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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
121.1-a1 121.1-a \(\Q(\sqrt{-163}) \) \( 11^{2} \) $0$ $\mathsf{trivial}$ $1$ $0.370308724$ 0.232038542 \( -\frac{52893159101157376}{11} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) ${y}^2+{y}={x}^3-{x}^2-7820{x}-263580$
121.1-a2 121.1-a \(\Q(\sqrt{-163}) \) \( 11^{2} \) $0$ $\Z/5\Z$ $1$ $1.851543623$ 0.232038542 \( -\frac{122023936}{161051} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) ${y}^2+{y}={x}^3-{x}^2-10{x}-20$
121.1-a3 121.1-a \(\Q(\sqrt{-163}) \) \( 11^{2} \) $0$ $\Z/5\Z$ $1$ $9.257718117$ 0.232038542 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3-{x}^2$
163.1-a1 163.1-a \(\Q(\sqrt{-163}) \) \( 163 \) $1$ $\mathsf{trivial}$ $0.189909232$ $5.483364664$ 2.610053345 \( -\frac{884736}{163} \) \( \bigl[0\) , \( 0\) , \( 1\) , \( -2\) , \( 1\bigr] \) ${y}^2+{y}={x}^3-2{x}+1$
196.1-a1 196.1-a \(\Q(\sqrt{-163}) \) \( 2^{2} \cdot 7^{2} \) $0 \le r \le 1$ $\Z/2\Z$ $1$ $0.875417135$ 6.228078249 \( -\frac{548347731625}{1835008} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-171{x}-874$
196.1-a2 196.1-a \(\Q(\sqrt{-163}) \) \( 2^{2} \cdot 7^{2} \) $0 \le r \le 1$ $\Z/6\Z$ $1$ $7.878754216$ 6.228078249 \( -\frac{15625}{28} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-{x}$
196.1-a3 196.1-a \(\Q(\sqrt{-163}) \) \( 2^{2} \cdot 7^{2} \) $0 \le r \le 1$ $\Z/6\Z$ $1$ $2.626251405$ 6.228078249 \( \frac{9938375}{21952} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+4{x}-6$
196.1-a4 196.1-a \(\Q(\sqrt{-163}) \) \( 2^{2} \cdot 7^{2} \) $0 \le r \le 1$ $\Z/6\Z$ $1$ $1.313125702$ 6.228078249 \( \frac{4956477625}{941192} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-36{x}-70$
196.1-a5 196.1-a \(\Q(\sqrt{-163}) \) \( 2^{2} \cdot 7^{2} \) $0 \le r \le 1$ $\Z/6\Z$ $1$ $3.939377108$ 6.228078249 \( \frac{128787625}{98} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-11{x}+12$
196.1-a6 196.1-a \(\Q(\sqrt{-163}) \) \( 2^{2} \cdot 7^{2} \) $0 \le r \le 1$ $\Z/2\Z$ $1$ $0.437708567$ 6.228078249 \( \frac{2251439055699625}{25088} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-2731{x}-55146$
225.1-a1 225.1-a \(\Q(\sqrt{-163}) \) \( 3^{2} \cdot 5^{2} \) $0 \le r \le 1$ $\Z/2\Z$ $1$ $0.558925428$ 4.313443944 \( -\frac{147281603041}{215233605} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$
225.1-a2 225.1-a \(\Q(\sqrt{-163}) \) \( 3^{2} \cdot 5^{2} \) $0 \le r \le 1$ $\Z/4\Z$ $1$ $8.942806850$ 4.313443944 \( -\frac{1}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2$
225.1-a3 225.1-a \(\Q(\sqrt{-163}) \) \( 3^{2} \cdot 5^{2} \) $0 \le r \le 1$ $\Z/8\Z$ $1$ $1.117850856$ 4.313443944 \( \frac{4733169839}{3515625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2+35{x}-28$
225.1-a4 225.1-a \(\Q(\sqrt{-163}) \) \( 3^{2} \cdot 5^{2} \) $0 \le r \le 1$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $2.235701712$ 4.313443944 \( \frac{111284641}{50625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$
225.1-a5 225.1-a \(\Q(\sqrt{-163}) \) \( 3^{2} \cdot 5^{2} \) $0 \le r \le 1$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $4.471403425$ 4.313443944 \( \frac{13997521}{225} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$
225.1-a6 225.1-a \(\Q(\sqrt{-163}) \) \( 3^{2} \cdot 5^{2} \) $0 \le r \le 1$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1.117850856$ 4.313443944 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$
225.1-a7 225.1-a \(\Q(\sqrt{-163}) \) \( 3^{2} \cdot 5^{2} \) $0 \le r \le 1$ $\Z/4\Z$ $1$ $2.235701712$ 4.313443944 \( \frac{56667352321}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-80{x}+242$
225.1-a8 225.1-a \(\Q(\sqrt{-163}) \) \( 3^{2} \cdot 5^{2} \) $0 \le r \le 1$ $\Z/2\Z$ $1$ $0.558925428$ 4.313443944 \( \frac{1114544804970241}{405} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-2160{x}-39540$
