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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
1.1-a1 1.1-a \(\Q(\zeta_{20})^+\) \( 1 \) $0$ $\Z/10\Z$ $-4$ $1$ $1512.581761$ 0.338223563 \( 1728 \) \( \bigl[a^{2} + a - 3\) , \( a^{3} - 3 a - 1\) , \( a^{2} + a - 2\) , \( -a^{3} - 2 a^{2} + 3 a + 5\) , \( -a - 1\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(-a^{3}-2a^{2}+3a+5\right){x}-a-1$
1.1-a2 1.1-a \(\Q(\zeta_{20})^+\) \( 1 \) $0$ $\Z/2\Z$ $-100$ $1$ $2.420130817$ 0.338223563 \( 19691491018752 a^{2} - 27212977933632 \) \( \bigl[a^{2} + a - 3\) , \( a^{3} - 3 a - 1\) , \( a^{2} + a - 2\) , \( 119 a^{3} - 152 a^{2} - 217 a + 135\) , \( 1098 a^{3} - 1803 a^{2} - 1718 a + 2224\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(119a^{3}-152a^{2}-217a+135\right){x}+1098a^{3}-1803a^{2}-1718a+2224$
1.1-a3 1.1-a \(\Q(\zeta_{20})^+\) \( 1 \) $0$ $\Z/10\Z$ $-100$ $1$ $1512.581761$ 0.338223563 \( 19691491018752 a^{2} - 27212977933632 \) \( \bigl[a^{2} + a - 3\) , \( a^{3} - 3 a - 1\) , \( a^{2} + a - 2\) , \( 119 a^{3} - 152 a^{2} - 217 a + 135\) , \( -1268 a^{3} + 1963 a^{2} + 2076 a - 2326\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(119a^{3}-152a^{2}-217a+135\right){x}-1268a^{3}+1963a^{2}+2076a-2326$
1.1-a4 1.1-a \(\Q(\zeta_{20})^+\) \( 1 \) $0$ $\Z/2\Z$ $-100$ $1$ $2.420130817$ 0.338223563 \( -19691491018752 a^{2} + 71244477160128 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a - 1\) , \( a^{2} + a - 2\) , \( 140 a^{3} + 150 a^{2} - 541 a - 619\) , \( 1727 a^{3} + 1963 a^{2} - 6449 a - 7491\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(140a^{3}+150a^{2}-541a-619\right){x}+1727a^{3}+1963a^{2}-6449a-7491$
1.1-a5 1.1-a \(\Q(\zeta_{20})^+\) \( 1 \) $0$ $\Z/10\Z$ $-100$ $1$ $1512.581761$ 0.338223563 \( -19691491018752 a^{2} + 71244477160128 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a - 1\) , \( a^{2} + a - 2\) , \( 140 a^{3} + 150 a^{2} - 541 a - 619\) , \( -1577 a^{3} - 1803 a^{2} + 5829 a + 6789\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(140a^{3}+150a^{2}-541a-619\right){x}-1577a^{3}-1803a^{2}+5829a+6789$
1.1-a6 1.1-a \(\Q(\zeta_{20})^+\) \( 1 \) $0$ $\Z/10\Z$ $-4$ $1$ $1512.581761$ 0.338223563 \( 1728 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a - 1\) , \( a^{2} + a - 2\) , \( -a + 1\) , \( -1\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+1\right){x}-1$
25.1-a1 25.1-a \(\Q(\zeta_{20})^+\) \( 5^{2} \) $0$ $\Z/10\Z$ $-20$ $1$ $2086.205928$ 0.932979654 \( 565760 a^{2} - 782400 \) \( \bigl[a^{3} - 2 a + 1\) , \( -a^{2} + 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -6 a^{3} + 6 a^{2} + 22 a - 24\) , \( 25 a^{3} - 28 a^{2} - 91 a + 102\bigr] \) ${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-6a^{3}+6a^{2}+22a-24\right){x}+25a^{3}-28a^{2}-91a+102$
