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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
27.1-a1 27.1-a \(\Q(\zeta_{7})^+\) \( 3^{3} \) $0$ $\mathsf{trivial}$ $1$ $0.216755369$ 0.402545685 \( -\frac{1713910976512}{1594323} \) \( \bigl[0\) , \( -a\) , \( a\) , \( 652 a^{2} - 391 a - 1564\) , \( 10528 a^{2} - 5979 a - 24046\bigr] \) ${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(652a^{2}-391a-1564\right){x}+10528a^{2}-5979a-24046$
27.1-a2 27.1-a \(\Q(\zeta_{7})^+\) \( 3^{3} \) $0$ $\Z/13\Z$ $1$ $476.2115463$ 0.402545685 \( -\frac{28672}{3} \) \( \bigl[0\) , \( -a\) , \( a\) , \( 2 a^{2} - a - 4\) , \( -2 a^{2} + a + 4\bigr] \) ${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(2a^{2}-a-4\right){x}-2a^{2}+a+4$
41.1-a1 41.1-a \(\Q(\zeta_{7})^+\) \( 41 \) $0$ $\Z/2\Z$ $1$ $1.357827366$ 0.484938345 \( \frac{182915726357803972950650}{13422659310152401} a^{2} - \frac{357571850055303381213985}{13422659310152401} a + \frac{50482569444763032743584}{13422659310152401} \) \( \bigl[1\) , \( -a^{2} + 3\) , \( 1\) , \( 99 a^{2} - 10 a - 348\) , \( 952 a^{2} - 216 a - 2798\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(99a^{2}-10a-348\right){x}+952a^{2}-216a-2798$
41.1-a2 41.1-a \(\Q(\zeta_{7})^+\) \( 41 \) $0$ $\Z/2\Z$ $1$ $2.715654732$ 0.484938345 \( -\frac{1469483101129546552831}{115856201} a^{2} + \frac{815501597212588028076}{115856201} a + \frac{3301898555789100922576}{115856201} \) \( \bigl[1\) , \( -a^{2} + 3\) , \( 1\) , \( 144 a^{2} - 75 a - 328\) , \( 1172 a^{2} - 646 a - 2650\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(144a^{2}-75a-328\right){x}+1172a^{2}-646a-2650$
41.1-a3 41.1-a \(\Q(\zeta_{7})^+\) \( 41 \) $0$ $\Z/10\Z$ $1$ $339.4568415$ 0.484938345 \( -\frac{968480}{41} a^{2} - \frac{734681}{41} a + \frac{589810}{41} \) \( \bigl[1\) , \( -a^{2} + 3\) , \( 1\) , \( -a^{2} + 2\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-a^{2}+2\right){x}$
41.1-a4 41.1-a \(\Q(\zeta_{7})^+\) \( 41 \) $0$ $\Z/10\Z$ $1$ $169.7284207$ 0.484938345 \( \frac{3693705667625}{1681} a^{2} + \frac{2962060985575}{1681} a - \frac{2049821964241}{1681} \) \( \bigl[1\) , \( -a^{2} + 3\) , \( 1\) , \( -6 a^{2} + 7\) , \( 2 a^{2} + 4 a + 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-6a^{2}+7\right){x}+2a^{2}+4a+2$
41.2-a1 41.2-a \(\Q(\zeta_{7})^+\) \( 41 \) $0$ $\Z/2\Z$ $1$ $1.357827366$ 0.484938345 \( -\frac{357571850055303381213985}{13422659310152401} a^{2} + \frac{174656123697499408263335}{13422659310152401} a + \frac{773885872215674359858869}{13422659310152401} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -10 a^{2} - 89 a - 140\) , \( -216 a^{2} - 736 a - 678\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-10a^{2}-89a-140\right){x}-216a^{2}-736a-678$
41.2-a2 41.2-a \(\Q(\zeta_{7})^+\) \( 41 \) $0$ $\Z/10\Z$ $1$ $169.7284207$ 0.484938345 \( \frac{2962060985575}{1681} a^{2} - \frac{6655766653200}{1681} a + \frac{2375528385434}{1681} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( 6 a - 5\) , \( 4 a^{2} - 6 a + 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-5\right){x}+4a^{2}-6a+2$
41.2-a3 41.2-a \(\Q(\zeta_{7})^+\) \( 41 \) $0$ $\Z/10\Z$ $1$ $339.4568415$ 0.484938345 \( -\frac{734681}{41} a^{2} + \frac{1703161}{41} a - \frac{612469}{41} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( a\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}$
