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Results (6 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
31.1-a1 31.1-a \(\Q(\sqrt{5}) \) \( 31 \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $51.50883971$ 0.359928959 \( -\frac{106208}{31} a + \frac{51455}{31} \) \( \bigl[1\) , \( \phi + 1\) , \( \phi\) , \( \phi\) , \( 0\bigr] \) ${y}^2+{x}{y}+\phi{y}={x}^{3}+\left(\phi+1\right){x}^{2}+\phi{x}$
775.1-a1 775.1-a \(\Q(\sqrt{5}) \) \( 5^{2} \cdot 31 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.746456922$ 1.508553628 \( -\frac{106208}{31} a + \frac{51455}{31} \) \( \bigl[\phi + 1\) , \( \phi - 1\) , \( 1\) , \( -\phi - 2\) , \( -3 \phi - 2\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-\phi-2\right){x}-3\phi-2$
961.2-c1 961.2-c \(\Q(\sqrt{5}) \) \( 31^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.774176701$ $3.447362312$ 1.367630581 \( -\frac{106208}{31} a + \frac{51455}{31} \) \( \bigl[\phi + 1\) , \( -\phi\) , \( 0\) , \( 7 \phi - 23\) , \( -24 \phi + 20\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}-\phi{x}^{2}+\left(7\phi-23\right){x}-24\phi+20$
2511.1-f1 2511.1-f \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 31 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.028512095$ 1.124409487 \( -\frac{106208}{31} a + \frac{51455}{31} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 3 \phi - 8\) , \( 2 \phi - 5\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(3\phi-8\right){x}+2\phi-5$
3751.4-b1 3751.4-b \(\Q(\sqrt{5}) \) \( 11^{2} \cdot 31 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $12.20614154$ 2.729376224 \( -\frac{106208}{31} a + \frac{51455}{31} \) \( \bigl[\phi + 1\) , \( \phi\) , \( \phi + 1\) , \( 6 \phi - 12\) , \( 6 \phi - 11\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\phi{x}^{2}+\left(6\phi-12\right){x}+6\phi-11$
3751.6-a1 3751.6-a \(\Q(\sqrt{5}) \) \( 11^{2} \cdot 31 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.787239209$ 2.588132054 \( -\frac{106208}{31} a + \frac{51455}{31} \) \( \bigl[\phi\) , \( 1\) , \( 0\) , \( 2 \phi - 7\) , \( -5 \phi + 1\bigr] \) ${y}^2+\phi{x}{y}={x}^{3}+{x}^{2}+\left(2\phi-7\right){x}-5\phi+1$
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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.