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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
49.1-CMa1 49.1-CMa \(\Q(\sqrt{-3}) \) \( 7^{2} \) $0$ $\Z/7\Z$ $-3$ $1$ $10.15449534$ 0.239293902 \( 0 \) \( \bigl[0\) , \( a + 1\) , \( a\) , \( a\) , \( 0\bigr] \) ${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}$
49.3-CMa1 49.3-CMa \(\Q(\sqrt{-3}) \) \( 7^{2} \) $0$ $\Z/7\Z$ $-3$ $1$ $10.15449534$ 0.239293902 \( 0 \) \( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( a\) , \( -a\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-a$
73.1-a1 73.1-a \(\Q(\sqrt{-3}) \) \( 73 \) $0$ $\Z/6\Z$ $1$ $3.242334089$ 0.311993743 \( \frac{60988685561}{389017} a - \frac{169775626841}{389017} \) \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 6 a + 10\) , \( -11 a + 20\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a+10\right){x}-11a+20$
73.1-a2 73.1-a \(\Q(\sqrt{-3}) \) \( 73 \) $0$ $\Z/6\Z$ $1$ $4.863501133$ 0.311993743 \( -\frac{927841113}{5329} a - \frac{395933743}{5329} \) \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 5\) , \( -4 a + 4\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+5{x}-4a+4$
73.1-a3 73.1-a \(\Q(\sqrt{-3}) \) \( 73 \) $0$ $\Z/6\Z$ $1$ $9.727002267$ 0.311993743 \( \frac{9927}{73} a + \frac{20960}{73} \) \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}$
73.1-a4 73.1-a \(\Q(\sqrt{-3}) \) \( 73 \) $0$ $\Z/6\Z$ $1$ $1.621167044$ 0.311993743 \( -\frac{55816089234767}{151334226289} a + \frac{107352826006104}{151334226289} \) \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 11 a + 5\) , \( -20 a + 11\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(11a+5\right){x}-20a+11$
73.2-a1 73.2-a \(\Q(\sqrt{-3}) \) \( 73 \) $0$ $\Z/6\Z$ $1$ $3.242334089$ 0.311993743 \( -\frac{60988685561}{389017} a - \frac{108786941280}{389017} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -4 a + 14\) , \( 16 a - 6\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a+14\right){x}+16a-6$
73.2-a2 73.2-a \(\Q(\sqrt{-3}) \) \( 73 \) $0$ $\Z/6\Z$ $1$ $4.863501133$ 0.311993743 \( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -6 a - 1\) , \( 4 a\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a-1\right){x}+4a$
73.2-a3 73.2-a \(\Q(\sqrt{-3}) \) \( 73 \) $0$ $\Z/6\Z$ $1$ $9.727002267$ 0.311993743 \( -\frac{9927}{73} a + \frac{30887}{73} \) \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-1\right){x}$
73.2-a4 73.2-a \(\Q(\sqrt{-3}) \) \( 73 \) $0$ $\Z/6\Z$ $1$ $1.621167044$ 0.311993743 \( \frac{55816089234767}{151334226289} a + \frac{51536736771337}{151334226289} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -9 a + 14\) , \( 30 a - 24\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9a+14\right){x}+30a-24$
75.1-a1 75.1-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $0.558925428$ 0.322695746 \( -\frac{147281603041}{215233605} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-110{x}-880$
75.1-a2 75.1-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \) $0$ $\Z/8\Z$ $1$ $8.942806850$ 0.322695746 \( -\frac{1}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$
75.1-a3 75.1-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \) $0$ $\Z/8\Z$ $1$ $1.117850856$ 0.322695746 \( \frac{4733169839}{3515625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$
75.1-a4 75.1-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $2.235701712$ 0.322695746 \( \frac{111284641}{50625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$
75.1-a5 75.1-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $4.471403425$ 0.322695746 \( \frac{13997521}{225} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$
75.1-a6 75.1-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1.117850856$ 0.322695746 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-135{x}-660$
75.1-a7 75.1-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \) $0$ $\Z/4\Z$ $1$ $2.235701712$ 0.322695746 \( \frac{56667352321}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$
75.1-a8 75.1-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $0.558925428$ 0.322695746 \( \frac{1114544804970241}{405} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$
81.1-CMa1 81.1-CMa \(\Q(\sqrt{-3}) \) \( 3^{4} \) $0$ $\Z/3\Z\oplus\Z/3\Z$ $-3$ $1$ $8.108628264$ 0.346779163 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}$
