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Results (12 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
96.1-a6 96.1-a \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3 \) $0$ $\Z/2\Z$ $1$ $3.261257214$ 0.941443865 \( \frac{164847992914}{3} a + \frac{285525100658}{3} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -109 a + 195\) , \( 1392 a - 2409\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-109a+195\right){x}+1392a-2409$
96.1-c6 96.1-c \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3 \) $0$ $\Z/4\Z$ $1$ $17.97674429$ 1.297359770 \( \frac{164847992914}{3} a + \frac{285525100658}{3} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -110 a + 194\) , \( -1310 a + 2270\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-110a+194\right){x}-1310a+2270$
288.1-b6 288.1-b \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) $0$ $\Z/2\Z$ $1$ $2.510861184$ 1.449646380 \( \frac{164847992914}{3} a + \frac{285525100658}{3} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -34 a + 24\) , \( -164 a + 214\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-34a+24\right){x}-164a+214$
288.1-d6 288.1-d \(\Q(\sqrt{3}) \) \( 2^{5} \cdot 3^{2} \) $1$ $\Z/2\Z$ $0.820391757$ $7.783091503$ 1.843243885 \( \frac{164847992914}{3} a + \frac{285525100658}{3} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -34 a + 24\) , \( 164 a - 214\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-34a+24\right){x}+164a-214$
768.1-c6 768.1-c \(\Q(\sqrt{3}) \) \( 2^{8} \cdot 3 \) $1$ $\Z/2\Z$ $0.211834002$ $8.988372149$ 2.198599305 \( \frac{164847992914}{3} a + \frac{285525100658}{3} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -444 a + 766\) , \( -10806 a + 18720\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-444a+766\right){x}-10806a+18720$
768.1-n6 768.1-n \(\Q(\sqrt{3}) \) \( 2^{8} \cdot 3 \) $0$ $\Z/2\Z$ $1$ $1.630628607$ 1.882887730 \( \frac{164847992914}{3} a + \frac{285525100658}{3} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -444 a + 766\) , \( 10806 a - 18720\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-444a+766\right){x}+10806a-18720$
2304.1-b6 2304.1-b \(\Q(\sqrt{3}) \) \( 2^{8} \cdot 3^{2} \) $0$ $\Z/2\Z$ $1$ $1.255430592$ 1.449646380 \( \frac{164847992914}{3} a + \frac{285525100658}{3} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -136 a + 96\) , \( -1312 a + 1712\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-136a+96\right){x}-1312a+1712$
2304.1-e6 2304.1-e \(\Q(\sqrt{3}) \) \( 2^{8} \cdot 3^{2} \) $0$ $\Z/2\Z$ $1$ $3.891545751$ 2.246784987 \( \frac{164847992914}{3} a + \frac{285525100658}{3} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -136 a + 96\) , \( 1312 a - 1712\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-136a+96\right){x}+1312a-1712$
3072.1-b6 3072.1-b \(\Q(\sqrt{3}) \) \( 2^{10} \cdot 3 \) $1$ $\Z/4\Z$ $2.120342961$ $4.766150701$ 2.917314563 \( \frac{164847992914}{3} a + \frac{285525100658}{3} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -244 a + 400\) , \( 4260 a - 7308\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-244a+400\right){x}+4260a-7308$
3072.1-i6 3072.1-i \(\Q(\sqrt{3}) \) \( 2^{10} \cdot 3 \) $0$ $\Z/2\Z$ $1$ $4.766150701$ 2.751738390 \( \frac{164847992914}{3} a + \frac{285525100658}{3} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3308 a + 5728\) , \( 220380 a - 381708\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3308a+5728\right){x}+220380a-381708$
3072.1-br6 3072.1-br \(\Q(\sqrt{3}) \) \( 2^{10} \cdot 3 \) $0$ $\Z/2\Z$ $1$ $1.537582179$ 1.775446970 \( \frac{164847992914}{3} a + \frac{285525100658}{3} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -244 a + 400\) , \( -4260 a + 7308\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-244a+400\right){x}-4260a+7308$
3072.1-cd6 3072.1-cd \(\Q(\sqrt{3}) \) \( 2^{10} \cdot 3 \) $1$ $\Z/2\Z$ $3.739974475$ $1.537582179$ 3.320063175 \( \frac{164847992914}{3} a + \frac{285525100658}{3} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -3308 a + 5728\) , \( -220380 a + 381708\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-3308a+5728\right){x}-220380a+381708$
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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.