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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 \(\Q(\zeta_{16})^+\) \( 1 \) $0$ $\Z/10\Z$ $1$ $1018.917972$ 0.225151189 \( 5699182696 a^{3} - 4361830336 a^{2} - 19458081104 a + 14892491272 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} - a + 3\) , \( 1\) , \( a^{3} - 4 a\) , \( -22 a^{3} - 17 a^{2} + 75 a + 58\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(a^{3}-4a\right){x}-22a^{3}-17a^{2}+75a+58$
1.1-a2 1.1-a \(\Q(\zeta_{16})^+\) \( 1 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $6.521075021$ 0.225151189 \( 75602392581248 a^{2} - 44286841602368 \) \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{2} - 1\) , \( 120 a^{3} - 250 a^{2} + 40 a + 19\) , \( 2105 a^{3} - 4179 a^{2} - 366 a + 1660\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(120a^{3}-250a^{2}+40a+19\right){x}+2105a^{3}-4179a^{2}-366a+1660$
1.1-a3 1.1-a \(\Q(\zeta_{16})^+\) \( 1 \) $0$ $\Z/2\Z\oplus\Z/10\Z$ $1$ $4075.671888$ 0.225151189 \( -55168 a^{2} + 190144 \) \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -2 a^{3} - 2 a^{2} + 4 a + 3\) , \( -a^{3} - 2 a^{2} + a + 2\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+2\right){x}^{2}+\left(-2a^{3}-2a^{2}+4a+3\right){x}-a^{3}-2a^{2}+a+2$
1.1-a4 1.1-a \(\Q(\zeta_{16})^+\) \( 1 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $6.521075021$ 0.225151189 \( -75602392581248 a^{2} + 258122728722624 \) \( \bigl[a^{2} - 2\) , \( a^{3} - a^{2} - 2 a + 3\) , \( a + 1\) , \( 120 a^{3} + 108 a^{2} - 523 a - 576\) , \( 1768 a^{3} + 1361 a^{2} - 7025 a - 6474\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+3\right){x}^{2}+\left(120a^{3}+108a^{2}-523a-576\right){x}+1768a^{3}+1361a^{2}-7025a-6474$
1.1-a5 1.1-a \(\Q(\zeta_{16})^+\) \( 1 \) $0$ $\Z/2\Z\oplus\Z/10\Z$ $1$ $4075.671888$ 0.225151189 \( 55168 a^{2} - 30528 \) \( \bigl[a^{2} - 2\) , \( a^{3} - a^{2} - 2 a + 3\) , \( a + 1\) , \( -2 a^{2} - 3 a + 4\) , \( a^{3} - 3 a\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+3\right){x}^{2}+\left(-2a^{2}-3a+4\right){x}+a^{3}-3a$
1.1-a6 1.1-a \(\Q(\zeta_{16})^+\) \( 1 \) $0$ $\Z/10\Z$ $1$ $1018.917972$ 0.225151189 \( 2360533016 a^{3} + 4361830336 a^{2} - 1382416352 a - 2554830072 \) \( \bigl[a^{2} + a - 2\) , \( a^{2} - a - 1\) , \( 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( -9 a^{3} + 17 a^{2} + 5 a - 10\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(a^{3}-a^{2}-2a+2\right){x}-9a^{3}+17a^{2}+5a-10$
1.1-a7 1.1-a \(\Q(\zeta_{16})^+\) \( 1 \) $0$ $\Z/10\Z$ $1$ $1018.917972$ 0.225151189 \( -2360533016 a^{3} + 4361830336 a^{2} + 1382416352 a - 2554830072 \) \( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( 1\) , \( -a^{3} - a^{2} + a + 2\) , \( 9 a^{3} + 17 a^{2} - 5 a - 10\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(-a^{3}-a^{2}+a+2\right){x}+9a^{3}+17a^{2}-5a-10$
1.1-a8 1.1-a \(\Q(\zeta_{16})^+\) \( 1 \) $0$ $\Z/10\Z$ $1$ $1018.917972$ 0.225151189 \( -5699182696 a^{3} - 4361830336 a^{2} + 19458081104 a + 14892491272 \) \( \bigl[a^{2} + a - 2\) , \( a^{3} - 3 a\) , \( a^{3} - 2 a + 1\) , \( 4 a^{3} - 5 a + 3\) , \( 3 a^{3} - 2 a\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(a^{3}-3a\right){x}^{2}+\left(4a^{3}-5a+3\right){x}+3a^{3}-2a$