25.1-a2 25.1-a \(\Q(\zeta_{20})^+\) \( 5^{2} \) $0$ $\Z/10\Z$ $-20$ $1$ $2086.205928$ 0.932979654 \( -565760 a^{2} + 2046400 \) \( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} - a^{2} + 3 a + 2\) , \( a^{2} + a - 2\) , \( -5 a^{3} - 9 a^{2} + 8 a + 13\) , \( 15 a^{3} + 28 a^{2} - 21 a - 38\bigr] \) ${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+2\right){x}^{2}+\left(-5a^{3}-9a^{2}+8a+13\right){x}+15a^{3}+28a^{2}-21a-38$
25.1-a3 25.1-a \(\Q(\zeta_{20})^+\) \( 5^{2} \) $0$ $\Z/2\Z$ $-20$ $1$ $83.44823715$ 0.932979654 \( 565760 a^{2} - 782400 \) \( \bigl[a^{3} - 2 a + 1\) , \( -a^{2} + 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 6 a^{3} + 6 a^{2} - 22 a - 23\) , \( 31 a^{3} + 36 a^{2} - 113 a - 132\bigr] \) ${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(6a^{3}+6a^{2}-22a-23\right){x}+31a^{3}+36a^{2}-113a-132$
25.1-a4 25.1-a \(\Q(\zeta_{20})^+\) \( 5^{2} \) $0$ $\Z/2\Z$ $-20$ $1$ $83.44823715$ 0.932979654 \( -565760 a^{2} + 2046400 \) \( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( a^{2} + a - 2\) , \( 3 a^{3} - 9 a^{2} - 4 a + 14\) , \( 19 a^{3} - 36 a^{2} - 27 a + 48\bigr] \) ${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+3\right){x}^{2}+\left(3a^{3}-9a^{2}-4a+14\right){x}+19a^{3}-36a^{2}-27a+48$
59.1-a1 59.1-a \(\Q(\zeta_{20})^+\) \( 59 \) $0$ $\mathsf{trivial}$ $1$ $67.12316258$ 1.500919544 \( -\frac{7276684815}{205379} a^{3} + \frac{7434481239}{205379} a^{2} + \frac{25389289053}{205379} a - \frac{28299397059}{205379} \) \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a^{2} - 2\) , \( -a^{3} + 4 a + 3\) , \( 5 a^{3} + 6 a^{2} - 18 a - 22\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-3\right){x}^{2}+\left(-a^{3}+4a+3\right){x}+5a^{3}+6a^{2}-18a-22$
59.1-b1 59.1-b \(\Q(\zeta_{20})^+\) \( 59 \) $1$ $\mathsf{trivial}$ $0.003152340$ $1465.929300$ 1.239973629 \( -\frac{7276684815}{205379} a^{3} + \frac{7434481239}{205379} a^{2} + \frac{25389289053}{205379} a - \frac{28299397059}{205379} \) \( \bigl[a^{3} - 3 a + 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a + 1\) , \( -a^{3} - 2 a^{2} + 3 a + 6\) , \( -4 a^{3} - 5 a^{2} + 14 a + 17\bigr] \) ${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(-a^{3}-2a^{2}+3a+6\right){x}-4a^{3}-5a^{2}+14a+17$
59.2-a1 59.2-a \(\Q(\zeta_{20})^+\) \( 59 \) $0$ $\mathsf{trivial}$ $1$ $67.12316258$ 1.500919544 \( -\frac{3559234608}{205379} a^{3} - \frac{7434481239}{205379} a^{2} + \frac{3401019009}{205379} a + \frac{8873009136}{205379} \) \( \bigl[a^{3} + a^{2} - 2 a - 3\) , \( a + 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + 2 a^{2} - 2 a - 3\) , \( 4 a^{3} - 3 a^{2} - 7 a + 2\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a^{3}+2a^{2}-2a-3\right){x}+4a^{3}-3a^{2}-7a+2$
