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Results (5 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
55.2-a3 55.2-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $19.86707574$ 0.493601465 \( -\frac{48555143354501}{275} a + \frac{78563872776324}{275} \) \( \bigl[\phi\) , \( -\phi + 1\) , \( \phi\) , \( 4 \phi - 30\) , \( -29 \phi + 37\bigr] \) ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(4\phi-30\right){x}-29\phi+37$
275.1-a3 275.1-a \(\Q(\sqrt{5}) \) \( 5^{2} \cdot 11 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.219468538$ 0.992576504 \( -\frac{48555143354501}{275} a + \frac{78563872776324}{275} \) \( \bigl[1\) , \( \phi + 1\) , \( \phi + 1\) , \( -101 \phi - 126\) , \( 159 \phi - 110\bigr] \) ${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(\phi+1\right){x}^{2}+\left(-101\phi-126\right){x}+159\phi-110$
605.2-b3 605.2-b \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.409545383$ 1.260735718 \( -\frac{48555143354501}{275} a + \frac{78563872776324}{275} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 140 \phi - 407\) , \( 1855 \phi - 3286\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(140\phi-407\right){x}+1855\phi-3286$
3025.2-e3 3025.2-e \(\Q(\sqrt{5}) \) \( 5^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.425671977$ $2.843879507$ 2.165515227 \( -\frac{48555143354501}{275} a + \frac{78563872776324}{275} \) \( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( -637 \phi - 1337\) , \( -1816 \phi + 10216\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\phi{x}^{2}+\left(-637\phi-1337\right){x}-1816\phi+10216$
4455.2-a3 4455.2-a \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5 \cdot 11 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.654294174$ 1.479645692 \( -\frac{48555143354501}{275} a + \frac{78563872776324}{275} \) \( \bigl[\phi\) , \( -\phi - 1\) , \( \phi + 1\) , \( 44 \phi - 272\) , \( 1045 \phi - 1319\bigr] \) ${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(44\phi-272\right){x}+1045\phi-1319$
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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.