1.1-a9 1.1-a \(\Q(\zeta_{16})^+\) \( 1 \) $0$ $\Z/2\Z$ $1$ $1.630268755$ 0.225151189 \( 10561278147056904530419721864 a^{3} - 8083252342956303105729121856 a^{2} - 36058459085676274419182662496 a + 27597949777405506664334735112 \) \( \bigl[a^{3} - 3 a\) , \( -a^{3} + 2 a - 1\) , \( a + 1\) , \( 1096 a^{3} + 877 a^{2} - 3737 a - 3004\) , \( 30377 a^{3} + 23405 a^{2} - 103704 a - 79930\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+2a-1\right){x}^{2}+\left(1096a^{3}+877a^{2}-3737a-3004\right){x}+30377a^{3}+23405a^{2}-103704a-79930$
1.1-a10 1.1-a \(\Q(\zeta_{16})^+\) \( 1 \) $0$ $\Z/2\Z$ $1$ $1.630268755$ 0.225151189 \( 4374624644505560827923496904 a^{3} + 8083252342956303105729121856 a^{2} - 2562595786459777953350768848 a - 4735059594419705758581752312 \) \( \bigl[a^{3} - 3 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 1\) , \( -113 a^{3} + 112 a^{2} + 423 a - 455\) , \( -1225 a^{3} + 1100 a^{2} + 4334 a - 4038\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+{y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(-113a^{3}+112a^{2}+423a-455\right){x}-1225a^{3}+1100a^{2}+4334a-4038$
1.1-a11 1.1-a \(\Q(\zeta_{16})^+\) \( 1 \) $0$ $\Z/2\Z$ $1$ $1.630268755$ 0.225151189 \( -4374624644505560827923496904 a^{3} + 8083252342956303105729121856 a^{2} + 2562595786459777953350768848 a - 4735059594419705758581752312 \) \( \bigl[a^{3} - 3 a\) , \( -a^{3} - a^{2} + 3 a + 2\) , \( 1\) , \( 112 a^{3} + 112 a^{2} - 420 a - 455\) , \( 1225 a^{3} + 1100 a^{2} - 4334 a - 4038\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+{y}={x}^{3}+\left(-a^{3}-a^{2}+3a+2\right){x}^{2}+\left(112a^{3}+112a^{2}-420a-455\right){x}+1225a^{3}+1100a^{2}-4334a-4038$
1.1-a12 1.1-a \(\Q(\zeta_{16})^+\) \( 1 \) $0$ $\Z/2\Z$ $1$ $1.630268755$ 0.225151189 \( -10561278147056904530419721864 a^{3} - 8083252342956303105729121856 a^{2} + 36058459085676274419182662496 a + 27597949777405506664334735112 \) \( \bigl[a\) , \( a^{2} + a - 2\) , \( 1\) , \( -84 a^{3} - 112 a^{2} + 139 a - 7\) , \( -659 a^{3} - 1100 a^{2} + 752 a + 362\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(-84a^{3}-112a^{2}+139a-7\right){x}-659a^{3}-1100a^{2}+752a+362$
16.1-a1 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $154.9911952$ 0.856213478 \( 5699182696 a^{3} - 4361830336 a^{2} - 19458081104 a + 14892491272 \) \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( a^{3} - 2 a\) , \( a^{2} - 2\) , \( a^{3} + 4 a^{2} - 4 a - 5\) , \( 6 a^{3} + 4 a^{2} - 18 a - 14\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-2a\right){x}^{2}+\left(a^{3}+4a^{2}-4a-5\right){x}+6a^{3}+4a^{2}-18a-14$
16.1-a2 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $154.9911952$ 0.856213478 \( -5699182696 a^{3} - 4361830336 a^{2} + 19458081104 a + 14892491272 \) \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} + 3 a\) , \( a^{3} + a^{2} - 2 a - 2\) , \( 2 a - 1\) , \( -4 a^{3} + 5 a^{2} + 15 a - 13\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}+a^{2}-2a-2\right){y}={x}^{3}+\left(-a^{3}+3a\right){x}^{2}+\left(2a-1\right){x}-4a^{3}+5a^{2}+15a-13$
