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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-a3 31.1-a \(\Q(\sqrt{5}) \) \( 31 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.438604964$ 0.359928959 \( -\frac{156520379364360}{923521} a + \frac{253260256463213}{923521} \) \( \bigl[\phi\) , \( -1\) , \( \phi + 1\) , \( -12 \phi - 21\) , \( 42 \phi + 10\bigr] \) ${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}-{x}^{2}+\left(-12\phi-21\right){x}+42\phi+10$
775.1-a3 775.1-a \(\Q(\sqrt{5}) \) \( 5^{2} \cdot 31 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.746456922$ 1.508553628 \( -\frac{156520379364360}{923521} a + \frac{253260256463213}{923521} \) \( \bigl[\phi + 1\) , \( \phi - 1\) , \( 1\) , \( 49 \phi - 152\) , \( -583 \phi + 688\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(49\phi-152\right){x}-583\phi+688$
961.2-c3 961.2-c \(\Q(\sqrt{5}) \) \( 31^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $7.096706804$ $0.861840578$ 1.367630581 \( -\frac{156520379364360}{923521} a + \frac{253260256463213}{923521} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -474 \phi - 655\) , \( -6456 \phi - 6672\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-474\phi-655\right){x}-6456\phi-6672$
2511.1-f3 2511.1-f \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 31 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.028512095$ 1.124409487 \( -\frac{156520379364360}{923521} a + \frac{253260256463213}{923521} \) \( \bigl[\phi\) , \( -\phi - 1\) , \( 1\) , \( -98 \phi - 186\) , \( -1056 \phi - 98\bigr] \) ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-98\phi-186\right){x}-1056\phi-98$
3751.4-b3 3751.4-b \(\Q(\sqrt{5}) \) \( 11^{2} \cdot 31 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.103070773$ 2.729376224 \( -\frac{156520379364360}{923521} a + \frac{253260256463213}{923521} \) \( \bigl[1\) , \( \phi - 1\) , \( 0\) , \( -47 \phi - 236\) , \( 185 \phi + 1360\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-47\phi-236\right){x}+185\phi+1360$
3751.6-a3 3751.6-a \(\Q(\sqrt{5}) \) \( 11^{2} \cdot 31 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.446809802$ 2.588132054 \( -\frac{156520379364360}{923521} a + \frac{253260256463213}{923521} \) \( \bigl[\phi + 1\) , \( \phi + 1\) , \( 0\) , \( -201 \phi - 238\) , \( -2077 \phi - 1767\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\left(\phi+1\right){x}^{2}+\left(-201\phi-238\right){x}-2077\phi-1767$
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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.