59.2-b1 59.2-b \(\Q(\zeta_{20})^+\) \( 59 \) $1$ $\mathsf{trivial}$ $0.003152340$ $1465.929300$ 1.239973629 \( -\frac{3559234608}{205379} a^{3} - \frac{7434481239}{205379} a^{2} + \frac{3401019009}{205379} a + \frac{8873009136}{205379} \) \( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a^{3} - 3 a + 1\) , \( -a^{3} + 2 a + 1\) , \( -3 a^{3} + 5 a^{2} + 5 a - 8\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-a^{3}+2a+1\right){x}-3a^{3}+5a^{2}+5a-8$
59.3-a1 59.3-a \(\Q(\zeta_{20})^+\) \( 59 \) $0$ $\mathsf{trivial}$ $1$ $67.12316258$ 1.500919544 \( \frac{3559234608}{205379} a^{3} - \frac{7434481239}{205379} a^{2} - \frac{3401019009}{205379} a + \frac{8873009136}{205379} \) \( \bigl[a^{3} + a^{2} - 2 a - 3\) , \( a + 1\) , \( 1\) , \( 2 a^{2} + 3 a - 1\) , \( -2 a^{3} - 3 a^{2} + 4 a + 4\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-3\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a^{2}+3a-1\right){x}-2a^{3}-3a^{2}+4a+4$
59.3-b1 59.3-b \(\Q(\zeta_{20})^+\) \( 59 \) $1$ $\mathsf{trivial}$ $0.003152340$ $1465.929300$ 1.239973629 \( \frac{3559234608}{205379} a^{3} - \frac{7434481239}{205379} a^{2} - \frac{3401019009}{205379} a + \frac{8873009136}{205379} \) \( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a^{3} + a^{2} - 2 a - 3\) , \( -2 a^{3} - a^{2} + 6 a + 3\) , \( 3 a^{3} + 4 a^{2} - 5 a - 5\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-2a-3\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-2a^{3}-a^{2}+6a+3\right){x}+3a^{3}+4a^{2}-5a-5$
59.4-a1 59.4-a \(\Q(\zeta_{20})^+\) \( 59 \) $0$ $\mathsf{trivial}$ $1$ $67.12316258$ 1.500919544 \( \frac{7276684815}{205379} a^{3} + \frac{7434481239}{205379} a^{2} - \frac{25389289053}{205379} a - \frac{28299397059}{205379} \) \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a\) , \( -a^{2} + 2 a + 5\) , \( -3 a^{3} + 6 a^{2} + 13 a - 21\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+a{y}={x}^{3}+\left(a^{3}+a^{2}-4a-3\right){x}^{2}+\left(-a^{2}+2a+5\right){x}-3a^{3}+6a^{2}+13a-21$
59.4-b1 59.4-b \(\Q(\zeta_{20})^+\) \( 59 \) $1$ $\mathsf{trivial}$ $0.003152340$ $1465.929300$ 1.239973629 \( \frac{7276684815}{205379} a^{3} + \frac{7434481239}{205379} a^{2} - \frac{25389289053}{205379} a - \frac{28299397059}{205379} \) \( \bigl[a^{3} - 3 a + 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{3} + a^{2} - 2 a - 2\) , \( -2 a^{2} + 5\) , \( 4 a^{3} - 6 a^{2} - 16 a + 20\bigr] \) ${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{3}+a^{2}-2a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(-2a^{2}+5\right){x}+4a^{3}-6a^{2}-16a+20$
64.1-a1 64.1-a \(\Q(\zeta_{20})^+\) \( 2^{6} \) $0$ $\Z/8\Z$ $1$ $1471.388299$ 1.028163831 \( -548896 a^{2} + 1987376 \) \( \bigl[a^{2} + a - 3\) , \( a^{2} - 4\) , \( a^{3} - 2 a + 1\) , \( 4 a^{3} + 5 a^{2} - 9 a - 9\) , \( 2 a^{2} + 7 a + 5\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(4a^{3}+5a^{2}-9a-9\right){x}+2a^{2}+7a+5$
