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Results (40 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
15.1-a1 15.1-a \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.636997307$ 1.315775981 \( -\frac{27637502042636079391}{15} a + 7135972342793472744 \) \( \bigl[a\) , \( 1\) , \( a\) , \( 155 a - 680\) , \( 2486 a - 10032\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(155a-680\right){x}+2486a-10032$
15.1-a2 15.1-a \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2.547989231$ 1.315775981 \( -\frac{147281603041}{215233605} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -110\) , \( 660\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-110{x}+660$
15.1-a3 15.1-a \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 1.315775981 \( -\frac{1}{15} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}$
15.1-a4 15.1-a \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2.547989231$ 1.315775981 \( \frac{4733169839}{3515625} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 35\) , \( 98\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+35{x}+98$
15.1-a5 15.1-a \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 1.315775981 \( \frac{111284641}{50625} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -10\) , \( -10\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-10{x}-10$
15.1-a6 15.1-a \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 1.315775981 \( \frac{13997521}{225} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -5\) , \( -12\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-5{x}-12$
15.1-a7 15.1-a \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 1.315775981 \( \frac{272223782641}{164025} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -135\) , \( 390\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-135{x}+390$
15.1-a8 15.1-a \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.547989231$ 1.315775981 \( \frac{56667352321}{15} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -80\) , \( -402\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-80{x}-402$
15.1-a9 15.1-a \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 1.315775981 \( \frac{1114544804970241}{405} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -2160\) , \( 35220\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-2160{x}+35220$
15.1-a10 15.1-a \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.636997307$ 1.315775981 \( \frac{27637502042636079391}{15} a + 7135972342793472744 \) \( \bigl[a\) , \( 1\) , \( a\) , \( -155 a - 680\) , \( -2486 a - 10032\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-155a-680\right){x}-2486a-10032$
15.1-b1 15.1-b \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.636997307$ 1.315775981 \( -\frac{27637502042636079391}{15} a + 7135972342793472744 \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -2539 a - 9913\) , \( -145850 a - 565247\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-2539a-9913\right){x}-145850a-565247$
15.1-b2 15.1-b \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.547989231$ 1.315775981 \( -\frac{147281603041}{215233605} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -3519 a - 13633\) , \( 412186 a + 1596397\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-3519a-13633\right){x}+412186a+1596397$
15.1-b3 15.1-b \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 1.315775981 \( -\frac{1}{15} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( a + 7\) , \( -94 a - 363\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(a+7\right){x}-94a-363$
15.1-b4 15.1-b \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.547989231$ 1.315775981 \( \frac{4733169839}{3515625} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 1121 a + 4347\) , \( 23958 a + 92793\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(1121a+4347\right){x}+23958a+92793$
15.1-b5 15.1-b \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 1.315775981 \( \frac{111284641}{50625} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -319 a - 1233\) , \( 2106 a + 8157\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-319a-1233\right){x}+2106a+8157$
15.1-b6 15.1-b \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 1.315775981 \( \frac{13997521}{225} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -159 a - 613\) , \( -2522 a - 9767\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-159a-613\right){x}-2522a-9767$
15.1-b7 15.1-b \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 1.315775981 \( \frac{272223782641}{164025} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -4319 a - 16733\) , \( 294206 a + 1139457\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-4319a-16733\right){x}+294206a+1139457$
15.1-b8 15.1-b \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.547989231$ 1.315775981 \( \frac{56667352321}{15} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -2559 a - 9913\) , \( -144782 a - 560747\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-2559a-9913\right){x}-144782a-560747$
15.1-b9 15.1-b \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 1.315775981 \( \frac{1114544804970241}{405} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -69119 a - 267833\) , \( 19314626 a + 74805717\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-69119a-267833\right){x}+19314626a+74805717$
15.1-b10 15.1-b \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.636997307$ 1.315775981 \( \frac{27637502042636079391}{15} a + 7135972342793472744 \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -40979 a - 158713\) , \( -8981954 a - 34786967\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-40979a-158713\right){x}-8981954a-34786967$
