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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
605.2-a1 605.2-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.076619226$ 1.358773366 \( -\frac{20192}{25} a + \frac{32421}{25} \) \( \bigl[\phi\) , \( \phi\) , \( 0\) , \( 8 \phi - 15\) , \( 11 \phi + 17\bigr] \) ${y}^2+\phi{x}{y}={x}^{3}+\phi{x}^{2}+\left(8\phi-15\right){x}+11\phi+17$
605.2-a2 605.2-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.038309613$ 1.358773366 \( -\frac{393466}{25} a + \frac{17856881}{125} \) \( \bigl[\phi\) , \( \phi\) , \( 0\) , \( 3 \phi - 195\) , \( 847 \phi - 500\bigr] \) ${y}^2+\phi{x}{y}={x}^{3}+\phi{x}^{2}+\left(3\phi-195\right){x}+847\phi-500$
605.2-b1 605.2-b \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $11.27636307$ 1.260735718 \( -\frac{45227}{55} a + \frac{72206}{55} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -2\) , \( 7 \phi + 3\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-2{x}+7\phi+3$
605.2-b2 605.2-b \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $3.758787690$ 1.260735718 \( -\frac{754904381777}{33275} a + \frac{1221461532231}{33275} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 65 \phi - 82\) , \( -390 \phi + 231\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(65\phi-82\right){x}-390\phi+231$
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 \( -\frac{48555143354501}{275} a + \frac{78563872776324}{275} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 140 \phi - 407\) , \( 1855 \phi - 3286\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(140\phi-407\right){x}+1855\phi-3286$
605.2-b4 605.2-b \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.939696922$ 1.260735718 \( \frac{114278307303626907}{78460709418025} a + \frac{89325070732461329}{78460709418025} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -935 \phi - 387\) , \( 8620 \phi + 7934\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-935\phi-387\right){x}+8620\phi+7934$
605.2-b5 605.2-b \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.879393845$ 1.260735718 \( \frac{1485675267531}{221445125} a + \frac{2666389392178}{221445125} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -260 \phi - 287\) , \( -3445 \phi - 1696\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-260\phi-287\right){x}-3445\phi-1696$
605.2-b6 605.2-b \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.638181535$ 1.260735718 \( -\frac{132583563}{605} a + \frac{59730809}{121} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -35 \phi - 52\) , \( 210 \phi + 51\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-35\phi-52\right){x}+210\phi+51$
605.2-b7 605.2-b \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.469848461$ 1.260735718 \( \frac{4560282420936767}{20796875} a + \frac{563715628160969}{4159375} \) \( \bigl[\phi + 1\) , \( \phi - 1\) , \( \phi\) , \( 832 \phi - 2982\) , \( 18800 \phi - 57148\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(832\phi-2982\right){x}+18800\phi-57148$
605.2-b8 605.2-b \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.819090767$ 1.260735718 \( \frac{626283905886387}{73205} a + \frac{387064721079604}{73205} \) \( \bigl[\phi + 1\) , \( \phi - 1\) , \( \phi\) , \( -48 \phi - 177\) , \( 1428 \phi - 947\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-48\phi-177\right){x}+1428\phi-947$
605.2-c1 605.2-c \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.044025197$ $19.13415901$ 1.130178257 \( -\frac{20192}{25} a + \frac{32421}{25} \) \( \bigl[\phi + 1\) , \( -\phi - 1\) , \( \phi + 1\) , \( -\phi - 2\) , \( 0\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-\phi-2\right){x}$
605.2-c2 605.2-c \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.022012598$ $19.13415901$ 1.130178257 \( -\frac{393466}{25} a + \frac{17856881}{125} \) \( \bigl[\phi + 1\) , \( -\phi - 1\) , \( \phi + 1\) , \( -6 \phi - 17\) , \( 13 \phi + 28\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-6\phi-17\right){x}+13\phi+28$
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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.