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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
24.1-a7 24.1-a \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.325279868$ 0.671250479 \( \frac{3065617154}{9} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 385 a - 671\) , \( 5582 a - 9681\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(385a-671\right){x}+5582a-9681$
24.1-b7 24.1-b \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 3 \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $22.73403407$ 0.820343793 \( \frac{3065617154}{9} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 383 a - 674\) , \( -5198 a + 9008\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(383a-674\right){x}-5198a+9008$
144.1-a7 144.1-a \(\Q(\sqrt{3}) \) \( 2^{4} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.197737158$ 1.211782339 \( \frac{3065617154}{9} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 290\) , \( -1040 a - 1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-290\right){x}-1040a-1$
144.1-c7 144.1-c \(\Q(\sqrt{3}) \) \( 2^{4} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.197737158$ 1.211782339 \( \frac{3065617154}{9} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 16142 a - 27960\) , \( 1464590 a - 2536744\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(16142a-27960\right){x}+1464590a-2536744$
768.1-e7 768.1-e \(\Q(\sqrt{3}) \) \( 2^{8} \cdot 3 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $11.36701703$ 1.640687586 \( \frac{3065617154}{9} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -1538 a - 2689\) , \( 43117 a + 74761\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-1538a-2689\right){x}+43117a+74761$
768.1-l7 768.1-l \(\Q(\sqrt{3}) \) \( 2^{8} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.079273864$ $1.162639934$ 2.897852395 \( \frac{3065617154}{9} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -1538 a - 2689\) , \( -43117 a - 74761\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1538a-2689\right){x}-43117a-74761$
2304.1-q7 2304.1-q \(\Q(\sqrt{3}) \) \( 2^{8} \cdot 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.786181258$ $2.098868579$ 3.376245242 \( \frac{3065617154}{9} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -1152\) , \( -8316 a\bigr] \) ${y}^2={x}^{3}-a{x}^{2}-1152{x}-8316a$
2304.1-bb7 2304.1-bb \(\Q(\sqrt{3}) \) \( 2^{8} \cdot 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.786181258$ $2.098868579$ 3.376245242 \( \frac{3065617154}{9} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -1152\) , \( 8316 a\bigr] \) ${y}^2={x}^{3}+a{x}^{2}-1152{x}+8316a$
3072.1-e7 3072.1-e \(\Q(\sqrt{3}) \) \( 2^{10} \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.570578528$ 2.968248410 \( \frac{3065617154}{9} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 768 a - 1536\) , \( -16632 a + 27720\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(768a-1536\right){x}-16632a+27720$
3072.1-f7 3072.1-f \(\Q(\sqrt{3}) \) \( 2^{10} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.929871924$ $2.570578528$ 2.760090861 \( \frac{3065617154}{9} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -768 a - 1536\) , \( -16632 a - 27720\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-768a-1536\right){x}-16632a-27720$
3072.1-bt7 3072.1-bt \(\Q(\sqrt{3}) \) \( 2^{10} \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.570578528$ 2.968248410 \( \frac{3065617154}{9} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -768 a - 1536\) , \( 16632 a + 27720\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-768a-1536\right){x}+16632a+27720$
3072.1-cc7 3072.1-cc \(\Q(\sqrt{3}) \) \( 2^{10} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.929871924$ $2.570578528$ 2.760090861 \( \frac{3065617154}{9} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 768 a - 1536\) , \( 16632 a - 27720\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(768a-1536\right){x}+16632a-27720$
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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.