16.1-a3 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $154.9911952$ 0.856213478 \( 2360533016 a^{3} + 4361830336 a^{2} - 1382416352 a - 2554830072 \) \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 2 a - 2\) , \( 4 a^{3} - 2 a^{2} - 14 a + 3\) , \( 4 a^{3} - 6 a^{2} - 9 a + 9\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}+a^{2}-2a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(4a^{3}-2a^{2}-14a+3\right){x}+4a^{3}-6a^{2}-9a+9$
16.1-a4 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $154.9911952$ 0.856213478 \( -2360533016 a^{3} + 4361830336 a^{2} + 1382416352 a - 2554830072 \) \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{2} - 2\) , \( -5 a^{3} - 2 a^{2} + 16 a + 7\) , \( -6 a^{3} - 9 a^{2} + 14 a + 18\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+2\right){x}^{2}+\left(-5a^{3}-2a^{2}+16a+7\right){x}-6a^{3}-9a^{2}+14a+18$
16.1-a5 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $154.9911952$ 0.856213478 \( -10561278147056904530419721864 a^{3} - 8083252342956303105729121856 a^{2} + 36058459085676274419182662496 a + 27597949777405506664334735112 \) \( \bigl[a^{2} - 2\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{3} - 2 a\) , \( -394 a^{3} + 255 a^{2} + 1292 a - 1002\) , \( 5759 a^{3} - 4221 a^{2} - 19434 a + 14903\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(-394a^{3}+255a^{2}+1292a-1002\right){x}+5759a^{3}-4221a^{2}-19434a+14903$
16.1-a6 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $154.9911952$ 0.856213478 \( 10561278147056904530419721864 a^{3} - 8083252342956303105729121856 a^{2} - 36058459085676274419182662496 a + 27597949777405506664334735112 \) \( \bigl[a^{2} - 2\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{3} - 2 a\) , \( 394 a^{3} + 255 a^{2} - 1294 a - 1002\) , \( -5759 a^{3} - 4221 a^{2} + 19434 a + 14903\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(394a^{3}+255a^{2}-1294a-1002\right){x}-5759a^{3}-4221a^{2}+19434a+14903$
16.1-a7 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $154.9911952$ 0.856213478 \( -4374624644505560827923496904 a^{3} + 8083252342956303105729121856 a^{2} + 2562595786459777953350768848 a - 4735059594419705758581752312 \) \( \bigl[a^{2} - 2\) , \( a^{3} - a^{2} - 2 a + 3\) , \( a^{3} - 2 a\) , \( -111 a^{3} - 255 a^{2} - 62 a + 18\) , \( 2157 a^{3} + 4220 a^{2} - 712 a - 1979\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+3\right){x}^{2}+\left(-111a^{3}-255a^{2}-62a+18\right){x}+2157a^{3}+4220a^{2}-712a-1979$
16.1-a8 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $154.9911952$ 0.856213478 \( 4374624644505560827923496904 a^{3} + 8083252342956303105729121856 a^{2} - 2562595786459777953350768848 a - 4735059594419705758581752312 \) \( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 2 a + 3\) , \( a^{3} - 2 a\) , \( 111 a^{3} - 255 a^{2} + 60 a + 18\) , \( -2157 a^{3} + 4220 a^{2} + 712 a - 1979\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{3}-a^{2}+2a+3\right){x}^{2}+\left(111a^{3}-255a^{2}+60a+18\right){x}-2157a^{3}+4220a^{2}+712a-1979$
