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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 \(\Q(\sqrt{2}, \sqrt{3})\) \( 1 \) $0$ $\Z/6\Z$ $-288$ $1$ $644.1430735$ 0.372767982 \( 10657126796357691195000 a^{3} + 20587988013278347844000 a^{2} - 2855568518720121841000 a - 5516534761939567995000 \) \( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{2} - a - 1\) , \( a^{3} - 3 a + 1\) , \( 5 a^{3} + 3 a^{2} - 40 a - 41\) , \( -23 a^{3} + 8 a^{2} + 135 a + 72\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(5a^{3}+3a^{2}-40a-41\right){x}-23a^{3}+8a^{2}+135a+72$
1.1-a2 1.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 1 \) $0$ $\Z/6\Z$ $-288$ $1$ $644.1430735$ 0.372767982 \( -10657126796357691195000 a^{3} + 20587988013278347844000 a^{2} + 2855568518720121841000 a - 5516534761939567995000 \) \( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{2} - 2\) , \( -7 a^{3} + 2 a^{2} + 42 a - 39\) , \( 60 a^{3} - 15 a^{2} - 251 a + 108\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(-7a^{3}+2a^{2}+42a-39\right){x}+60a^{3}-15a^{2}-251a+108$
1.1-a3 1.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 1 \) $0$ $\Z/6\Z$ $-288$ $1$ $644.1430735$ 0.372767982 \( -39772938666710642939000 a^{3} - 20587988013278347844000 a^{2} + 148434627870484880561000 a + 76835417291173823381000 \) \( \bigl[a^{2} + a - 2\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{3} - 3 a + 1\) , \( 20 a^{3} - 4 a^{2} - 86 a - 27\) , \( -44 a^{3} - 8 a^{2} + 198 a + 104\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+3\right){x}^{2}+\left(20a^{3}-4a^{2}-86a-27\right){x}-44a^{3}-8a^{2}+198a+104$
1.1-a4 1.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 1 \) $0$ $\Z/6\Z$ $-32$ $1$ $644.1430735$ 0.372767982 \( -18473000 a^{3} + 55419000 a + 26125000 \) \( \bigl[a + 1\) , \( -a^{3} - a^{2} + 5 a + 2\) , \( a^{3} - 3 a + 1\) , \( a^{3} + a^{2} - 5 a - 2\) , \( -a^{3} + 4 a - 1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+5a+2\right){x}^{2}+\left(a^{3}+a^{2}-5a-2\right){x}-a^{3}+4a-1$
1.1-a5 1.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 1 \) $0$ $\Z/6\Z$ $-288$ $1$ $644.1430735$ 0.372767982 \( 39772938666710642939000 a^{3} - 20587988013278347844000 a^{2} - 148434627870484880561000 a + 76835417291173823381000 \) \( \bigl[a^{2} + a - 2\) , \( a^{3} - a^{2} - 3 a + 3\) , \( a^{2} - 2\) , \( -14 a^{3} - 2 a^{2} + 63 a - 31\) , \( 11 a^{3} + 15 a^{2} - 104 a + 48\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+3\right){x}^{2}+\left(-14a^{3}-2a^{2}+63a-31\right){x}+11a^{3}+15a^{2}-104a+48$
1.1-a6 1.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 1 \) $0$ $\Z/6\Z$ $-32$ $1$ $644.1430735$ 0.372767982 \( 18473000 a^{3} - 55419000 a + 26125000 \) \( \bigl[a^{2} + a - 2\) , \( a^{3} - a^{2} - 3 a + 3\) , \( a^{2} - 2\) , \( a^{3} - 2 a^{2} - 7 a + 4\) , \( -a^{3} - 5 a^{2} - 4 a + 3\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+3\right){x}^{2}+\left(a^{3}-2a^{2}-7a+4\right){x}-a^{3}-5a^{2}-4a+3$
