] \) ${y}^2={x}^{3}-a{x}^{2}-4{x}+4a$
256.1-c6 256.1-c \(\Q(\sqrt{3}) \) \( 2^{8} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $1$ $17.69503190$ 1.277028929 \( 54000 \) \( \bigl[0\) , \( a\) , \( 0\) , \( -4\) , \( -4 a\bigr] \) ${y}^2={x}^{3}+a{x}^{2}-4{x}-4a$
484.2-c5 484.2-c \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $1$ $18.48185806$ 1.333813215 \( 54000 \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 5 a - 16\) , \( -14 a + 30\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(5a-16\right){x}-14a+30$
484.2-c6 484.2-c \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $1$ $6.160619353$ 1.333813215 \( 54000 \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 5 a - 16\) , \( 14 a - 30\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a-16\right){x}+14a-30$
484.3-c5 484.3-c \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $1$ $18.48185806$ 1.333813215 \( 54000 \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 424 a - 738\) , \( -6054 a + 10484\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(424a-738\right){x}-6054a+10484$
484.3-c6 484.3-c \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $1$ $6.160619353$ 1.333813215 \( 54000 \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 424 a - 738\) , \( 6053 a - 10486\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(424a-738\right){x}+6053a-10486$
676.2-a5 676.2-a \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 13^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $1.691749403$ $9.815437671$ 2.396762951 \( 54000 \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 165 a - 286\) , \( -1448 a + 2508\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(165a-286\right){x}-1448a+2508$
676.2-a6 676.2-a \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 13^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $0.563916467$ $9.815437671$ 2.396762951 \( 54000 \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 165 a - 286\) , \( 1448 a - 2508\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(165a-286\right){x}+1448a-2508$
676.3-a5 676.3-a \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 13^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $1.691749403$ $9.815437671$ 2.396762951 \( 54000 \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 24 a - 48\) , \( 85 a - 148\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(24a-48\right){x}+85a-148$
676.3-a6 676.3-a \(\Q(\sqrt{3}) \) \( 2^{2} \cdot 13^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $0.563916467$ $9.815437671$ 2.396762951 \( 54000 \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 24 a - 48\) , \( -86 a + 146\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(24a-48\right){x}-86a+146$
1024.1-j5 1024.1-j \(\Q(\sqrt{3}) \) \( 2^{10} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $0.859914975$ $21.67189957$ 2.689873605 \( 54000 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -10 a - 19\) , \( 31 a + 54\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-10a-19\right){x}+31a+54$
1024.1-j6 1024.1-j \(\Q(\sqrt{3}) \) \( 2^{10} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $2.579744927$ $7.223966526$ 2.689873605 \( 54000 \) \( \bigl[0\) , \( a\) , \( 0\) , \( -10 a - 19\) , \( -31 a - 54\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-10a-19\right){x}-31a-54$
1024.1-k5 1024.1-k \(\Q(\sqrt{3}) \) \( 2^{10} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $2.579744927$ $7.223966526$ 2.689873605 \( 54000 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 10 a - 19\) , \( 31 a - 54\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(10a-19\right){x}+31a-54$
1024.1-k6 1024.1-k \(\Q(\sqrt{3}) \) \( 2^{10} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $0.859914975$ $21.67189957$ 2.689873605 \( 54000 \) \( \bigl[0\) , \( a\) , \( 0\) , \( 10 a - 19\) , \( -31 a + 54\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(10a-19\right){x}-31a+54$
2304.1-v5 2304.1-v \(\Q(\sqrt{3}) \) \( 2^{8} \cdot 3^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $0.979852016$ $5.898343969$ 3.336798323 \( 54000 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -60 a - 105\) , \( -330 a - 572\bigr] \) ${y}^2={x}^{3}+\left(-60a-105\right){x}-330a-572$
2304.1-v6 2304.1-v \(\Q(\sqrt{3}) \) \( 2^{8} \cdot 3^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $0.326617338$ $17.69503190$ 3.336798323 \( 54000 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -60 a - 105\) , \( 330 a + 572\bigr] \) ${y}^2={x}^{3}+\left(-60a-105\right){x}+330a+572$
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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.