64.1-a2 64.1-a \(\Q(\zeta_{20})^+\) \( 2^{6} \) $0$ $\Z/2\Z$ $1$ $22.99044218$ 1.028163831 \( 2711191688 a^{2} - 3746774764 \) \( \bigl[a^{2} + a - 3\) , \( -a^{2} + a + 2\) , \( a^{2} + a - 3\) , \( -15 a^{3} + 12 a^{2} + 50 a - 50\) , \( -1451 a^{3} + 1696 a^{2} + 5243 a - 6150\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-15a^{3}+12a^{2}+50a-50\right){x}-1451a^{3}+1696a^{2}+5243a-6150$
64.1-a3 64.1-a \(\Q(\zeta_{20})^+\) \( 2^{6} \) $0$ $\Z/2\Z$ $1$ $22.99044218$ 1.028163831 \( -2711191688 a^{2} + 9809183676 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 5 a^{3} - 12 a^{2} - 2 a + 10\) , \( 890 a^{3} - 1696 a^{2} - 1220 a + 2330\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-3\right){x}^{2}+\left(5a^{3}-12a^{2}-2a+10\right){x}+890a^{3}-1696a^{2}-1220a+2330$
64.1-a4 64.1-a \(\Q(\zeta_{20})^+\) \( 2^{6} \) $0$ $\Z/8\Z$ $1$ $1471.388299$ 1.028163831 \( 548896 a^{2} - 757104 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} - a + 4\) , \( a^{2} + a - 3\) , \( 4 a^{3} - 10 a^{2} - 18 a + 31\) , \( 11 a^{3} - 11 a^{2} - 38 a + 43\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(4a^{3}-10a^{2}-18a+31\right){x}+11a^{3}-11a^{2}-38a+43$
64.1-a5 64.1-a \(\Q(\zeta_{20})^+\) \( 2^{6} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $1471.388299$ 1.028163831 \( 2048 \) \( \bigl[0\) , \( a^{2} - 3\) , \( 0\) , \( -a^{2} + 2\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-a^{2}+2\right){x}$
64.1-a6 64.1-a \(\Q(\zeta_{20})^+\) \( 2^{6} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $367.8470749$ 1.028163831 \( 78608 \) \( \bigl[a^{3} - 2 a + 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 0\) , \( 12 a^{3} + 13 a^{2} - 39 a - 44\) , \( 20 a^{3} + 22 a^{2} - 69 a - 79\bigr] \) ${y}^2+\left(a^{3}-2a+1\right){x}{y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(12a^{3}+13a^{2}-39a-44\right){x}+20a^{3}+22a^{2}-69a-79$
64.1-b1 64.1-b \(\Q(\zeta_{20})^+\) \( 2^{6} \) $1$ $\Z/4\Z$ $0.073302756$ $949.4144128$ 1.556184659 \( 2711191688 a^{2} - 3746774764 \) \( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 2 a - 4\) , \( a^{2} + a - 3\) , \( -15 a^{3} + 12 a^{2} + 50 a - 50\) , \( 1450 a^{3} - 1696 a^{2} - 5240 a + 6148\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-4\right){x}^{2}+\left(-15a^{3}+12a^{2}+50a-50\right){x}+1450a^{3}-1696a^{2}-5240a+6148$
64.1-b2 64.1-b \(\Q(\zeta_{20})^+\) \( 2^{6} \) $1$ $\Z/2\Z$ $0.146605513$ $237.3536032$ 1.556184659 \( -548896 a^{2} + 1987376 \) \( \bigl[a^{2} + a - 3\) , \( -a^{3} - a^{2} + 3 a + 2\) , \( a^{3} - 2 a + 1\) , \( 4 a^{3} + 5 a^{2} - 9 a - 9\) , \( -a^{3} - 4 a^{2} - 5 a - 3\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+2\right){x}^{2}+\left(4a^{3}+5a^{2}-9a-9\right){x}-a^{3}-4a^{2}-5a-3$
