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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
225.5-a1 225.5-a \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.666073956$ $0.558925428$ 1.123082843 \( -\frac{147281603041}{215233605} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-110{x}-880$
225.5-a2 225.5-a \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.666073956$ $8.942806850$ 1.123082843 \( -\frac{1}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$
225.5-a3 225.5-a \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/8\Z$ $\mathrm{SU}(2)$ $0.208259244$ $1.117850856$ 1.123082843 \( \frac{4733169839}{3515625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$
225.5-a4 225.5-a \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $0.416518489$ $2.235701712$ 1.123082843 \( \frac{111284641}{50625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$
225.5-a5 225.5-a \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $0.833036978$ $4.471403425$ 1.123082843 \( \frac{13997521}{225} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$
225.5-a6 225.5-a \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.833036978$ $1.117850856$ 1.123082843 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-135{x}-660$
225.5-a7 225.5-a \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.666073956$ $2.235701712$ 1.123082843 \( \frac{56667352321}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$
225.5-a8 225.5-a \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.666073956$ $0.558925428$ 1.123082843 \( \frac{1114544804970241}{405} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$
225.5-b1 225.5-b \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.676292688$ 1.631279343 \( \frac{5020579657727137}{31640625} a - \frac{15548725694657158}{31640625} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -385 a - 144\) , \( -4471 a + 3234\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-385a-144\right){x}-4471a+3234$
225.5-b2 225.5-b \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.338146344$ 1.631279343 \( \frac{785995287207294187003}{1001129150390625} a - \frac{4434281600575826892151}{1001129150390625} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -980 a + 901\) , \( 6920 a - 26670\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-980a+901\right){x}+6920a-26670$
225.5-b3 225.5-b \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $1.352585377$ 1.631279343 \( -\frac{10492718831}{820125} a + \frac{3853977841}{4100625} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -25 a - 9\) , \( -70 a + 75\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-25a-9\right){x}-70a+75$
225.5-b4 225.5-b \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2.705170755$ 1.631279343 \( -\frac{2328193}{32805} a - \frac{9002158}{54675} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -4\) , \( -5 a + 7\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}-4{x}-5a+7$
225.5-b5 225.5-b \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.338146344$ 1.631279343 \( -\frac{1003477310557125250603}{1158137618032400625} a + \frac{1313609484592825399351}{1158137618032400625} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 210 a + 71\) , \( 826 a - 3542\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(210a+71\right){x}+826a-3542$
225.5-b6 225.5-b \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.676292688$ 1.631279343 \( \frac{19658857399239023}{16815125390625} a + \frac{8228798640710134}{16815125390625} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -65 a + 46\) , \( 71 a - 372\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-65a+46\right){x}+71a-372$
225.5-b7 225.5-b \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $5.410341510$ 1.631279343 \( \frac{3229921}{405} a - \frac{210241}{135} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+{x}$
225.5-b8 225.5-b \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $1.352585377$ 1.631279343 \( \frac{29881004028839}{215233605} a + \frac{30104948010361}{71744535} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 25 a - 79\) , \( -160 a + 247\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(25a-79\right){x}-160a+247$
225.5-c1 225.5-c \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.676292688$ 1.631279343 \( -\frac{5020579657727137}{31640625} a - \frac{3509382012310007}{10546875} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( 384 a - 531\) , \( 4327 a - 2390\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(384a-531\right){x}+4327a-2390$
225.5-c2 225.5-c \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.338146344$ 1.631279343 \( -\frac{785995287207294187003}{1001129150390625} a - \frac{1216095437789510901716}{333709716796875} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( 979 a - 81\) , \( -6019 a - 22688\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(979a-81\right){x}-6019a-22688$
225.5-c3 225.5-c \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $1.352585377$ 1.631279343 \( \frac{10492718831}{820125} a - \frac{16203205438}{1366875} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( 24 a - 36\) , \( 61 a - 68\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(24a-36\right){x}+61a-68$
225.5-c4 225.5-c \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2.705170755$ 1.631279343 \( \frac{2328193}{32805} a - \frac{38647439}{164025} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -a - 6\) , \( a + 4\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-a-6\right){x}+a+4$
225.5-c5 225.5-c \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.338146344$ 1.631279343 \( \frac{1003477310557125250603}{1158137618032400625} a + \frac{103377391345233382916}{386045872677466875} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -211 a + 279\) , \( -755 a - 2084\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-211a+279\right){x}-755a-2084$
225.5-c6 225.5-c \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.676292688$ 1.631279343 \( -\frac{19658857399239023}{16815125390625} a + \frac{9295885346649719}{5605041796875} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( 64 a - 21\) , \( -25 a - 494\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(64a-21\right){x}-25a-494$
225.5-c7 225.5-c \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $5.410341510$ 1.631279343 \( -\frac{3229921}{405} a + \frac{2599198}{405} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -a - 1\) , \( a + 2\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-a-1\right){x}+a+2$
225.5-c8 225.5-c \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $1.352585377$ 1.631279343 \( -\frac{29881004028839}{215233605} a + \frac{120195848059922}{215233605} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -26 a - 56\) , \( 81 a + 164\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-26a-56\right){x}+81a+164$
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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.