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Results (26 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
57800.4-a1 57800.4-a \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.137996157$ 2.137996157 \( -\frac{71702}{125} a + \frac{470336}{125} \) \( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( 8 i + 7\) , \( -3 i + 5\bigr] \) ${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(8i+7\right){x}-3i+5$
57800.4-a2 57800.4-a \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.068998078$ 2.137996157 \( \frac{70930131}{15625} a + \frac{299889467}{15625} \) \( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( 58 i + 37\) , \( 7 i - 261\bigr] \) ${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(58i+37\right){x}+7i-261$
57800.4-b1 57800.4-b \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.518540234$ 1.555620703 \( -\frac{71702}{125} a + \frac{470336}{125} \) \( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -210 i - 31\) , \( 849 i - 449\bigr] \) ${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-210i-31\right){x}+849i-449$
57800.4-b2 57800.4-b \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.259270117$ 1.555620703 \( \frac{70930131}{15625} a + \frac{299889467}{15625} \) \( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -1200 i - 81\) , \( -11373 i + 9653\bigr] \) ${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-1200i-81\right){x}-11373i+9653$
57800.4-c1 57800.4-c \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $2.303606929$ $0.217024174$ 3.999507146 \( -\frac{2226135040016}{425} a - \frac{4178441913604}{425} \) \( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( -6933 i + 6265\) , \( 109144 i + 335983\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-6933i+6265\right){x}+109144i+335983$
57800.4-c2 57800.4-c \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.151803464$ $0.434048349$ 3.999507146 \( \frac{18495673728}{180625} a - \frac{897072368}{36125} \) \( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( -433 i + 390\) , \( 1769 i + 5508\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-433i+390\right){x}+1769i+5508$
57800.4-c3 57800.4-c \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $4.607213858$ $0.108512087$ 3.999507146 \( -\frac{624467745025896476}{4359848400625} a - \frac{74500491067519382}{4359848400625} \) \( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( 5887 i + 7905\) , \( -212070 i + 307155\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(5887i+7905\right){x}-212070i+307155$
57800.4-c4 57800.4-c \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $2.303606929$ $0.217024174$ 3.999507146 \( \frac{1142278337424}{32625390625} a + \frac{4669682943668}{32625390625} \) \( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( -13 i + 455\) , \( -1940 i + 12245\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-13i+455\right){x}-1940i+12245$
57800.4-c5 57800.4-c \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.575901732$ $0.434048349$ 3.999507146 \( -\frac{2845155328}{6640625} a + \frac{8254109696}{6640625} \) \( \bigl[0\) , \( -i\) , \( 0\) , \( 216 i - 77\) , \( 261 i + 979\bigr] \) ${y}^2={x}^{3}-i{x}^{2}+\left(216i-77\right){x}+261i+979$
57800.4-c6 57800.4-c \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $4.607213858$ $0.108512087$ 3.999507146 \( -\frac{54765023102363044}{44097900390625} a + \frac{449923792854324742}{44097900390625} \) \( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( 807 i - 5955\) , \( -37466 i + 157543\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(807i-5955\right){x}-37466i+157543$
57800.4-d1 57800.4-d \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.207456378$ $5.029645956$ 4.173728546 \( -2048 a - \frac{6144}{5} \) \( \bigl[0\) , \( -i\) , \( i + 1\) , \( i - 2\) , \( -i + 1\bigr] \) ${y}^2+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(i-2\right){x}-i+1$
57800.4-e1 57800.4-e \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.363426171$ 2.907409369 \( -\frac{35999730234}{390625} a - \frac{51700389912}{390625} \) \( \bigl[i + 1\) , \( i\) , \( 0\) , \( 796 i + 408\) , \( 936 i + 9924\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(796i+408\right){x}+936i+9924$