81.1-CMa2 81.1-CMa \(\Q(\sqrt{-3}) \) \( 3^{4} \) $0$ $\Z/3\Z$ $-27$ $1$ $2.702876088$ 0.346779163 \( -12288000 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( -30\) , \( 63\bigr] \) ${y}^2+{y}={x}^{3}-30{x}+63$
121.1-a1 121.1-a \(\Q(\sqrt{-3}) \) \( 11^{2} \) $0$ $\mathsf{trivial}$ $1$ $0.370308724$ 0.427595683 \( -\frac{52893159101157376}{11} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$
121.1-a2 121.1-a \(\Q(\sqrt{-3}) \) \( 11^{2} \) $0$ $\Z/5\Z$ $1$ $1.851543623$ 0.427595683 \( -\frac{122023936}{161051} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$
121.1-a3 121.1-a \(\Q(\sqrt{-3}) \) \( 11^{2} \) $0$ $\Z/5\Z$ $1$ $9.257718117$ 0.427595683 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}$
124.1-a1 124.1-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 31 \) $0$ $\mathsf{trivial}$ $1$ $0.368431786$ 0.425428381 \( -\frac{936087656892551}{1040187392} a + \frac{51401239062153}{520093696} \) \( \bigl[a + 1\) , \( a\) , \( a\) , \( 1300 a - 550\) , \( -9800 a - 7280\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(1300a-550\right){x}-9800a-7280$
124.1-a2 124.1-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 31 \) $0$ $\Z/5\Z$ $1$ $9.210794651$ 0.425428381 \( -\frac{24551}{62} a + \frac{45753}{31} \) \( \bigl[a + 1\) , \( a\) , \( a\) , \( 0\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}$
124.1-a3 124.1-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 31 \) $0$ $\Z/5\Z$ $1$ $1.842158930$ 0.425428381 \( \frac{511363962461}{916132832} a + \frac{1018073036305}{916132832} \) \( \bigl[a + 1\) , \( a\) , \( a\) , \( -15 a + 5\) , \( -7 a + 21\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-15a+5\right){x}-7a+21$
124.2-a1 124.2-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 31 \) $0$ $\mathsf{trivial}$ $1$ $0.368431786$ 0.425428381 \( \frac{936087656892551}{1040187392} a - \frac{833285178768245}{1040187392} \) \( \bigl[a\) , \( a - 1\) , \( a\) , \( -1301 a + 751\) , \( 10550 a - 16530\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1301a+751\right){x}+10550a-16530$
124.2-a2 124.2-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 31 \) $0$ $\Z/5\Z$ $1$ $9.210794651$ 0.425428381 \( \frac{24551}{62} a + \frac{66955}{62} \) \( \bigl[a\) , \( a - 1\) , \( a\) , \( -a + 1\) , \( 0\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+1\right){x}$
124.2-a3 124.2-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 31 \) $0$ $\Z/5\Z$ $1$ $1.842158930$ 0.425428381 \( -\frac{511363962461}{916132832} a + \frac{764718499383}{458066416} \) \( \bigl[a\) , \( a - 1\) , \( a\) , \( 14 a - 9\) , \( -3 a + 9\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(14a-9\right){x}-3a+9$
144.1-CMa1 144.1-CMa \(\Q(\sqrt{-3}) \) \( 2^{4} \cdot 3^{2} \) $0$ $\Z/2\Z\oplus\Z/6\Z$ $-3$ $1$ $5.108115717$ 0.491528664 \( 0 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 1\bigr] \) ${y}^2={x}^{3}+1$
144.1-CMa2 144.1-CMa \(\Q(\sqrt{-3}) \) \( 2^{4} \cdot 3^{2} \) $0$ $\Z/6\Z$ $-12$ $1$ $2.554057858$ 0.491528664 \( 54000 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -15\) , \( 22\bigr] \) ${y}^2={x}^{3}-15{x}+22$
147.2-a1 147.2-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.431038464$ 0.497720347 \( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -470 a + 321\) , \( 1866 a - 3772\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-470a+321\right){x}+1866a-3772$
147.2-a2 147.2-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.431038464$ 0.497720347 \( \frac{1866593950165482334}{99698791708803} a - \frac{1072967896631695607}{99698791708803} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 470 a - 149\) , \( -1866 a - 1906\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(470a-149\right){x}-1866a-1906$
147.2-a3 147.2-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.862076929$ 0.497720347 \( -\frac{4354703137}{17294403} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \) ${y}^2+{x}{y}={x}^{3}-34{x}-217$
147.2-a4 147.2-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 7^{2} \) $0$ $\Z/8\Z$ $1$ $6.896615437$ 0.497720347 \( \frac{103823}{63} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}$
147.2-a5 147.2-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/8\Z$ $1$ $3.448307718$ 0.497720347 \( \frac{7189057}{3969} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \) ${y}^2+{x}{y}={x}^{3}-4{x}-1$