41.2-a4 41.2-a \(\Q(\zeta_{7})^+\) \( 41 \) $0$ $\Z/2\Z$ $1$ $2.715654732$ 0.484938345 \( \frac{815501597212588028076}{115856201} a^{2} + \frac{653981503916958524755}{115856201} a - \frac{452569243682580211162}{115856201} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -75 a^{2} - 69 a + 35\) , \( -646 a^{2} - 526 a + 340\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-75a^{2}-69a+35\right){x}-646a^{2}-526a+340$
41.3-a1 41.3-a \(\Q(\zeta_{7})^+\) \( 41 \) $0$ $\Z/2\Z$ $1$ $1.357827366$ 0.484938345 \( \frac{174656123697499408263335}{13422659310152401} a^{2} + \frac{182915726357803972950650}{13422659310152401} a - \frac{115913951592431810832436}{13422659310152401} \) \( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( -91 a^{2} + 101 a - 68\) , \( -646 a^{2} + 852 a - 304\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-91a^{2}+101a-68\right){x}-646a^{2}+852a-304$
41.3-a2 41.3-a \(\Q(\zeta_{7})^+\) \( 41 \) $0$ $\Z/2\Z$ $1$ $2.715654732$ 0.484938345 \( \frac{653981503916958524755}{115856201} a^{2} - \frac{1469483101129546552831}{115856201} a + \frac{524452446825637320235}{115856201} \) \( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( -71 a^{2} + 146 a - 43\) , \( -456 a^{2} + 1027 a - 381\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-71a^{2}+146a-43\right){x}-456a^{2}+1027a-381$
41.3-a3 41.3-a \(\Q(\zeta_{7})^+\) \( 41 \) $0$ $\Z/10\Z$ $1$ $169.7284207$ 0.484938345 \( -\frac{6655766653200}{1681} a^{2} + \frac{3693705667625}{1681} a + \frac{14955417009784}{1681} \) \( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( 4 a^{2} - 4 a - 8\) , \( -11 a^{2} + 7 a + 26\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(4a^{2}-4a-8\right){x}-11a^{2}+7a+26$
41.3-a4 41.3-a \(\Q(\zeta_{7})^+\) \( 41 \) $0$ $\Z/10\Z$ $1$ $339.4568415$ 0.484938345 \( \frac{1703161}{41} a^{2} - \frac{968480}{41} a - \frac{3784992}{41} \) \( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( -a^{2} + a + 2\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-a^{2}+a+2\right){x}$
49.1-a1 49.1-a \(\Q(\zeta_{7})^+\) \( 7^{2} \) $0$ $\Z/14\Z$ $-28$ $1$ $354.0802648$ 0.516151989 \( 16581375 \) \( \bigl[a^{2} - 2\) , \( a^{2} - a - 3\) , \( a + 1\) , \( 62 a^{2} - 26 a - 156\) , \( -380 a^{2} + 192 a + 886\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(62a^{2}-26a-156\right){x}-380a^{2}+192a+886$
49.1-a2 49.1-a \(\Q(\zeta_{7})^+\) \( 7^{2} \) $0$ $\Z/14\Z$ $-7$ $1$ $354.0802648$ 0.516151989 \( -3375 \) \( \bigl[a^{2} - 2\) , \( a^{2} - a - 3\) , \( a + 1\) , \( 2 a^{2} - a - 6\) , \( -9 a^{2} + 4 a + 20\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(2a^{2}-a-6\right){x}-9a^{2}+4a+20$
49.1-a3 49.1-a \(\Q(\zeta_{7})^+\) \( 7^{2} \) $0$ $\Z/2\Z$ $-28$ $1$ $7.226127854$ 0.516151989 \( 16581375 \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -37\) , \( -78\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-37{x}-78$
49.1-a4 49.1-a \(\Q(\zeta_{7})^+\) \( 7^{2} \) $0$ $\Z/2\Z$ $-7$ $1$ $7.226127854$ 0.516151989 \( -3375 \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -2\) , \( -1\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-2{x}-1$
56.1-a1 56.1-a \(\Q(\zeta_{7})^+\) \( 2^{3} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.288080952$ 0.555584693 \( \frac{2251439055699625}{25088} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$
56.1-a2 56.1-a \(\Q(\zeta_{7})^+\) \( 2^{3} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.288080952$ 0.555584693 \( -\frac{548347731625}{1835008} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$
56.1-a3 56.1-a \(\Q(\zeta_{7})^+\) \( 2^{3} \cdot 7 \) $0$ $\Z/6\Z$ $1$ $7.778185713$ 0.555584693 \( \frac{4956477625}{941192} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$