1.1-a7 1.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 1 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ $-72$ $1$ $2576.572294$ 0.372767982 \( 77092288000 a^{3} - 385461440000 a + 188837384000 \) \( \bigl[a^{3} - 3 a\) , \( a^{3} - 5 a - 1\) , \( 1\) , \( 15 a^{3} - 76 a - 40\) , \( -73 a^{3} + 365 a + 179\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+{y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}+\left(15a^{3}-76a-40\right){x}-73a^{3}+365a+179$
1.1-a8 1.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 1 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ $-8$ $1$ $2576.572294$ 0.372767982 \( 8000 \) \( \bigl[a^{3} - 3 a\) , \( a^{3} - 5 a - 1\) , \( 1\) , \( -a\) , \( 0\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+{y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}-a{x}$
1.1-a9 1.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 1 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $-72$ $1$ $31.80953449$ 0.372767982 \( -77092288000 a^{3} + 385461440000 a + 188837384000 \) \( \bigl[a^{3} - 3 a\) , \( a^{3} - 5 a\) , \( a^{2} - 2\) , \( -15 a^{3} + 75 a - 40\) , \( -73 a^{3} + 365 a - 180\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+\left(-15a^{3}+75a-40\right){x}-73a^{3}+365a-180$
1.1-a10 1.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 1 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ $-72$ $1$ $2576.572294$ 0.372767982 \( -77092288000 a^{3} + 385461440000 a + 188837384000 \) \( \bigl[a^{3} - 3 a\) , \( -a^{3} + 5 a - 1\) , \( 1\) , \( -16 a^{3} + 79 a - 40\) , \( 73 a^{3} - 365 a + 179\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+5a-1\right){x}^{2}+\left(-16a^{3}+79a-40\right){x}+73a^{3}-365a+179$
1.1-a11 1.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 1 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $-72$ $1$ $31.80953449$ 0.372767982 \( 77092288000 a^{3} - 385461440000 a + 188837384000 \) \( \bigl[a^{3} - 3 a\) , \( -a^{3} + 5 a\) , \( a^{2} - 2\) , \( 16 a^{3} - 80 a - 40\) , \( 73 a^{3} - 365 a - 180\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(16a^{3}-80a-40\right){x}+73a^{3}-365a-180$
1.1-a12 1.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 1 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ $-8$ $1$ $2576.572294$ 0.372767982 \( 8000 \) \( \bigl[a^{3} - 3 a\) , \( -a^{3} + 5 a\) , \( a^{2} - 2\) , \( a^{3} - 5 a\) , \( -1\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(a^{3}-5a\right){x}-1$
1.1-a13 1.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 1 \) $0$ $\Z/2\Z$ $-288$ $1$ $7.952383624$ 0.372767982 \( -39772938666710642939000 a^{3} - 20587988013278347844000 a^{2} + 148434627870484880561000 a + 76835417291173823381000 \) \( \bigl[a^{3} - 4 a + 1\) , \( a^{3} + a^{2} - 5 a - 2\) , \( a^{3} - 3 a + 1\) , \( 14 a^{3} - a^{2} - 65 a - 33\) , \( 27 a^{3} - 10 a^{2} - 136 a - 66\bigr] \) ${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-2\right){x}^{2}+\left(14a^{3}-a^{2}-65a-33\right){x}+27a^{3}-10a^{2}-136a-66$
1.1-a14 1.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 1 \) $0$ $\Z/6\Z$ $-32$ $1$ $644.1430735$ 0.372767982 \( -18473000 a^{3} + 55419000 a + 26125000 \) \( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{2} - 2\) , \( 3 a^{3} + 2 a^{2} - 13 a - 4\) , \( 8 a^{3} + 5 a^{2} - 31 a - 17\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(3a^{3}+2a^{2}-13a-4\right){x}+8a^{3}+5a^{2}-31a-17$