147.2-a6 147.2-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 7^{2} \) $0$ $\Z/8\Z$ $1$ $1.724153859$ 0.497720347 \( \frac{6570725617}{45927} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \) ${y}^2+{x}{y}={x}^{3}-39{x}+90$
147.2-a7 147.2-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $1.724153859$ 0.497720347 \( \frac{13027640977}{21609} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \) ${y}^2+{x}{y}={x}^{3}-49{x}-136$
147.2-a8 147.2-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 7^{2} \) $0$ $\Z/4\Z$ $1$ $0.862076929$ 0.497720347 \( \frac{53297461115137}{147} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \) ${y}^2+{x}{y}={x}^{3}-784{x}-8515$
171.1-a1 171.1-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19 \) $0$ $\Z/6\Z$ $1$ $2.713137527$ 0.522143560 \( \frac{29840721}{6859} a - \frac{35267232}{6859} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -5 a - 5\) , \( 9 a + 3\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-5a-5\right){x}+9a+3$
171.1-a2 171.1-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19 \) $0$ $\Z/6\Z$ $1$ $1.356568763$ 0.522143560 \( -\frac{36038181633}{47045881} a - \frac{39546962313}{47045881} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -20 a + 25\) , \( 18 a + 48\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-20a+25\right){x}+18a+48$
171.1-a3 171.1-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19 \) $0$ $\Z/6\Z$ $1$ $8.139412583$ 0.522143560 \( -\frac{9153}{19} a + \frac{36801}{19} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( 0\) , \( -a\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}-a$
171.1-a4 171.1-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19 \) $0$ $\Z/6\Z$ $1$ $4.069706291$ 0.522143560 \( -\frac{363527109}{361} a + \frac{287391186}{361} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( 5 a + 5\) , \( -11 a + 11\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(5a+5\right){x}-11a+11$
171.2-a1 171.2-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19 \) $0$ $\Z/6\Z$ $1$ $2.713137527$ 0.522143560 \( -\frac{29840721}{6859} a - \frac{5426511}{6859} \) \( \bigl[1\) , \( -1\) , \( a\) , \( 4 a - 9\) , \( -10 a + 13\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(4a-9\right){x}-10a+13$
171.2-a2 171.2-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19 \) $0$ $\Z/6\Z$ $1$ $1.356568763$ 0.522143560 \( \frac{36038181633}{47045881} a - \frac{75585143946}{47045881} \) \( \bigl[1\) , \( -1\) , \( a\) , \( 19 a + 6\) , \( -19 a + 67\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(19a+6\right){x}-19a+67$
171.2-a3 171.2-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19 \) $0$ $\Z/6\Z$ $1$ $8.139412583$ 0.522143560 \( \frac{9153}{19} a + \frac{27648}{19} \) \( \bigl[1\) , \( -1\) , \( a\) , \( -a + 1\) , \( 0\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-a+1\right){x}$
171.2-a4 171.2-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19 \) $0$ $\Z/6\Z$ $1$ $4.069706291$ 0.522143560 \( \frac{363527109}{361} a - \frac{76135923}{361} \) \( \bigl[1\) , \( -1\) , \( a\) , \( -6 a + 11\) , \( 10 a + 1\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-6a+11\right){x}+10a+1$
192.1-a1 192.1-a \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \) $0$ $\Z/4\Z$ $1$ $3.635347017$ 0.524717144 \( -\frac{73696}{3} a - \frac{550672}{3} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 11 a - 6\) , \( 11 a - 1\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(11a-6\right){x}+11a-1$
192.1-a2 192.1-a \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \) $0$ $\Z/4\Z$ $1$ $3.635347017$ 0.524717144 \( \frac{73696}{3} a - \frac{624368}{3} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 6 a - 11\) , \( -11 a + 10\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(6a-11\right){x}-11a+10$
192.1-a3 192.1-a \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \) $0$ $\Z/2\Z$ $1$ $0.908836754$ 0.524717144 \( \frac{207646}{6561} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 16 a - 16\) , \( -180\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(16a-16\right){x}-180$
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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.