56.1-a4 56.1-a \(\Q(\zeta_{7})^+\) \( 2^{3} \cdot 7 \) $0$ $\Z/18\Z$ $1$ $210.0110142$ 0.555584693 \( \frac{128787625}{98} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$
56.1-a5 56.1-a \(\Q(\zeta_{7})^+\) \( 2^{3} \cdot 7 \) $0$ $\Z/18\Z$ $1$ $210.0110142$ 0.555584693 \( -\frac{15625}{28} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}$
56.1-a6 56.1-a \(\Q(\zeta_{7})^+\) \( 2^{3} \cdot 7 \) $0$ $\Z/6\Z$ $1$ $7.778185713$ 0.555584693 \( \frac{9938375}{21952} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$
64.1-a1 64.1-a \(\Q(\zeta_{7})^+\) \( 2^{6} \) $0$ $\Z/2\Z$ $1$ $1.746658170$ 0.561425840 \( -72061125694419920 a^{2} + 39990907711475312 a + 161919879656286672 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 1742 a^{2} - 971 a - 3929\) , \( 42399 a^{2} - 23535 a - 95292\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(1742a^{2}-971a-3929\right){x}+42399a^{2}-23535a-95292$
64.1-a2 64.1-a \(\Q(\zeta_{7})^+\) \( 2^{6} \) $0$ $\Z/2\Z$ $1$ $1.746658170$ 0.561425840 \( 32070217982944608 a^{2} - 72061125694419920 a + 25718317995977536 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 72 a^{2} + 4 a - 264\) , \( 500 a^{2} - 16 a - 1624\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(72a^{2}+4a-264\right){x}+500a^{2}-16a-1624$
64.1-a3 64.1-a \(\Q(\zeta_{7})^+\) \( 2^{6} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $6.986632680$ 0.561425840 \( 406749952 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 102 a^{2} - 61 a - 244\) , \( 640 a^{2} - 360 a - 1460\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(102a^{2}-61a-244\right){x}+640a^{2}-360a-1460$
64.1-a4 64.1-a \(\Q(\zeta_{7})^+\) \( 2^{6} \) $0$ $\Z/2\Z$ $1$ $1.746658170$ 0.561425840 \( 39990907711475312 a^{2} + 32070217982944608 a - 22193279444028480 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 17 a^{2} - 131 a - 199\) , \( -6 a^{2} - 855 a - 1073\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(17a^{2}-131a-199\right){x}-6a^{2}-855a-1073$
64.1-a5 64.1-a \(\Q(\zeta_{7})^+\) \( 2^{6} \) $0$ $\Z/6\Z$ $1$ $47.15977059$ 0.561425840 \( -208912 a^{2} + 65520 a + 561936 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 22 a^{2} - 11 a - 49\) , \( 55 a^{2} - 31 a - 124\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(22a^{2}-11a-49\right){x}+55a^{2}-31a-124$
64.1-a6 64.1-a \(\Q(\zeta_{7})^+\) \( 2^{6} \) $0$ $\Z/6\Z$ $1$ $47.15977059$ 0.561425840 \( 65520 a^{2} + 143392 a + 78592 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 17 a^{2} - 11 a - 39\) , \( -46 a^{2} + 25 a + 103\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(17a^{2}-11a-39\right){x}-46a^{2}+25a+103$
64.1-a7 64.1-a \(\Q(\zeta_{7})^+\) \( 2^{6} \) $0$ $\Z/2\Z\oplus\Z/6\Z$ $1$ $188.6390823$ 0.561425840 \( 1792 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a^{2} - a - 4\) , \( 0\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(2a^{2}-a-4\right){x}$
64.1-a8 64.1-a \(\Q(\zeta_{7})^+\) \( 2^{6} \) $0$ $\Z/6\Z$ $1$ $47.15977059$ 0.561425840 \( 143392 a^{2} - 208912 a + 66240 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -8 a^{2} + 4 a + 16\) , \( 4 a^{2} - 8\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-8a^{2}+4a+16\right){x}+4a^{2}-8$
71.1-a1 71.1-a \(\Q(\zeta_{7})^+\) \( 71 \) $0$ $\Z/2\Z$ $1$ $1.644803638$ 0.587429871 \( \frac{808193592087701284035551}{3255243551009881201} a^{2} - \frac{1936929577866441496465968}{3255243551009881201} a + \frac{752245811606895893913582}{3255243551009881201} \) \( \bigl[1\) , \( -a\) , \( a + 1\) , \( -190 a^{2} + 410 a - 171\) , \( -2384 a^{2} + 5309 a - 1936\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-190a^{2}+410a-171\right){x}-2384a^{2}+5309a-1936$
