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Results (10 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
4.1-b2 4.1-b \(\Q(\sqrt{57}) \) \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $37.29397324$ 2.469853714 \( -\frac{489}{4} a + 1841 \) \( \bigl[1\) , \( -a\) , \( a\) , \( a - 1\) , \( -7\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(a-1\right){x}-7$
4.1-c2 4.1-c \(\Q(\sqrt{57}) \) \( 2^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $28.41051943$ 0.209059179 \( -\frac{489}{4} a + 1841 \) \( \bigl[1\) , \( -a - 1\) , \( a\) , \( 150 a + 495\) , \( -1331 a - 4361\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(150a+495\right){x}-1331a-4361$
36.1-d2 36.1-d \(\Q(\sqrt{57}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $18.79309404$ 2.489206115 \( -\frac{489}{4} a + 1841 \) \( \bigl[1\) , \( a\) , \( 0\) , \( 1207 a - 5153\) , \( -22427 a + 95877\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(1207a-5153\right){x}-22427a+95877$
36.1-g2 36.1-g \(\Q(\sqrt{57}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $18.79309404$ 2.489206115 \( -\frac{489}{4} a + 1841 \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( a + 10\) , \( -a\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a+10\right){x}-a$
128.5-g2 128.5-g \(\Q(\sqrt{57}) \) \( 2^{7} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.606502331$ $11.50837277$ 3.698017476 \( -\frac{489}{4} a + 1841 \) \( \bigl[a\) , \( 1\) , \( 0\) , \( 3 a - 2\) , \( 5 a - 14\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(3a-2\right){x}+5a-14$
128.5-m2 128.5-m \(\Q(\sqrt{57}) \) \( 2^{7} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $11.50837277$ 1.524321212 \( -\frac{489}{4} a + 1841 \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 5892 a + 19304\) , \( -268068 a - 877896\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5892a+19304\right){x}-268068a-877896$
128.6-g2 128.6-g \(\Q(\sqrt{57}) \) \( 2^{7} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.213004663$ $11.50837277$ 3.698017476 \( -\frac{489}{4} a + 1841 \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 54 a - 219\) , \( -186 a + 803\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(54a-219\right){x}-186a+803$
128.6-m2 128.6-m \(\Q(\sqrt{57}) \) \( 2^{7} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $11.50837277$ 1.524321212 \( -\frac{489}{4} a + 1841 \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 246 a + 806\) , \( 3071 a + 10055\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(246a+806\right){x}+3071a+10055$
256.1-c2 256.1-c \(\Q(\sqrt{57}) \) \( 2^{8} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.102629859$ 1.881532613 \( -\frac{489}{4} a + 1841 \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 21 a - 86\) , \( 20 a - 84\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(21a-86\right){x}+20a-84$
256.1-s2 256.1-s \(\Q(\sqrt{57}) \) \( 2^{8} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $9.323493311$ 4.939707428 \( -\frac{489}{4} a + 1841 \) \( \bigl[0\) , \( a\) , \( 0\) , \( 2395 a + 7847\) , \( 72492 a + 237404\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(2395a+7847\right){x}+72492a+237404$
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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.