64.1-b3 64.1-b \(\Q(\zeta_{20})^+\) \( 2^{6} \) $1$ $\Z/2\Z$ $0.146605513$ $237.3536032$ 1.556184659 \( 548896 a^{2} - 757104 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} - 3\) , \( a^{3} - 2 a + 1\) , \( 3 a^{3} - 8 a^{2} - 14 a + 23\) , \( -8 a^{3} + 2 a^{2} + 24 a - 18\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(3a^{3}-8a^{2}-14a+23\right){x}-8a^{3}+2a^{2}+24a-18$
64.1-b4 64.1-b \(\Q(\zeta_{20})^+\) \( 2^{6} \) $1$ $\Z/4\Z$ $0.073302756$ $949.4144128$ 1.556184659 \( -2711191688 a^{2} + 9809183676 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{3} - a^{2} + 3 a + 4\) , \( 0\) , \( 3 a^{3} - 14 a^{2} + 6 a + 19\) , \( -886 a^{3} + 1683 a^{2} + 1222 a - 2316\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}={x}^{3}+\left(-a^{3}-a^{2}+3a+4\right){x}^{2}+\left(3a^{3}-14a^{2}+6a+19\right){x}-886a^{3}+1683a^{2}+1222a-2316$
64.1-b5 64.1-b \(\Q(\zeta_{20})^+\) \( 2^{6} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.073302756$ $949.4144128$ 1.556184659 \( 2048 \) \( \bigl[0\) , \( -a^{2} + 3\) , \( 0\) , \( -a^{2} + 2\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-a^{2}+2\right){x}$
64.1-b6 64.1-b \(\Q(\zeta_{20})^+\) \( 2^{6} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $0.146605513$ $3797.657651$ 1.556184659 \( 78608 \) \( \bigl[a^{3} - 2 a + 1\) , \( a^{3} - 4 a - 1\) , \( 0\) , \( 11 a^{3} + 10 a^{2} - 38 a - 38\) , \( -45 a^{3} - 52 a^{2} + 162 a + 190\bigr] \) ${y}^2+\left(a^{3}-2a+1\right){x}{y}={x}^{3}+\left(a^{3}-4a-1\right){x}^{2}+\left(11a^{3}+10a^{2}-38a-38\right){x}-45a^{3}-52a^{2}+162a+190$
79.1-a1 79.1-a \(\Q(\zeta_{20})^+\) \( 79 \) $0$ $\Z/2\Z$ $1$ $111.2348527$ 1.243643460 \( -\frac{5510821934592}{38950081} a^{3} + \frac{6690282255360}{38950081} a^{2} + \frac{19512202644480}{38950081} a - \frac{23230349035840}{38950081} \) \( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( a^{3} - 2 a\) , \( -a^{3} - 3 a^{2} + 3 a + 7\) , \( 7 a^{3} + 7 a^{2} - 26 a - 29\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-2\right){x}^{2}+\left(-a^{3}-3a^{2}+3a+7\right){x}+7a^{3}+7a^{2}-26a-29$
79.1-a2 79.1-a \(\Q(\zeta_{20})^+\) \( 79 \) $0$ $\Z/2\Z$ $1$ $111.2348527$ 1.243643460 \( \frac{613406825313792}{6241} a^{3} - \frac{721103039411200}{6241} a^{2} - \frac{2219326741908480}{6241} a + \frac{2608975307898560}{6241} \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} + 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 6 a^{2} + 3 a - 15\) , \( -6 a^{3} - 2 a^{2} + 14 a - 7\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(6a^{2}+3a-15\right){x}-6a^{3}-2a^{2}+14a-7$
