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Results (16 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
4096.1-CMb1 4096.1-CMb \(\Q(\sqrt{-3}) \) \( 2^{12} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $-3$ $\mathrm{U}(1)$ $1$ $4.423757977$ 1.277028929 \( 0 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a\) , \( 2 a - 1\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+a{x}+2a-1$
4096.1-CMb2 4096.1-CMb \(\Q(\sqrt{-3}) \) \( 2^{12} \) 0 $\Z/2\Z$ $-12$ $\mathrm{U}(1)$ $1$ $2.211878988$ 1.277028929 \( 54000 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -19 a\) , \( 26 a - 13\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}-19a{x}+26a-13$
4096.1-CMa1 4096.1-CMa \(\Q(\sqrt{-3}) \) \( 2^{12} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $-3$ $\mathrm{U}(1)$ $1$ $4.423757977$ 1.277028929 \( 0 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( -2 a + 1\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-2a+1$
4096.1-CMa2 4096.1-CMa \(\Q(\sqrt{-3}) \) \( 2^{12} \) 0 $\Z/2\Z$ $-12$ $\mathrm{U}(1)$ $1$ $2.211878988$ 1.277028929 \( 54000 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 21 a - 20\) , \( -46 a + 33\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(21a-20\right){x}-46a+33$
4096.1-a1 4096.1-a \(\Q(\sqrt{-3}) \) \( 2^{12} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.368673504$ $6.572645946$ 1.399012318 \( -1088 a - 2304 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( -a\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+{x}-a$
4096.1-a2 4096.1-a \(\Q(\sqrt{-3}) \) \( 2^{12} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.184336752$ $3.286322973$ 1.399012318 \( 1088 a - 3392 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -5 a + 1\) , \( -4 a + 3\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-5a+1\right){x}-4a+3$
4096.1-b1 4096.1-b \(\Q(\sqrt{-3}) \) \( 2^{12} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.184336752$ $3.286322973$ 1.399012318 \( -1088 a - 2304 \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 5 a - 4\) , \( 4 a - 1\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(5a-4\right){x}+4a-1$
4096.1-b2 4096.1-b \(\Q(\sqrt{-3}) \) \( 2^{12} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.368673504$ $6.572645946$ 1.399012318 \( 1088 a - 3392 \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 1\) , \( a - 1\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+{x}+a-1$
4096.1-c1 4096.1-c \(\Q(\sqrt{-3}) \) \( 2^{12} \) $1$ $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $0.444312937$ $6.875185818$ 1.763651500 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( a - 1\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}$
4096.1-c2 4096.1-c \(\Q(\sqrt{-3}) \) \( 2^{12} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $0.888625874$ $3.437592909$ 1.763651500 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 4\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-4a+4\right){x}$
4096.1-c3 4096.1-c \(\Q(\sqrt{-3}) \) \( 2^{12} \) $1$ $\Z/2\Z$ $-16$ $N(\mathrm{U}(1))$ $0.444312937$ $1.718796454$ 1.763651500 \( 287496 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -44 a + 44\) , \( -112\bigr] \) ${y}^2={x}^{3}+\left(-44a+44\right){x}-112$
4096.1-c4 4096.1-c \(\Q(\sqrt{-3}) \) \( 2^{12} \) $1$ $\Z/4\Z$ $-16$ $N(\mathrm{U}(1))$ $1.777251749$ $1.718796454$ 1.763651500 \( 287496 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -44 a + 44\) , \( 112\bigr] \) ${y}^2={x}^{3}+\left(-44a+44\right){x}+112$
4096.1-d1 4096.1-d \(\Q(\sqrt{-3}) \) \( 2^{12} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.286322973$ 1.897359453 \( -1088 a - 2304 \) \( \bigl[0\) , \( a\) , \( 0\) , \( -a + 5\) , \( -4 a + 1\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-a+5\right){x}-4a+1$
4096.1-d2 4096.1-d \(\Q(\sqrt{-3}) \) \( 2^{12} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.572645946$ 1.897359453 \( 1088 a - 3392 \) \( \bigl[0\) , \( a\) , \( 0\) , \( -a\) , \( -a + 1\bigr] \) ${y}^2={x}^{3}+a{x}^{2}-a{x}-a+1$
4096.1-e1 4096.1-e \(\Q(\sqrt{-3}) \) \( 2^{12} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.572645946$ 1.897359453 \( -1088 a - 2304 \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a - 1\) , \( a\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-1\right){x}+a$
4096.1-e2 4096.1-e \(\Q(\sqrt{-3}) \) \( 2^{12} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.286322973$ 1.897359453 \( 1088 a - 3392 \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a + 4\) , \( 4 a - 3\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(a+4\right){x}+4a-3$
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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.