71.1-a2 71.1-a \(\Q(\zeta_{7})^+\) \( 71 \) $0$ $\Z/2\Z$ $1$ $3.289607277$ 0.587429871 \( \frac{385959155459705697}{1804229351} a^{2} + \frac{539799973605204231}{1804229351} a + \frac{72968192065230101}{1804229351} \) \( \bigl[1\) , \( -a\) , \( a + 1\) , \( -10 a^{2} + 5 a - 26\) , \( -61 a^{2} + 92 a - 76\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-10a^{2}+5a-26\right){x}-61a^{2}+92a-76$
71.1-a3 71.1-a \(\Q(\zeta_{7})^+\) \( 71 \) $0$ $\Z/10\Z$ $1$ $205.6004548$ 0.587429871 \( -\frac{1885779500418}{5041} a^{2} + \frac{1044582831031}{5041} a + \frac{4240814798194}{5041} \) \( \bigl[1\) , \( -a\) , \( a + 1\) , \( -5 a^{2} + 15 a - 11\) , \( 12 a^{2} - 31 a + 15\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-5a^{2}+15a-11\right){x}+12a^{2}-31a+15$
71.1-a4 71.1-a \(\Q(\zeta_{7})^+\) \( 71 \) $0$ $\Z/10\Z$ $1$ $411.2009097$ 0.587429871 \( -\frac{713073}{71} a^{2} + \frac{710952}{71} a + \frac{1959524}{71} \) \( \bigl[1\) , \( -a\) , \( a + 1\) , \( -1\) , \( -a\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}-{x}-a$
71.2-a1 71.2-a \(\Q(\zeta_{7})^+\) \( 71 \) $0$ $\Z/2\Z$ $1$ $1.644803638$ 0.587429871 \( -\frac{1936929577866441496465968}{3255243551009881201} a^{2} + \frac{1128735985778740212430417}{3255243551009881201} a + \frac{4305562573648739958450652}{3255243551009881201} \) \( \bigl[1\) , \( -a^{2} + a + 1\) , \( a^{2} + a - 2\) , \( 410 a^{2} - 221 a - 960\) , \( 5309 a^{2} - 2926 a - 12013\bigr] \) ${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(410a^{2}-221a-960\right){x}+5309a^{2}-2926a-12013$
71.2-a2 71.2-a \(\Q(\zeta_{7})^+\) \( 71 \) $0$ $\Z/2\Z$ $1$ $3.289607277$ 0.587429871 \( \frac{539799973605204231}{1804229351} a^{2} - \frac{925759129064909928}{1804229351} a + \frac{305086529379437264}{1804229351} \) \( \bigl[1\) , \( -a^{2} + a + 1\) , \( a^{2} + a - 2\) , \( 5 a^{2} + 4 a - 50\) , \( 92 a^{2} - 32 a - 290\bigr] \) ${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(5a^{2}+4a-50\right){x}+92a^{2}-32a-290$
71.2-a3 71.2-a \(\Q(\zeta_{7})^+\) \( 71 \) $0$ $\Z/10\Z$ $1$ $205.6004548$ 0.587429871 \( \frac{1044582831031}{5041} a^{2} + \frac{841196669387}{5041} a - \frac{575327033673}{5041} \) \( \bigl[1\) , \( -a^{2} + a + 1\) , \( a^{2} + a - 2\) , \( 15 a^{2} - 11 a - 35\) , \( -31 a^{2} + 18 a + 70\bigr] \) ${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(15a^{2}-11a-35\right){x}-31a^{2}+18a+70$
71.2-a4 71.2-a \(\Q(\zeta_{7})^+\) \( 71 \) $0$ $\Z/10\Z$ $1$ $411.2009097$ 0.587429871 \( \frac{710952}{71} a^{2} + \frac{2121}{71} a - \frac{177574}{71} \) \( \bigl[1\) , \( -a^{2} + a + 1\) , \( a^{2} + a - 2\) , \( -a\) , \( -a^{2} + 1\bigr] \) ${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}-a{x}-a^{2}+1$
71.3-a1 71.3-a \(\Q(\zeta_{7})^+\) \( 71 \) $0$ $\Z/2\Z$ $1$ $3.289607277$ 0.587429871 \( -\frac{925759129064909928}{1804229351} a^{2} + \frac{385959155459705697}{1804229351} a + \frac{2310445605654755654}{1804229351} \) \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( 4 a^{2} - 10 a - 44\) , \( -32 a^{2} - 61 a - 73\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(4a^{2}-10a-44\right){x}-32a^{2}-61a-73$
71.3-a2 71.3-a \(\Q(\zeta_{7})^+\) \( 71 \) $0$ $\Z/10\Z$ $1$ $411.2009097$ 0.587429871 \( \frac{2121}{71} a^{2} - \frac{713073}{71} a + \frac{1242209}{71} \) \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( -a^{2} + 1\) , \( 0\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-a^{2}+1\right){x}$