1.1-a15 1.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 1 \) $0$ $\Z/2\Z$ $-288$ $1$ $7.952383624$ 0.372767982 \( 39772938666710642939000 a^{3} - 20587988013278347844000 a^{2} - 148434627870484880561000 a + 76835417291173823381000 \) \( \bigl[a^{3} - 4 a + 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( a^{2} + a - 1\) , \( -16 a^{3} - 2 a^{2} + 71 a - 32\) , \( -62 a^{3} + 5 a^{2} + 275 a - 136\bigr] \) ${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-2\right){x}^{2}+\left(-16a^{3}-2a^{2}+71a-32\right){x}-62a^{3}+5a^{2}+275a-136$
1.1-a16 1.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 1 \) $0$ $\Z/6\Z$ $-32$ $1$ $644.1430735$ 0.372767982 \( 18473000 a^{3} - 55419000 a + 26125000 \) \( \bigl[a^{3} - 4 a + 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( a^{2} + a - 1\) , \( -a^{3} - 2 a^{2} + a + 3\) , \( -1\bigr] \) ${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-2\right){x}^{2}+\left(-a^{3}-2a^{2}+a+3\right){x}-1$
1.1-a17 1.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 1 \) $0$ $\Z/2\Z$ $-288$ $1$ $7.952383624$ 0.372767982 \( 10657126796357691195000 a^{3} + 20587988013278347844000 a^{2} - 2855568518720121841000 a - 5516534761939567995000 \) \( \bigl[a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 4 a - 1\) , \( 6 a^{3} + a^{2} - 42 a - 38\) , \( 29 a^{3} - 6 a^{2} - 177 a - 114\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(6a^{3}+a^{2}-42a-38\right){x}+29a^{3}-6a^{2}-177a-114$
1.1-a18 1.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 1 \) $0$ $\Z/2\Z$ $-288$ $1$ $7.952383624$ 0.372767982 \( -10657126796357691195000 a^{3} + 20587988013278347844000 a^{2} + 2855568518720121841000 a - 5516534761939567995000 \) \( \bigl[a + 1\) , \( -a^{3} - a^{2} + 5 a + 2\) , \( a^{3} - 3 a + 1\) , \( -9 a^{3} + a^{2} + 50 a - 37\) , \( -28 a^{3} + 10 a^{2} + 139 a - 106\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+5a+2\right){x}^{2}+\left(-9a^{3}+a^{2}+50a-37\right){x}-28a^{3}+10a^{2}+139a-106$
9.1-a1 9.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $285.8329267$ 1.488713160 \( -\frac{320418987231990328}{27} a^{3} + \frac{1602094936159951640}{27} a + 29069000837710152 \) \( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a\) , \( a\) , \( -2463 a^{3} + 1265 a^{2} + 9170 a - 4780\) , \( 84852 a^{3} - 43876 a^{2} - 316598 a + 163923\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-2463a^{3}+1265a^{2}+9170a-4780\right){x}+84852a^{3}-43876a^{2}-316598a+163923$
9.1-a2 9.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $285.8329267$ 1.488713160 \( \frac{467951528}{3} a^{3} - \frac{2339757640}{3} a + 382083912 \) \( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{3} + a^{2} - 4 a - 1\) , \( -2 a^{3} + a^{2} + 4 a - 14\) , \( -6 a^{3} + 2 a^{2} + 24 a - 7\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(-2a^{3}+a^{2}+4a-14\right){x}-6a^{3}+2a^{2}+24a-7$
9.1-a3 9.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 3^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $571.6658535$ 1.488713160 \( \frac{58591911104}{243} \) \( \bigl[a^{3} - 3 a\) , \( -a^{3} + 3 a - 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -161 a^{3} + 482 a - 243\) , \( 1495 a^{3} - 4486 a + 2128\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(-a^{3}+3a-1\right){x}^{2}+\left(-161a^{3}+482a-243\right){x}+1495a^{3}-4486a+2128$