244.1-a1 244.1-a \(\Q(\sqrt{-163}) \) \( 2^{2} \cdot 61 \) $1$ $\mathsf{trivial}$ $1.247542028$ $5.847212706$ 4.570884663 \( -\frac{4757391}{7442} a + \frac{9390068}{3721} \) \( \bigl[a\) , \( -a\) , \( 1\) , \( 5 a + 26\) , \( -9 a - 7\bigr] \) ${y}^2+a{x}{y}+{y}={x}^3-a{x}^2+\left(5a+26\right){x}-9a-7$
244.2-a1 244.2-a \(\Q(\sqrt{-163}) \) \( 2^{2} \cdot 61 \) $1$ $\mathsf{trivial}$ $1.247542028$ $5.847212706$ 4.570884663 \( \frac{4757391}{7442} a + \frac{14022745}{7442} \) \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -6 a + 31\) , \( 9 a - 16\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-{x}^2+\left(-6a+31\right){x}+9a-16$
256.1-a1 256.1-a \(\Q(\sqrt{-163}) \) \( 2^{8} \) $0$ $\mathsf{trivial}$ $1$ $2.142899731$ 1.342758886 \( \frac{132651}{8} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 17\) , \( -4 a + 2\bigr] \) ${y}^2={x}^3+17{x}-4a+2$
256.1-b1 256.1-b \(\Q(\sqrt{-163}) \) \( 2^{8} \) $0$ $\mathsf{trivial}$ $1$ $2.142899731$ 1.342758886 \( \frac{132651}{8} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 17\) , \( 4 a - 2\bigr] \) ${y}^2={x}^3+17{x}+4a-2$
289.1-a1 289.1-a \(\Q(\sqrt{-163}) \) \( 17^{2} \) $0$ $\Z/4\Z$ $1$ $2.123938699$ 0.083179859 \( -\frac{35937}{83521} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}-14$
289.1-a2 289.1-a \(\Q(\sqrt{-163}) \) \( 17^{2} \) $0$ $\Z/4\Z$ $1$ $8.495754796$ 0.083179859 \( \frac{35937}{17} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}$
289.1-a3 289.1-a \(\Q(\sqrt{-163}) \) \( 17^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $4.247877398$ 0.083179859 \( \frac{20346417}{289} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-{x}^2-6{x}-4$
289.1-a4 289.1-a \(\Q(\sqrt{-163}) \) \( 17^{2} \) $0$ $\Z/2\Z$ $1$ $2.123938699$ 0.083179859 \( \frac{82483294977}{17} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-{x}^2-91{x}-310$
361.1-a1 361.1-a \(\Q(\sqrt{-163}) \) \( 19^{2} \) $0$ $\mathsf{trivial}$ $1$ $0.935309008$ 0.586072443 \( -\frac{50357871050752}{19} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -769\) , \( -8470\bigr] \) ${y}^2+{y}={x}^3+{x}^2-769{x}-8470$
361.1-a2 361.1-a \(\Q(\sqrt{-163}) \) \( 19^{2} \) $0$ $\Z/3\Z$ $1$ $2.805927025$ 0.586072443 \( -\frac{89915392}{6859} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -9\) , \( -15\bigr] \) ${y}^2+{y}={x}^3+{x}^2-9{x}-15$
361.1-a3 361.1-a \(\Q(\sqrt{-163}) \) \( 19^{2} \) $0$ $\Z/3\Z$ $1$ $8.417781075$ 0.586072443 \( \frac{32768}{19} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( 0\bigr] \) ${y}^2+{y}={x}^3+{x}^2+{x}$
400.1-a1 400.1-a \(\Q(\sqrt{-163}) \) \( 2^{4} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $1.070515942$ 0.754643519 \( -\frac{20720464}{15625} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -36\) , \( -140\bigr] \) ${y}^2={x}^3+{x}^2-36{x}-140$
400.1-a2 400.1-a \(\Q(\sqrt{-163}) \) \( 2^{4} \cdot 5^{2} \) $0$ $\Z/6\Z$ $1$ $3.211547828$ 0.754643519 \( \frac{21296}{25} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 4\) , \( 4\bigr] \) ${y}^2={x}^3+{x}^2+4{x}+4$
400.1-a3 400.1-a \(\Q(\sqrt{-163}) \) \( 2^{4} \cdot 5^{2} \) $0$ $\Z/6\Z$ $1$ $6.423095656$ 0.754643519 \( \frac{16384}{5} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) ${y}^2={x}^3+{x}^2-{x}$
400.1-a4 400.1-a \(\Q(\sqrt{-163}) \) \( 2^{4} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $2.141031885$ 0.754643519 \( \frac{488095744}{125} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \) ${y}^2={x}^3+{x}^2-41{x}-116$
441.1-a1 441.1-a \(\Q(\sqrt{-163}) \) \( 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $7.677157865$ $0.862076929$ 4.147082535 \( -\frac{4354703137}{17294403} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \) ${y}^2+{x}{y}={x}^3-34{x}-217$
441.1-a2 441.1-a \(\Q(\sqrt{-163}) \) \( 3^{2} \cdot 7^{2} \) $1$ $\Z/4\Z$ $15.35431573$ $6.896615437$ 4.147082535 \( \frac{103823}{63} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^3+{x}$