79.1-b1 79.1-b \(\Q(\zeta_{20})^+\) \( 79 \) $0$ $\Z/2\Z$ $1$ $155.2093026$ 1.735292756 \( -\frac{51970850297981607}{6241} a^{3} + \frac{98854431667475790}{6241} a^{2} + \frac{71821948689392780}{6241} a - \frac{136613464610314700}{6241} \) \( \bigl[a^{3} - 3 a + 1\) , \( a^{2} - 3\) , \( 0\) , \( -4 a - 8\) , \( -7 a^{3} - 10 a^{2} + 18 a + 22\bigr] \) ${y}^2+\left(a^{3}-3a+1\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-4a-8\right){x}-7a^{3}-10a^{2}+18a+22$
79.1-b2 79.1-b \(\Q(\zeta_{20})^+\) \( 79 \) $0$ $\Z/2\Z$ $1$ $310.4186052$ 1.735292756 \( -\frac{78157332}{79} a^{3} + \frac{148661440}{79} a^{2} + \frac{107998540}{79} a - \frac{205350795}{79} \) \( \bigl[a^{3} - 3 a + 1\) , \( a^{2} - 3\) , \( 0\) , \( a + 2\) , \( 0\bigr] \) ${y}^2+\left(a^{3}-3a+1\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(a+2\right){x}$
79.1-c1 79.1-c \(\Q(\zeta_{20})^+\) \( 79 \) $1$ $\Z/2\Z$ $0.034185335$ $921.5828295$ 1.408929375 \( -\frac{51970850297981607}{6241} a^{3} + \frac{98854431667475790}{6241} a^{2} + \frac{71821948689392780}{6241} a - \frac{136613464610314700}{6241} \) \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} + a^{2} + 2 a - 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{2} - 6 a - 10\) , \( 3 a^{3} + 3 a^{2} - 11 a - 9\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-3\right){x}^{2}+\left(a^{2}-6a-10\right){x}+3a^{3}+3a^{2}-11a-9$
79.1-c2 79.1-c \(\Q(\zeta_{20})^+\) \( 79 \) $1$ $\Z/2\Z$ $0.068370671$ $921.5828295$ 1.408929375 \( -\frac{78157332}{79} a^{3} + \frac{148661440}{79} a^{2} + \frac{107998540}{79} a - \frac{205350795}{79} \) \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} + a^{2} + 2 a - 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{2} - a\) , \( a^{3} + 3 a^{2} - 3 a - 7\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-3\right){x}^{2}+\left(a^{2}-a\right){x}+a^{3}+3a^{2}-3a-7$
79.1-d1 79.1-d \(\Q(\zeta_{20})^+\) \( 79 \) $1$ $\Z/2\Z$ $0.034572360$ $582.6052374$ 1.801558660 \( -\frac{5510821934592}{38950081} a^{3} + \frac{6690282255360}{38950081} a^{2} + \frac{19512202644480}{38950081} a - \frac{23230349035840}{38950081} \) \( \bigl[a^{2} + a - 3\) , \( -a^{2} + 3\) , \( a^{2} + a - 2\) , \( -a^{3} - 4 a^{2} + 3 a + 9\) , \( -8 a^{3} - 11 a^{2} + 29 a + 37\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-a^{3}-4a^{2}+3a+9\right){x}-8a^{3}-11a^{2}+29a+37$
79.1-d2 79.1-d \(\Q(\zeta_{20})^+\) \( 79 \) $1$ $\Z/2\Z$ $0.069144720$ $582.6052374$ 1.801558660 \( \frac{613406825313792}{6241} a^{3} - \frac{721103039411200}{6241} a^{2} - \frac{2219326741908480}{6241} a + \frac{2608975307898560}{6241} \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} - a - 4\) , \( a^{2} + a - 2\) , \( -a^{3} + 4 a^{2} + 6 a - 9\) , \( 6 a^{3} + 2 a^{2} - 15 a + 5\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-a^{3}+4a^{2}+6a-9\right){x}+6a^{3}+2a^{2}-15a+5$