15.1-c1 15.1-c \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $4.801950709$ $15.69351105$ 1.216108162 \( -\frac{27637502042636079391}{15} a + 7135972342793472744 \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 155 a - 680\) , \( -2176 a + 8672\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(155a-680\right){x}-2176a+8672$
15.1-c2 15.1-c \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $9.603901418$ $0.490422220$ 1.216108162 \( -\frac{147281603041}{215233605} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-110{x}-880$
15.1-c3 15.1-c \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.600243838$ $31.38702211$ 1.216108162 \( -\frac{1}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$
15.1-c4 15.1-c \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) $1$ $\Z/8\Z$ $\mathrm{SU}(2)$ $4.801950709$ $1.961688882$ 1.216108162 \( \frac{4733169839}{3515625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$
15.1-c5 15.1-c \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $2.400975354$ $7.846755528$ 1.216108162 \( \frac{111284641}{50625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$
15.1-c6 15.1-c \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1.200487677$ $31.38702211$ 1.216108162 \( \frac{13997521}{225} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$
15.1-c7 15.1-c \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $4.801950709$ $1.961688882$ 1.216108162 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-135{x}-660$
15.1-c8 15.1-c \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $2.400975354$ $31.38702211$ 1.216108162 \( \frac{56667352321}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$
15.1-c9 15.1-c \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $9.603901418$ $0.490422220$ 1.216108162 \( \frac{1114544804970241}{405} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$
15.1-c10 15.1-c \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $4.801950709$ $15.69351105$ 1.216108162 \( \frac{27637502042636079391}{15} a + 7135972342793472744 \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -155 a - 680\) , \( 2176 a + 8672\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-155a-680\right){x}+2176a+8672$
15.1-d1 15.1-d \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.600625687$ $15.69351105$ 2.634464464 \( -\frac{27637502042636079391}{15} a + 7135972342793472744 \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -2543 a - 9924\) , \( 138228 a + 535486\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-2543a-9924\right){x}+138228a+535486$
15.1-d2 15.1-d \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $5.201251375$ $0.490422220$ 2.634464464 \( -\frac{147281603041}{215233605} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -3523 a - 13644\) , \( -422748 a - 1637318\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-3523a-13644\right){x}-422748a-1637318$
15.1-d3 15.1-d \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.325078210$ $31.38702211$ 2.634464464 \( -\frac{1}{15} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -3 a - 4\) , \( 92 a + 362\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-3a-4\right){x}+92a+362$
15.1-d4 15.1-d \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.600625687$ $1.961688882$ 2.634464464 \( \frac{4733169839}{3515625} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 1117 a + 4336\) , \( -20600 a - 79774\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(1117a+4336\right){x}-20600a-79774$
15.1-d5 15.1-d \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.300312843$ $7.846755528$ 2.634464464 \( \frac{111284641}{50625} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -323 a - 1244\) , \( -3068 a - 11878\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-323a-1244\right){x}-3068a-11878$
15.1-d6 15.1-d \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.650156421$ $31.38702211$ 2.634464464 \( \frac{13997521}{225} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -163 a - 624\) , \( 2040 a + 7906\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-163a-624\right){x}+2040a+7906$
15.1-d7 15.1-d \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $2.600625687$ $1.961688882$ 2.634464464 \( \frac{272223782641}{164025} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -4323 a - 16744\) , \( -307168 a - 1189678\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-4323a-16744\right){x}-307168a-1189678$
15.1-d8 15.1-d \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.300312843$ $31.38702211$ 2.634464464 \( \frac{56667352321}{15} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -2563 a - 9924\) , \( 137100 a + 530986\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-2563a-9924\right){x}+137100a+530986$
15.1-d9 15.1-d \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $5.201251375$ $0.490422220$ 2.634464464 \( \frac{1114544804970241}{405} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -69123 a - 267844\) , \( -19521988 a - 75609238\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-69123a-267844\right){x}-19521988a-75609238$
15.1-d10 15.1-d \(\Q(\sqrt{15}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.600625687$ $15.69351105$ 2.634464464 \( \frac{27637502042636079391}{15} a + 7135972342793472744 \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -40983 a - 158724\) , \( 8859012 a + 34310806\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-40983a-158724\right){x}+8859012a+34310806$
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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.