441.1-a3 441.1-a \(\Q(\sqrt{-163}) \) \( 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $30.70863146$ $3.448307718$ 4.147082535 \( \frac{7189057}{3969} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \) ${y}^2+{x}{y}={x}^3-4{x}-1$
441.1-a4 441.1-a \(\Q(\sqrt{-163}) \) \( 3^{2} \cdot 7^{2} \) $1$ $\Z/8\Z$ $61.41726292$ $1.724153859$ 4.147082535 \( \frac{6570725617}{45927} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \) ${y}^2+{x}{y}={x}^3-39{x}+90$
441.1-a5 441.1-a \(\Q(\sqrt{-163}) \) \( 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $15.35431573$ $1.724153859$ 4.147082535 \( \frac{13027640977}{21609} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \) ${y}^2+{x}{y}={x}^3-49{x}-136$
441.1-a6 441.1-a \(\Q(\sqrt{-163}) \) \( 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $30.70863146$ $0.862076929$ 4.147082535 \( \frac{53297461115137}{147} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \) ${y}^2+{x}{y}={x}^3-784{x}-8515$
576.1-a1 576.1-a \(\Q(\sqrt{-163}) \) \( 2^{6} \cdot 3^{2} \) $0 \le r \le 1$ $\Z/2\Z$ $1$ $0.908836754$ 6.661758943 \( \frac{207646}{6561} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( -180\bigr] \) ${y}^2={x}^3-{x}^2+16{x}-180$
576.1-a2 576.1-a \(\Q(\sqrt{-163}) \) \( 2^{6} \cdot 3^{2} \) $0 \le r \le 1$ $\Z/4\Z$ $1$ $7.270694035$ 6.661758943 \( \frac{2048}{3} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2={x}^3-{x}^2+{x}$
576.1-a3 576.1-a \(\Q(\sqrt{-163}) \) \( 2^{6} \cdot 3^{2} \) $0 \le r \le 1$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $3.635347017$ 6.661758943 \( \frac{35152}{9} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( 4\bigr] \) ${y}^2={x}^3-{x}^2-4{x}+4$
576.1-a4 576.1-a \(\Q(\sqrt{-163}) \) \( 2^{6} \cdot 3^{2} \) $0 \le r \le 1$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1.817673508$ 6.661758943 \( \frac{1556068}{81} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -24\) , \( -36\bigr] \) ${y}^2={x}^3-{x}^2-24{x}-36$
576.1-a5 576.1-a \(\Q(\sqrt{-163}) \) \( 2^{6} \cdot 3^{2} \) $0 \le r \le 1$ $\Z/4\Z$ $1$ $1.817673508$ 6.661758943 \( \frac{28756228}{3} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 220\bigr] \) ${y}^2={x}^3-{x}^2-64{x}+220$
576.1-a6 576.1-a \(\Q(\sqrt{-163}) \) \( 2^{6} \cdot 3^{2} \) $0 \le r \le 1$ $\Z/2\Z$ $1$ $0.908836754$ 6.661758943 \( \frac{3065617154}{9} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -384\) , \( -2772\bigr] \) ${y}^2={x}^3-{x}^2-384{x}-2772$
593.1-a1 593.1-a \(\Q(\sqrt{-163}) \) \( 593 \) $0$ $\Z/2\Z$ $1$ $8.223475941$ 2.898505559 \( \frac{3503}{593} a - \frac{8168}{593} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 46\) , \( -3 a - 14\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+46{x}-3a-14$
593.1-a2 593.1-a \(\Q(\sqrt{-163}) \) \( 593 \) $0$ $\Z/2\Z$ $1$ $4.111737970$ 2.898505559 \( -\frac{672292257}{351649} a + \frac{6439664009}{351649} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 51\) , \( -4 a - 29\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+51{x}-4a-29$
593.2-a1 593.2-a \(\Q(\sqrt{-163}) \) \( 593 \) $0$ $\Z/2\Z$ $1$ $8.223475941$ 2.898505559 \( -\frac{3503}{593} a - \frac{4665}{593} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -2 a + 48\) , \( 2 a - 16\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+\left(-2a+48\right){x}+2a-16$
593.2-a2 593.2-a \(\Q(\sqrt{-163}) \) \( 593 \) $0$ $\Z/2\Z$ $1$ $4.111737970$ 2.898505559 \( \frac{672292257}{351649} a + \frac{5767371752}{351649} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -2 a + 53\) , \( 3 a - 32\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+\left(-2a+53\right){x}+3a-32$
604.1-a1 604.1-a \(\Q(\sqrt{-163}) \) \( 2^{2} \cdot 151 \) $2$ $\mathsf{trivial}$ $3.668638407$ $2.482552716$ 11.41378186 \( -\frac{2066959707}{2918528} a - \frac{868213747}{364816} \) \( \bigl[1\) , \( 1\) , \( a\) , \( a - 2\) , \( 2 a + 16\bigr] \) ${y}^2+{x}{y}+a{y}={x}^3+{x}^2+\left(a-2\right){x}+2a+16$
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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.