9.1-a4 9.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 3^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $571.6658535$ 1.488713160 \( \frac{85184}{3} \) \( \bigl[a^{3} - 3 a\) , \( -a^{3} + 3 a - 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -a^{3} + 2 a - 3\) , \( -a - 2\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(-a^{3}+3a-1\right){x}^{2}+\left(-a^{3}+2a-3\right){x}-a-2$
9.1-a5 9.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $142.9164633$ 1.488713160 \( \frac{64}{9} \) \( \bigl[a^{3} - 3 a\) , \( a^{3} - 3 a\) , \( a^{3} + a^{2} - 3 a - 2\) , \( a^{3} - 4 a\) , \( -a - 2\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{3}-3a\right){x}^{2}+\left(a^{3}-4a\right){x}-a-2$
9.1-a6 9.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $142.9164633$ 1.488713160 \( -\frac{873722816}{59049} \) \( \bigl[a^{3} - 3 a\) , \( -a^{3} + 3 a\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 40 a^{3} - 121 a - 60\) , \( -152 a^{3} + 455 a + 218\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(-a^{3}+3a\right){x}^{2}+\left(40a^{3}-121a-60\right){x}-152a^{3}+455a+218$
9.1-a7 9.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $285.8329267$ 1.488713160 \( -\frac{467951528}{3} a^{3} + \frac{2339757640}{3} a + 382083912 \) \( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a^{3} - 4 a\) , \( -67 a^{3} + 35 a^{2} + 251 a - 129\) , \( 381 a^{3} - 197 a^{2} - 1422 a + 735\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-3\right){x}^{2}+\left(-67a^{3}+35a^{2}+251a-129\right){x}+381a^{3}-197a^{2}-1422a+735$
9.1-a8 9.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $285.8329267$ 1.488713160 \( \frac{320418987231990328}{27} a^{3} - \frac{1602094936159951640}{27} a + 29069000837710152 \) \( \bigl[a + 1\) , \( -a^{2} + 3\) , \( a^{3} - 4 a\) , \( -372 a^{3} + 150 a^{2} + 1225 a - 878\) , \( 5455 a^{3} - 2171 a^{2} - 18929 a + 10866\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-372a^{3}+150a^{2}+1225a-878\right){x}+5455a^{3}-2171a^{2}-18929a+10866$
9.1-b1 9.1-b \(\Q(\sqrt{2}, \sqrt{3})\) \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $3.210189511$ 0.417993425 \( \frac{320418987231990328}{27} a^{3} - \frac{1602094936159951640}{27} a + 29069000837710152 \) \( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -370 a^{3} + 152 a^{2} + 1216 a - 885\) , \( -5826 a^{3} + 2322 a^{2} + 20149 a - 11749\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(-370a^{3}+152a^{2}+1216a-885\right){x}-5826a^{3}+2322a^{2}+20149a-11749$
9.1-b2 9.1-b \(\Q(\sqrt{2}, \sqrt{3})\) \( 3^{2} \) $0$ $\Z/10\Z$ $1$ $2006.368444$ 0.417993425 \( -\frac{467951528}{3} a^{3} + \frac{2339757640}{3} a + 382083912 \) \( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} - a^{2} + 4 a + 1\) , \( a^{2} - 2\) , \( -71 a^{3} + 34 a^{2} + 265 a - 128\) , \( -251 a^{3} + 128 a^{2} + 937 a - 478\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+1\right){x}^{2}+\left(-71a^{3}+34a^{2}+265a-128\right){x}-251a^{3}+128a^{2}+937a-478$
