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Results (24 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
3072.1-a1 3072.1-a \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.208930895$ $2.876942816$ 1.388139971 \( \frac{188632}{9} a - \frac{255448}{9} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 10 a - 11\) , \( -15 a + 6\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(10a-11\right){x}-15a+6$
3072.1-a2 3072.1-a \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.417861791$ $5.753885633$ 1.388139971 \( \frac{1216}{3} a - 384 \) \( \bigl[0\) , \( a\) , \( 0\) , \( -1\) , \( -a\bigr] \) ${y}^2={x}^{3}+a{x}^{2}-{x}-a$
3072.1-a3 3072.1-a \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.835723582$ $2.876942816$ 1.388139971 \( -\frac{27712}{3} a + \frac{20672}{3} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -5 a + 9\) , \( -4 a - 3\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-5a+9\right){x}-4a-3$
3072.1-a4 3072.1-a \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.835723582$ $2.876942816$ 1.388139971 \( -\frac{2285576}{3} a + \frac{2214136}{3} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -10 a - 11\) , \( -31 a - 6\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-10a-11\right){x}-31a-6$
3072.1-b1 3072.1-b \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.208930895$ $2.876942816$ 1.388139971 \( -\frac{188632}{9} a - 7424 \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -10 a - 1\) , \( 15 a - 9\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a-1\right){x}+15a-9$
3072.1-b2 3072.1-b \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.417861791$ $5.753885633$ 1.388139971 \( -\frac{1216}{3} a + \frac{64}{3} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -1\) , \( a - 1\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-{x}+a-1$
3072.1-b3 3072.1-b \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.835723582$ $2.876942816$ 1.388139971 \( \frac{27712}{3} a - \frac{7040}{3} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 5 a + 4\) , \( 4 a - 7\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(5a+4\right){x}+4a-7$
3072.1-b4 3072.1-b \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.835723582$ $2.876942816$ 1.388139971 \( \frac{2285576}{3} a - \frac{71440}{3} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 10 a - 21\) , \( 31 a - 37\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(10a-21\right){x}+31a-37$
3072.1-c1 3072.1-c \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.345364298$ 1.354096709 \( \frac{97336}{81} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 8 a - 8\) , \( -8\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(8a-8\right){x}-8$
3072.1-c2 3072.1-c \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.690728597$ 1.354096709 \( \frac{21952}{9} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -2 a + 2\) , \( 0\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-2a+2\right){x}$
3072.1-c3 3072.1-c \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2.345364298$ 1.354096709 \( \frac{140608}{3} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -17 a + 17\) , \( 33\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-17a+17\right){x}+33$
3072.1-c4 3072.1-c \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2.345364298$ 1.354096709 \( \frac{7301384}{3} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -32 a + 32\) , \( -60\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-32a+32\right){x}-60$
3072.1-d1 3072.1-d \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.155042418$ $2.345364298$ 1.679539426 \( \frac{97336}{81} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 8 a - 8\) , \( 8\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(8a-8\right){x}+8$
3072.1-d2 3072.1-d \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.310084836$ $4.690728597$ 1.679539426 \( \frac{21952}{9} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -2 a + 2\) , \( 0\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-2a+2\right){x}$
3072.1-d3 3072.1-d \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.620169672$ $2.345364298$ 1.679539426 \( \frac{140608}{3} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -17 a + 17\) , \( -33\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-17a+17\right){x}-33$
3072.1-d4 3072.1-d \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.620169672$ $2.345364298$ 1.679539426 \( \frac{7301384}{3} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -32 a + 32\) , \( 60\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-32a+32\right){x}+60$
3072.1-e1 3072.1-e \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2.876942816$ 1.661003709 \( -\frac{188632}{9} a - 7424 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 11 a - 10\) , \( -15 a + 9\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(11a-10\right){x}-15a+9$
3072.1-e2 3072.1-e \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.753885633$ 1.661003709 \( -\frac{1216}{3} a + \frac{64}{3} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( a\) , \( -a + 1\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+a{x}-a+1$
3072.1-e3 3072.1-e \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.876942816$ 1.661003709 \( \frac{27712}{3} a - \frac{7040}{3} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -9 a + 5\) , \( -4 a + 7\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-9a+5\right){x}-4a+7$
3072.1-e4 3072.1-e \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.876942816$ 1.661003709 \( \frac{2285576}{3} a - \frac{71440}{3} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 11 a + 10\) , \( -31 a + 37\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(11a+10\right){x}-31a+37$
3072.1-f1 3072.1-f \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2.876942816$ 1.661003709 \( \frac{188632}{9} a - \frac{255448}{9} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -11 a + 1\) , \( 15 a - 6\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-11a+1\right){x}+15a-6$
3072.1-f2 3072.1-f \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.753885633$ 1.661003709 \( \frac{1216}{3} a - 384 \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -a + 1\) , \( a\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+1\right){x}+a$
3072.1-f3 3072.1-f \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.876942816$ 1.661003709 \( -\frac{27712}{3} a + \frac{20672}{3} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 9 a - 4\) , \( 4 a + 3\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(9a-4\right){x}+4a+3$
3072.1-f4 3072.1-f \(\Q(\sqrt{-3}) \) \( 2^{10} \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.876942816$ 1.661003709 \( -\frac{2285576}{3} a + \frac{2214136}{3} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -11 a + 21\) , \( 31 a + 6\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-11a+21\right){x}+31a+6$
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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.