57800.4-e2 57800.4-e \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.363426171$ 2.907409369 \( \frac{35999730234}{390625} a - \frac{51700389912}{390625} \) \( \bigl[i + 1\) , \( i\) , \( 0\) , \( -104 i + 888\) , \( 10640 i + 1820\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-104i+888\right){x}+10640i+1820$
57800.4-e3 57800.4-e \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.726852342$ 2.907409369 \( \frac{237276}{625} \) \( \bigl[i + 1\) , \( i\) , \( 0\) , \( 26 i + 48\) , \( 224 i + 208\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(26i+48\right){x}+224i+208$
57800.4-e4 57800.4-e \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.181713085$ 2.907409369 \( -\frac{22845545233191}{152587890625} a + \frac{135893651813613}{152587890625} \) \( \bigl[i + 1\) , \( i\) , \( 0\) , \( -634 i + 978\) , \( 9964 i - 11152\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-634i+978\right){x}+9964i-11152$
57800.4-e5 57800.4-e \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.181713085$ 2.907409369 \( \frac{22845545233191}{152587890625} a + \frac{135893651813613}{152587890625} \) \( \bigl[i + 1\) , \( i\) , \( 0\) , \( 1166 i + 18\) , \( -12356 i + 7688\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(1166i+18\right){x}-12356i+7688$
57800.4-e6 57800.4-e \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.453704684$ 2.907409369 \( \frac{148176}{25} \) \( \bigl[i + 1\) , \( i\) , \( 0\) , \( -14 i - 27\) , \( 22 i + 46\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-14i-27\right){x}+22i+46$
57800.4-e7 57800.4-e \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.453704684$ 2.907409369 \( \frac{55296}{5} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 16 i + 30\) , \( 52 i - 47\bigr] \) ${y}^2={x}^{3}+\left(16i+30\right){x}+52i-47$
57800.4-e8 57800.4-e \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.726852342$ 2.907409369 \( \frac{132304644}{5} \) \( \bigl[i + 1\) , \( i\) , \( 0\) , \( -214 i - 402\) , \( 2302 i + 2876\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-214i-402\right){x}+2302i+2876$
57800.4-e9 57800.4-e \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.181713085$ 2.907409369 \( -\frac{15332659200009}{625} a + \frac{5763174879987}{625} \) \( \bigl[i + 1\) , \( i\) , \( 0\) , \( -1654 i + 14238\) , \( 657780 i + 114840\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-1654i+14238\right){x}+657780i+114840$
57800.4-e10 57800.4-e \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.181713085$ 2.907409369 \( \frac{15332659200009}{625} a + \frac{5763174879987}{625} \) \( \bigl[i + 1\) , \( i\) , \( 0\) , \( 12746 i + 6558\) , \( 51156 i + 652464\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(12746i+6558\right){x}+51156i+652464$
57800.4-f1 57800.4-f \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.219868325$ 2.439736651 \( -2048 a - \frac{6144}{5} \) \( \bigl[0\) , \( -i - 1\) , \( i + 1\) , \( -i + 33\) , \( 75 i + 14\bigr] \) ${y}^2+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-i+33\right){x}+75i+14$
57800.4-g1 57800.4-g \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.738190738$ 2.952762954 \( \frac{33574464}{180625} a + \frac{283128848}{180625} \) \( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 83 i + 12\) , \( -91 i + 28\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(83i+12\right){x}-91i+28$
57800.4-g2 57800.4-g \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.738190738$ 2.952762954 \( -\frac{2306048}{10625} a + \frac{19982336}{10625} \) \( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 86 i + 18\) , \( 16 i - 85\bigr] \) ${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(86i+18\right){x}+16i-85$
57800.4-g3 57800.4-g \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.369095369$ 2.952762954 \( -\frac{932738084712}{6640625} a + \frac{486943284916}{6640625} \) \( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 813 i + 297\) , \( 2696 i + 9697\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(813i+297\right){x}+2696i+9697$
57800.4-g4 57800.4-g \(\Q(\sqrt{-1}) \) \( 2^{3} \cdot 5^{2} \cdot 17^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.369095369$ 2.952762954 \( \frac{932967242152}{2088025} a + \frac{369264775804}{2088025} \) \( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 1033 i - 13\) , \( -8876 i - 8677\bigr] \) ${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(1033i-13\right){x}-8876i-8677$
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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.