79.2-a1 79.2-a \(\Q(\zeta_{20})^+\) \( 79 \) $0$ $\Z/2\Z$ $1$ $111.2348527$ 1.243643460 \( -\frac{379106265967104}{6241} a^{3} + \frac{721103039411200}{6241} a^{2} + \frac{523911972587520}{6241} a - \frac{996539889157440}{6241} \) \( \bigl[a^{2} + a - 3\) , \( a^{2} - 3\) , \( a^{2} + a - 2\) , \( 3 a^{3} - 6 a^{2} - 9 a + 15\) , \( -4 a^{3} + 2 a^{2} + 18 a - 17\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(3a^{3}-6a^{2}-9a+15\right){x}-4a^{3}+2a^{2}+18a-17$
79.2-a2 79.2-a \(\Q(\zeta_{20})^+\) \( 79 \) $0$ $\Z/2\Z$ $1$ $111.2348527$ 1.243643460 \( \frac{2979736840704}{38950081} a^{3} - \frac{6690282255360}{38950081} a^{2} - \frac{3428388587520}{38950081} a + \frac{10221062240960}{38950081} \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} + 3\) , \( a^{3} - 2 a\) , \( a^{2} - 3\) , \( -5 a^{3} - 9 a^{2} + 8 a + 11\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(a^{2}-3\right){x}-5a^{3}-9a^{2}+8a+11$
79.2-b1 79.2-b \(\Q(\zeta_{20})^+\) \( 79 \) $0$ $\Z/2\Z$ $1$ $155.2093026$ 1.735292756 \( -\frac{84090602204552041}{6241} a^{3} - \frac{98854431667475790}{6241} a^{2} + \frac{304242656911637730}{6241} a + \frac{357658693727064250}{6241} \) \( \bigl[a + 1\) , \( -a^{2} - a + 2\) , \( 0\) , \( -4 a^{3} + 12 a - 8\) , \( -3 a^{3} + 10 a^{2} + 16 a - 28\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-4a^{3}+12a-8\right){x}-3a^{3}+10a^{2}+16a-28$
79.2-b2 79.2-b \(\Q(\zeta_{20})^+\) \( 79 \) $0$ $\Z/2\Z$ $1$ $310.4186052$ 1.735292756 \( -\frac{126473456}{79} a^{3} - \frac{148661440}{79} a^{2} + \frac{457577700}{79} a + \frac{537956405}{79} \) \( \bigl[a + 1\) , \( -a^{2} - a + 2\) , \( 0\) , \( a^{3} - 3 a + 2\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(a^{3}-3a+2\right){x}$
79.2-c1 79.2-c \(\Q(\zeta_{20})^+\) \( 79 \) $1$ $\Z/2\Z$ $0.034185335$ $921.5828295$ 1.408929375 \( -\frac{84090602204552041}{6241} a^{3} - \frac{98854431667475790}{6241} a^{2} + \frac{304242656911637730}{6241} a + \frac{357658693727064250}{6241} \) \( \bigl[a^{3} + a^{2} - 2 a - 3\) , \( 1\) , \( a^{3} + a^{2} - 2 a - 3\) , \( -4 a^{3} + 12 a - 9\) , \( -a^{3} - 10 a^{2} - 4 a + 19\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-3\right){x}{y}+\left(a^{3}+a^{2}-2a-3\right){y}={x}^{3}+{x}^{2}+\left(-4a^{3}+12a-9\right){x}-a^{3}-10a^{2}-4a+19$
79.2-c2 79.2-c \(\Q(\zeta_{20})^+\) \( 79 \) $1$ $\Z/2\Z$ $0.068370671$ $921.5828295$ 1.408929375 \( -\frac{126473456}{79} a^{3} - \frac{148661440}{79} a^{2} + \frac{457577700}{79} a + \frac{537956405}{79} \) \( \bigl[a^{3} + a^{2} - 2 a - 3\) , \( 1\) , \( a^{3} + a^{2} - 2 a - 3\) , \( a^{3} - 3 a + 1\) , \( a^{3} - 3 a + 1\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-3\right){x}{y}+\left(a^{3}+a^{2}-2a-3\right){y}={x}^{3}+{x}^{2}+\left(a^{3}-3a+1\right){x}+a^{3}-3a+1$