16.1-a9 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $619.9647811$ 0.856213478 \( -75602392581248 a^{2} + 258122728722624 \) \( \bigl[a^{3} - 2 a\) , \( -a^{3} + 4 a + 1\) , \( 0\) , \( 409 a^{3} - 798 a^{2} - 82 a + 293\) , \( -11769 a^{3} + 22208 a^{2} + 5596 a - 11916\bigr] \) ${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(409a^{3}-798a^{2}-82a+293\right){x}-11769a^{3}+22208a^{2}+5596a-11916$
16.1-a10 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $619.9647811$ 0.856213478 \( 55168 a^{2} - 30528 \) \( \bigl[a^{3} - 2 a\) , \( a + 1\) , \( a^{3} - 2 a\) , \( -4 a^{3} - 11 a^{2} + 4 a + 6\) , \( -20 a^{3} - 43 a^{2} + 12 a + 25\bigr] \) ${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a^{3}-11a^{2}+4a+6\right){x}-20a^{3}-43a^{2}+12a+25$
16.1-a11 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $619.9647811$ 0.856213478 \( -55168 a^{2} + 190144 \) \( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 0\) , \( 5 a^{3} - 8 a^{2} - 6 a + 7\) , \( 0\bigr] \) ${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-4a+2\right){x}^{2}+\left(5a^{3}-8a^{2}-6a+7\right){x}$
16.1-a12 16.1-a \(\Q(\zeta_{16})^+\) \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $619.9647811$ 0.856213478 \( 75602392581248 a^{2} - 44286841602368 \) \( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 0\) , \( 1845 a^{3} - 3428 a^{2} - 1046 a + 1967\) , \( -98956 a^{3} + 182892 a^{2} + 57892 a - 107052\bigr] \) ${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-4a+2\right){x}^{2}+\left(1845a^{3}-3428a^{2}-1046a+1967\right){x}-98956a^{3}+182892a^{2}+57892a-107052$
17.1-a1 17.1-a \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/2\Z$ $1$ $76.35812246$ 1.687292068 \( \frac{3474454835624}{17} a^{3} + \frac{6438155264624}{17} a^{2} - \frac{2035288673232}{17} a - \frac{3771384141720}{17} \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{3} - a^{2} + 3 a + 1\) , \( a + 1\) , \( -12 a^{3} - 23 a^{2} + 11 a + 20\) , \( -38 a^{3} - 68 a^{2} + 26 a + 39\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+1\right){x}^{2}+\left(-12a^{3}-23a^{2}+11a+20\right){x}-38a^{3}-68a^{2}+26a+39$
17.1-a2 17.1-a \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $610.8649797$ 1.687292068 \( \frac{165365068800}{83521} a^{3} - \frac{126928507008}{83521} a^{2} - \frac{564595078656}{83521} a + \frac{433545361088}{83521} \) \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{3} - 2 a + 1\) , \( -a^{3} - 7 a^{2} - 4 a + 8\) , \( -4 a^{3} - 8 a^{2} + 2 a + 5\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+3\right){x}^{2}+\left(-a^{3}-7a^{2}-4a+8\right){x}-4a^{3}-8a^{2}+2a+5$
17.1-a3 17.1-a \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $610.8649797$ 1.687292068 \( -\frac{12542757888}{289} a^{3} - \frac{9552369536}{289} a^{2} + \frac{42933732864}{289} a + \frac{32833347776}{289} \) \( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 3 a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -8 a^{3} - 16 a^{2} + 6 a + 11\) , \( -23 a^{3} - 43 a^{2} + 14 a + 25\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+2\right){x}^{2}+\left(-8a^{3}-16a^{2}+6a+11\right){x}-23a^{3}-43a^{2}+14a+25$
