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Results (24 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
32400.1-CMc1 32400.1-CMc \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) 0 $\Z/2\Z$ $-4$ $\mathrm{U}(1)$ $1$ $0.884830445$ 0.884830445 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -54 i + 27\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-54i+27\right){x}$
32400.1-CMb1 32400.1-CMb \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) 0 $\Z/2\Z$ $-4$ $\mathrm{U}(1)$ $1$ $0.685386715$ 0.685386715 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -18 i + 99\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-18i+99\right){x}$
32400.1-CMa1 32400.1-CMa \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) 0 $\Z/2\Z$ $-4$ $\mathrm{U}(1)$ $1$ $2.654491335$ 2.654491335 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -6 i + 3\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-6i+3\right){x}$
32400.1-a1 32400.1-a \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.166712696$ $2.205171285$ 2.941040409 \( \frac{198261}{2} a - \frac{62613}{2} \) \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -22 i - 9\) , \( -45 i + 20\bigr] \) ${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-22i-9\right){x}-45i+20$
32400.1-a2 32400.1-a \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.500138089$ $0.735057095$ 2.941040409 \( -\frac{86643}{4} a - \frac{1971}{4} \) \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -82 i - 129\) , \( 455 i + 540\bigr] \) ${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-82i-129\right){x}+455i+540$
32400.1-a3 32400.1-a \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $2.500690447$ $0.147011419$ 2.941040409 \( \frac{15363}{256} a - \frac{47709}{256} \) \( \bigl[i + 1\) , \( i\) , \( 0\) , \( 999 i + 411\) , \( 14428 i + 39825\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(999i+411\right){x}+14428i+39825$
32400.1-a4 32400.1-a \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.833563482$ $0.441034257$ 2.941040409 \( -\frac{13670181}{8} a + \frac{19928133}{8} \) \( \bigl[i + 1\) , \( i\) , \( 0\) , \( -441 i + 831\) , \( 8688 i + 7645\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-441i+831\right){x}+8688i+7645$
32400.1-b1 32400.1-b \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.270962768$ 1.083851073 \( \frac{207646}{6561} \) \( \bigl[i + 1\) , \( i\) , \( 0\) , \( 141 i + 105\) , \( 6540 i + 1109\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(141i+105\right){x}+6540i+1109$
32400.1-b2 32400.1-b \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.083851073$ 1.083851073 \( \frac{2048}{3} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -24 i - 18\) , \( -14 i + 77\bigr] \) ${y}^2={x}^{3}+\left(-24i-18\right){x}-14i+77$
32400.1-b3 32400.1-b \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.083851073$ 1.083851073 \( \frac{35152}{9} \) \( \bigl[i + 1\) , \( i\) , \( 0\) , \( -39 i - 30\) , \( -111 i + 2\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-39i-30\right){x}-111i+2$
32400.1-b4 32400.1-b \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.541925536$ 1.083851073 \( \frac{1556068}{81} \) \( \bigl[i + 1\) , \( i\) , \( 0\) , \( -219 i - 165\) , \( 1554 i + 407\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-219i-165\right){x}+1554i+407$
32400.1-b5 32400.1-b \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.541925536$ 1.083851073 \( \frac{28756228}{3} \) \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -580 i - 435\) , \( 7155 i + 1630\bigr] \) ${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-580i-435\right){x}+7155i+1630$
32400.1-b6 32400.1-b \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.270962768$ 1.083851073 \( \frac{3065617154}{9} \) \( \bigl[i + 1\) , \( i\) , \( 0\) , \( -3459 i - 2595\) , \( 106368 i + 21305\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-3459i-2595\right){x}+106368i+21305$
32400.1-c1 32400.1-c \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) $1$ $\Z/2\Z$ $-3$ $N(\mathrm{U}(1))$ $0.417946696$ $2.284418796$ 3.819061154 \( 0 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 2 i - 11\bigr] \) ${y}^2={x}^{3}+2i-11$
32400.1-c2 32400.1-c \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) $1$ $\Z/2\Z$ $-3$ $N(\mathrm{U}(1))$ $1.253840088$ $0.761472932$ 3.819061154 \( 0 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -54 i + 297\bigr] \) ${y}^2={x}^{3}-54i+297$
32400.1-c3 32400.1-c \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) $1$ $\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $2.507680176$ $0.761472932$ 3.819061154 \( 54000 \) \( \bigl[i + 1\) , \( i\) , \( 0\) , \( -135 i - 102\) , \( 766 i + 216\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-135i-102\right){x}+766i+216$
32400.1-c4 32400.1-c \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) $1$ $\Z/2\Z$ $-12$ $N(\mathrm{U}(1))$ $0.835893392$ $2.284418796$ 3.819061154 \( 54000 \) \( \bigl[i + 1\) , \( i\) , \( 0\) , \( -15 i - 12\) , \( -36 i + 2\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-15i-12\right){x}-36i+2$
32400.1-d1 32400.1-d \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.493355371$ 1.973421484 \( \frac{1039}{24} a + \frac{13913}{24} \) \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -64 i - 123\) , \( 629 i - 502\bigr] \) ${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-64i-123\right){x}+629i-502$
32400.1-d2 32400.1-d \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.493355371$ 1.973421484 \( \frac{957521}{486} a + \frac{776647}{486} \) \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( 26 i + 207\) , \( -765 i + 540\bigr] \) ${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(26i+207\right){x}-765i+540$
32400.1-e1 32400.1-e \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.232411670$ $1.180177506$ 4.388592414 \( -\frac{2401}{3} a + \frac{343}{3} \) \( \bigl[i + 1\) , \( i\) , \( 0\) , \( 21 i + 15\) , \( -48 i + 43\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(21i+15\right){x}-48i+43$
32400.1-f1 32400.1-f \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.386917174$ $0.735057095$ 4.550499426 \( \frac{198261}{2} a - \frac{62613}{2} \) \( \bigl[i + 1\) , \( i\) , \( 0\) , \( -189 i - 75\) , \( -1124 i + 351\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-189i-75\right){x}-1124i+351$
32400.1-f2 32400.1-f \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.128972391$ $2.205171285$ 4.550499426 \( -\frac{86643}{4} a - \frac{1971}{4} \) \( \bigl[i + 1\) , \( i\) , \( 0\) , \( -9 i - 15\) , \( 12 i + 23\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-9i-15\right){x}+12i+23$
32400.1-f3 32400.1-f \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.644861957$ $0.441034257$ 4.550499426 \( \frac{15363}{256} a - \frac{47709}{256} \) \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( 110 i + 45\) , \( 549 i + 1438\bigr] \) ${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(110i+45\right){x}+549i+1438$
32400.1-f4 32400.1-f \(\Q(\sqrt{-1}) \) \( 2^{4} \cdot 3^{4} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.934585871$ $0.147011419$ 4.550499426 \( -\frac{13670181}{8} a + \frac{19928133}{8} \) \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -3970 i + 7485\) , \( 227093 i + 202446\bigr] \) ${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-3970i+7485\right){x}+227093i+202446$
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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.