9.1-b3 9.1-b \(\Q(\sqrt{2}, \sqrt{3})\) \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $1.605094755$ 0.417993425 \( -\frac{873722816}{59049} \) \( \bigl[a^{3} - 3 a\) , \( a^{3} - 3 a - 1\) , \( a^{3} - 3 a + 1\) , \( 39 a^{3} - 117 a - 60\) , \( 152 a^{3} - 456 a - 220\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(39a^{3}-117a-60\right){x}+152a^{3}-456a-220$
9.1-b4 9.1-b \(\Q(\sqrt{2}, \sqrt{3})\) \( 3^{2} \) $0$ $\Z/10\Z$ $1$ $1003.184222$ 0.417993425 \( \frac{64}{9} \) \( \bigl[a^{3} - 3 a\) , \( -a^{3} + 3 a - 1\) , \( a^{3} - 3 a + 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}+3a-1\right){x}^{2}$
9.1-b5 9.1-b \(\Q(\sqrt{2}, \sqrt{3})\) \( 3^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $6.420379023$ 0.417993425 \( \frac{58591911104}{243} \) \( \bigl[a^{3} - 3 a\) , \( a^{3} - 3 a\) , \( a^{3} - 3 a + 1\) , \( -162 a^{3} + 486 a - 243\) , \( -1495 a^{3} + 4485 a - 2130\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-3a\right){x}^{2}+\left(-162a^{3}+486a-243\right){x}-1495a^{3}+4485a-2130$
9.1-b6 9.1-b \(\Q(\sqrt{2}, \sqrt{3})\) \( 3^{2} \) $0$ $\Z/2\Z\oplus\Z/10\Z$ $1$ $4012.736889$ 0.417993425 \( \frac{85184}{3} \) \( \bigl[a^{3} - 3 a\) , \( a^{3} - 3 a\) , \( a^{3} - 3 a + 1\) , \( -2 a^{3} + 6 a - 3\) , \( 0\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-3a\right){x}^{2}+\left(-2a^{3}+6a-3\right){x}$
9.1-b7 9.1-b \(\Q(\sqrt{2}, \sqrt{3})\) \( 3^{2} \) $0$ $\Z/10\Z$ $1$ $2006.368444$ 0.417993425 \( \frac{467951528}{3} a^{3} - \frac{2339757640}{3} a + 382083912 \) \( \bigl[a + 1\) , \( -a^{2} - a + 1\) , \( a^{2} + a - 1\) , \( -4 a^{3} + 9 a - 11\) , \( 6 a^{3} - 3 a^{2} - 25 a + 6\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(-4a^{3}+9a-11\right){x}+6a^{3}-3a^{2}-25a+6$
9.1-b8 9.1-b \(\Q(\sqrt{2}, \sqrt{3})\) \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $3.210189511$ 0.417993425 \( -\frac{320418987231990328}{27} a^{3} + \frac{1602094936159951640}{27} a + 29069000837710152 \) \( \bigl[a + 1\) , \( a^{3} - 5 a + 1\) , \( a^{3} - 3 a + 1\) , \( -2461 a^{3} + 1265 a^{2} + 9161 a - 4781\) , \( -87314 a^{3} + 45141 a^{2} + 325764 a - 168705\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(-2461a^{3}+1265a^{2}+9161a-4781\right){x}-87314a^{3}+45141a^{2}+325764a-168705$
16.1-a1 16.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $-24$ $1$ $796.3913345$ 1.036967883 \( -1707264 a^{3} + 5121792 a + 2417472 \) \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -5 a^{2} - 12 a - 5\) , \( -10 a^{3} - 16 a^{2} + 12 a + 9\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}-a{x}^{2}+\left(-5a^{2}-12a-5\right){x}-10a^{3}-16a^{2}+12a+9$
16.1-a2 16.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $-24$ $1$ $796.3913345$ 1.036967883 \( 1707264 a^{3} - 5121792 a + 2417472 \) \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{2} - a + 2\) , \( 0\) , \( -5 a^{2} + 10 a - 2\) , \( -10 a^{3} + 11 a^{2} + 23 a - 13\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-5a^{2}+10a-2\right){x}-10a^{3}+11a^{2}+23a-13$