71.3-a3 71.3-a \(\Q(\zeta_{7})^+\) \( 71 \) $0$ $\Z/10\Z$ $1$ $205.6004548$ 0.587429871 \( \frac{841196669387}{5041} a^{2} - \frac{1885779500418}{5041} a + \frac{672641959002}{5041} \) \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( -11 a^{2} - 5 a + 6\) , \( 18 a^{2} + 12 a - 9\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-11a^{2}-5a+6\right){x}+18a^{2}+12a-9$
71.3-a4 71.3-a \(\Q(\zeta_{7})^+\) \( 71 \) $0$ $\Z/2\Z$ $1$ $1.644803638$ 0.587429871 \( \frac{1128735985778740212430417}{3255243551009881201} a^{2} + \frac{808193592087701284035551}{3255243551009881201} a - \frac{697032567862883246911701}{3255243551009881201} \) \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( -221 a^{2} - 190 a + 81\) , \( -2926 a^{2} - 2384 a + 1532\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-221a^{2}-190a+81\right){x}-2926a^{2}-2384a+1532$
91.1-a1 91.1-a \(\Q(\zeta_{7})^+\) \( 7 \cdot 13 \) $0$ $\Z/2\Z$ $1$ $0.284767587$ 0.650897342 \( \frac{3586352161337298910516}{19882681} a^{2} - \frac{8058460190096647498093}{19882681} a + \frac{2876031146228402085760}{19882681} \) \( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( -1030 a^{2} + 1620 a - 484\) , \( -21769 a^{2} + 41147 a - 14213\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-1030a^{2}+1620a-484\right){x}-21769a^{2}+41147a-14213$
91.1-a2 91.1-a \(\Q(\zeta_{7})^+\) \( 7 \cdot 13 \) $0$ $\Z/8\Z$ $1$ $145.8010047$ 0.650897342 \( -\frac{929922096412289245}{1183} a^{2} + \frac{516067794318659937}{1183} a + \frac{2089516047340720303}{1183} \) \( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( 15 a^{2} + 5 a - 89\) , \( -89 a^{2} - 20 a + 385\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(15a^{2}+5a-89\right){x}-89a^{2}-20a+385$
91.1-a3 91.1-a \(\Q(\zeta_{7})^+\) \( 7 \cdot 13 \) $0$ $\Z/2\Z\oplus\Z/8\Z$ $1$ $145.8010047$ 0.650897342 \( -\frac{3698907677516}{199927} a^{2} + \frac{293174005427}{28561} a + \frac{8312780816110}{199927} \) \( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( -4\) , \( -3 a^{2} - a + 9\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}-4{x}-3a^{2}-a+9$
91.1-a4 91.1-a \(\Q(\zeta_{7})^+\) \( 7 \cdot 13 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $18.22512558$ 0.650897342 \( \frac{20917603896641523}{39970805329} a^{2} + \frac{16797981605493841}{39970805329} a - \frac{11327303846528113}{39970805329} \) \( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( -15 a^{2} - 5 a + 1\) , \( -49 a^{2} - 26 a + 29\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-15a^{2}-5a+1\right){x}-49a^{2}-26a+29$
91.1-a5 91.1-a \(\Q(\zeta_{7})^+\) \( 7 \cdot 13 \) $0$ $\Z/8\Z$ $1$ $145.8010047$ 0.650897342 \( \frac{3379823}{1183} a^{2} - \frac{1448892}{1183} a - \frac{6890188}{1183} \) \( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+{x}$
91.1-a6 91.1-a \(\Q(\zeta_{7})^+\) \( 7 \cdot 13 \) $0$ $\Z/4\Z$ $1$ $2.278140698$ 0.650897342 \( -\frac{1202964810122504163047}{4657916264282258887} a^{2} - \frac{166312704815995127056}{665416609183179841} a + \frac{2026661189545263268136}{4657916264282258887} \) \( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( -10 a^{2} - 20 a + 21\) , \( -90 a^{2} + 20 a + 26\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-10a^{2}-20a+21\right){x}-90a^{2}+20a+26$
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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.