79.2-d1 79.2-d \(\Q(\zeta_{20})^+\) \( 79 \) $1$ $\Z/2\Z$ $0.069144720$ $582.6052374$ 1.801558660 \( -\frac{379106265967104}{6241} a^{3} + \frac{721103039411200}{6241} a^{2} + \frac{523911972587520}{6241} a - \frac{996539889157440}{6241} \) \( \bigl[a^{2} + a - 3\) , \( -a^{3} - a^{2} + 3 a + 4\) , \( a^{3} - 2 a\) , \( 3 a^{3} - 9 a^{2} - 9 a + 25\) , \( 7 a^{3} - 10 a^{2} - 27 a + 37\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+4\right){x}^{2}+\left(3a^{3}-9a^{2}-9a+25\right){x}+7a^{3}-10a^{2}-27a+37$
79.2-d2 79.2-d \(\Q(\zeta_{20})^+\) \( 79 \) $1$ $\Z/2\Z$ $0.034572360$ $582.6052374$ 1.801558660 \( \frac{2979736840704}{38950081} a^{3} - \frac{6690282255360}{38950081} a^{2} - \frac{3428388587520}{38950081} a + \frac{10221062240960}{38950081} \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} - a - 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{3} + 4 a^{2} - 4 a - 11\) , \( 6 a^{3} + 11 a^{2} - 11 a - 18\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(a^{3}+4a^{2}-4a-11\right){x}+6a^{3}+11a^{2}-11a-18$
79.3-a1 79.3-a \(\Q(\zeta_{20})^+\) \( 79 \) $0$ $\Z/2\Z$ $1$ $111.2348527$ 1.243643460 \( \frac{379106265967104}{6241} a^{3} + \frac{721103039411200}{6241} a^{2} - \frac{523911972587520}{6241} a - \frac{996539889157440}{6241} \) \( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{2} + a - 2\) , \( -5 a^{3} - 6 a^{2} + 14 a + 15\) , \( 3 a^{3} + 2 a^{2} - 16 a - 17\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(-5a^{3}-6a^{2}+14a+15\right){x}+3a^{3}+2a^{2}-16a-17$
79.3-a2 79.3-a \(\Q(\zeta_{20})^+\) \( 79 \) $0$ $\Z/2\Z$ $1$ $111.2348527$ 1.243643460 \( -\frac{2979736840704}{38950081} a^{3} - \frac{6690282255360}{38950081} a^{2} + \frac{3428388587520}{38950081} a + \frac{10221062240960}{38950081} \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} - a + 3\) , \( a^{3} - 2 a\) , \( -a^{3} + a^{2} + a - 3\) , \( 5 a^{3} - 9 a^{2} - 8 a + 11\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-a^{3}+a^{2}+a-3\right){x}+5a^{3}-9a^{2}-8a+11$
79.3-b1 79.3-b \(\Q(\zeta_{20})^+\) \( 79 \) $0$ $\Z/2\Z$ $1$ $155.2093026$ 1.735292756 \( \frac{84090602204552041}{6241} a^{3} - \frac{98854431667475790}{6241} a^{2} - \frac{304242656911637730}{6241} a + \frac{357658693727064250}{6241} \) \( \bigl[a + 1\) , \( -a^{2} + 2\) , \( 0\) , \( 4 a^{3} - 12 a - 8\) , \( 3 a^{3} + 10 a^{2} - 16 a - 28\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(4a^{3}-12a-8\right){x}+3a^{3}+10a^{2}-16a-28$
79.3-b2 79.3-b \(\Q(\zeta_{20})^+\) \( 79 \) $0$ $\Z/2\Z$ $1$ $310.4186052$ 1.735292756 \( \frac{126473456}{79} a^{3} - \frac{148661440}{79} a^{2} - \frac{457577700}{79} a + \frac{537956405}{79} \) \( \bigl[a + 1\) , \( -a^{2} + 2\) , \( 0\) , \( -a^{3} + 3 a + 2\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-a^{3}+3a+2\right){x}$
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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.