16.1-a3 16.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $-24$ $1$ $796.3913345$ 1.036967883 \( -1707264 a^{3} + 5121792 a + 2417472 \) \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{2} - a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -10 a^{3} + 3 a^{2} + 38 a - 21\) , \( -27 a^{3} + 15 a^{2} + 97 a - 53\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-10a^{3}+3a^{2}+38a-21\right){x}-27a^{3}+15a^{2}+97a-53$
16.1-a4 16.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $-24$ $1$ $796.3913345$ 1.036967883 \( 1707264 a^{3} - 5121792 a + 2417472 \) \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a\) , \( 0\) , \( 10 a^{3} + 5 a^{2} - 40 a - 22\) , \( -17 a^{3} - 11 a^{2} + 58 a + 31\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}={x}^{3}-a{x}^{2}+\left(10a^{3}+5a^{2}-40a-22\right){x}-17a^{3}-11a^{2}+58a+31$
16.1-a5 16.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 2^{4} \) $0$ $\Z/2\Z$ $-96$ $1$ $199.0978336$ 1.036967883 \( 6508137062232 a^{3} - 3368859648336 a^{2} - 24288698179512 a + 12572755370856 \) \( \bigl[a^{3} - 3 a\) , \( a^{3} - 5 a + 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -7 a^{3} + 5 a^{2} + 23 a - 17\) , \( 8 a^{3} - 4 a^{2} - 32 a + 14\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(-7a^{3}+5a^{2}+23a-17\right){x}+8a^{3}-4a^{2}-32a+14$
16.1-a6 16.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 2^{4} \) $0$ $\Z/2\Z$ $-96$ $1$ $199.0978336$ 1.036967883 \( -1743850069416 a^{3} + 3368859648336 a^{2} + 467263215432 a - 902683222488 \) \( \bigl[a^{3} - 3 a\) , \( a^{3} - 5 a + 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 4 a^{3} - 5 a^{2} - 10 a + 3\) , \( -a^{3} + 3 a^{2} - 5 a\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(4a^{3}-5a^{2}-10a+3\right){x}-a^{3}+3a^{2}-5a$
16.1-a7 16.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 2^{4} \) $0$ $\Z/2\Z$ $-96$ $1$ $199.0978336$ 1.036967883 \( -6508137062232 a^{3} - 3368859648336 a^{2} + 24288698179512 a + 12572755370856 \) \( \bigl[a^{3} - 3 a\) , \( a^{3} - 5 a + 1\) , \( a^{2} - 1\) , \( 9 a^{3} + 5 a^{2} - 35 a - 16\) , \( 16 a^{3} + 8 a^{2} - 60 a - 31\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(9a^{3}+5a^{2}-35a-16\right){x}+16a^{3}+8a^{2}-60a-31$
16.1-a8 16.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 2^{4} \) $0$ $\Z/2\Z$ $-96$ $1$ $199.0978336$ 1.036967883 \( 1743850069416 a^{3} + 3368859648336 a^{2} - 467263215432 a - 902683222488 \) \( \bigl[a^{3} - 3 a\) , \( a^{3} - 5 a + 1\) , \( a^{2} - 1\) , \( -2 a^{3} - 5 a^{2} - 2 a + 4\) , \( -4 a^{3} - 9 a^{2} + 3\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(-2a^{3}-5a^{2}-2a+4\right){x}-4a^{3}-9a^{2}+3$
16.1-a9 16.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 2^{4} \) $0$ $\Z/2\Z$ $-96$ $1$ $199.0978336$ 1.036967883 \( -6508137062232 a^{3} - 3368859648336 a^{2} + 24288698179512 a + 12572755370856 \) \( \bigl[a^{3} - 3 a\) , \( -a^{3} + 5 a + 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 7 a^{3} + 5 a^{2} - 25 a - 17\) , \( -8 a^{3} - 4 a^{2} + 30 a + 14\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(7a^{3}+5a^{2}-25a-17\right){x}-8a^{3}-4a^{2}+30a+14$
16.1-a10 16.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 2^{4} \) $0$ $\Z/2\Z$ $-96$ $1$ $199.0978336$ 1.036967883 \( 1743850069416 a^{3} + 3368859648336 a^{2} - 467263215432 a - 902683222488 \) \( \bigl[a^{3} - 3 a\) , \( -a^{3} + 5 a + 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -4 a^{3} - 5 a^{2} + 8 a + 3\) , \( a^{3} + 3 a^{2} + 3 a\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(-4a^{3}-5a^{2}+8a+3\right){x}+a^{3}+3a^{2}+3a$
16.1-a11 16.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 2^{4} \) $0$ $\Z/2\Z$ $-96$ $1$ $199.0978336$ 1.036967883 \( 6508137062232 a^{3} - 3368859648336 a^{2} - 24288698179512 a + 12572755370856 \) \( \bigl[a^{3} - 3 a\) , \( -a^{3} + 5 a + 1\) , \( a^{2} - 1\) , \( -9 a^{3} + 5 a^{2} + 33 a - 16\) , \( -16 a^{3} + 8 a^{2} + 60 a - 31\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(-9a^{3}+5a^{2}+33a-16\right){x}-16a^{3}+8a^{2}+60a-31$
16.1-a12 16.1-a \(\Q(\sqrt{2}, \sqrt{3})\) \( 2^{4} \) $0$ $\Z/2\Z$ $-96$ $1$ $199.0978336$ 1.036967883 \( -1743850069416 a^{3} + 3368859648336 a^{2} + 467263215432 a - 902683222488 \) \( \bigl[a^{3} - 3 a\) , \( -a^{3} + 5 a + 1\) , \( a^{2} - 1\) , \( 2 a^{3} - 5 a^{2} + 4\) , \( 4 a^{3} - 9 a^{2} + 3\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(2a^{3}-5a^{2}+4\right){x}+4a^{3}-9a^{2}+3$
16.1-b1 16.1-b \(\Q(\sqrt{2}, \sqrt{3})\) \( 2^{4} \) $0$ $\Z/4\Z$ $-192$ $1$ $626.2283084$ 0.815401443 \( -600840130180059000 a^{3} + 1160733998424384000 a^{2} + 160994627660022750 a - 311017737504159000 \) \( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{2} - 1\) , \( a^{3} - 4 a + 1\) , \( -49 a^{3} - 26 a^{2} + 177 a + 85\) , \( -168 a^{3} - 86 a^{2} + 634 a + 334\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{2}-1\right){x}^{2}+\left(-49a^{3}-26a^{2}+177a+85\right){x}-168a^{3}-86a^{2}+634a+334$
16.1-b2 16.1-b \(\Q(\sqrt{2}, \sqrt{3})\) \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $-48$ $1$ $2504.913233$ 0.815401443 \( 818626500 a^{2} - 219348000 \) \( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{2} - 1\) , \( a^{3} - 4 a + 1\) , \( 11 a^{3} + 4 a^{2} - 48 a - 25\) , \( -5 a^{3} + a^{2} + 25 a + 10\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{2}-1\right){x}^{2}+\left(11a^{3}+4a^{2}-48a-25\right){x}-5a^{3}+a^{2}+25a+10$
16.1-b3 16.1-b \(\Q(\sqrt{2}, \sqrt{3})\) \( 2^{4} \) $0$ $\Z/4\Z$ $-192$ $1$ $626.2283084$ 0.815401443 \( 600840130180059000 a^{3} + 1160733998424384000 a^{2} - 160994627660022750 a - 311017737504159000 \) \( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 49 a^{3} - 27 a^{2} - 175 a + 89\) , \( 81 a^{3} - 38 a^{2} - 313 a + 160\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(49a^{3}-27a^{2}-175a+89\right){x}+81a^{3}-38a^{2}-313a+160$
16.1-b4 16.1-b \(\Q(\sqrt{2}, \sqrt{3})\) \( 2^{4} \) $0$ $\Z/4\Z$ $-192$ $1$ $626.2283084$ 0.815401443 \( 2242365893060213250 a^{3} - 1160733998424384000 a^{2} - 8368623442060794000 a + 4331918256193377000 \) \( \bigl[a^{2} + a - 2\) , \( -a^{2} + 3\) , \( a + 1\) , \( 19 a^{3} + 25 a^{2} - 28 a - 17\) , \( 38 a^{3} + 86 a^{2} + 15 a - 10\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(19a^{3}+25a^{2}-28a-17\right){x}+38a^{3}+86a^{2}+15a-10$
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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.