17.1-a4 17.1-a \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/2\Z$ $1$ $305.4324898$ 1.687292068 \( -\frac{139504668627740072}{17} a^{3} - \frac{106772250842960368}{17} a^{2} + \frac{476298731643191760}{17} a + \frac{364543266913132200}{17} \) \( \bigl[a^{2} + a - 2\) , \( a^{3} - 3 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 3 a^{3} + 3 a^{2} - 13 a - 14\) , \( -15 a^{3} - 14 a^{2} + 47 a + 39\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(3a^{3}+3a^{2}-13a-14\right){x}-15a^{3}-14a^{2}+47a+39$
17.1-a5 17.1-a \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/2\Z$ $1$ $152.7162449$ 1.687292068 \( \frac{33560279785800}{6975757441} a^{3} + \frac{82992167336432}{6975757441} a^{2} + \frac{12329668327776}{6975757441} a - \frac{39834319232952}{6975757441} \) \( \bigl[a^{3} - 3 a\) , \( a + 1\) , \( 1\) , \( -3 a^{3} - 2 a^{2} + 6 a\) , \( 3 a^{2} + 3 a - 5\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-3a^{3}-2a^{2}+6a\right){x}+3a^{2}+3a-5$
17.1-a6 17.1-a \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/2\Z$ $1$ $152.7162449$ 1.687292068 \( \frac{4920808663186872}{289} a^{3} - \frac{3766223840964720}{289} a^{2} - \frac{16800691825638240}{289} a + \frac{12858692794214600}{289} \) \( \bigl[a\) , \( a^{2} + a - 1\) , \( a + 1\) , \( -14 a^{3} + 14 a^{2} + 52 a - 42\) , \( -43 a^{3} + 36 a^{2} + 150 a - 117\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(-14a^{3}+14a^{2}+52a-42\right){x}-43a^{3}+36a^{2}+150a-117$
17.1-b1 17.1-b \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/6\Z$ $1$ $594.0223287$ 0.729231279 \( -\frac{592518613480}{83521} a^{3} - \frac{453481639872}{83521} a^{2} + \frac{2022986926112}{83521} a + \frac{1548430713016}{83521} \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} + 3\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -5 a^{3} - 9 a^{2} + 5 a + 9\) , \( -4 a^{3} - 7 a^{2} + 4 a + 6\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-5a^{3}-9a^{2}+5a+9\right){x}-4a^{3}-7a^{2}+4a+6$
17.1-b2 17.1-b \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/6\Z$ $1$ $1188.044657$ 0.729231279 \( \frac{6336256}{17} a^{3} - \frac{4283264}{17} a^{2} - \frac{23118848}{17} a + \frac{17368512}{17} \) \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{2} - 1\) , \( 2 a^{2} + 3 a + 1\) , \( a^{3} + 2 a^{2} + a\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(2a^{2}+3a+1\right){x}+a^{3}+2a^{2}+a$
17.1-b3 17.1-b \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ $1$ $2376.089315$ 0.729231279 \( \frac{3698944}{289} a^{3} + \frac{7079808}{289} a^{2} - \frac{1393664}{289} a - \frac{2911808}{289} \) \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} - a^{2} + 3 a + 1\) , \( a^{3} - 2 a + 1\) , \( 8 a^{3} + 5 a^{2} - 29 a - 21\) , \( -9 a^{3} - 7 a^{2} + 30 a + 22\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+1\right){x}^{2}+\left(8a^{3}+5a^{2}-29a-21\right){x}-9a^{3}-7a^{2}+30a+22$
17.1-b4 17.1-b \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $29.33443598$ 0.729231279 \( \frac{12570783870096128}{24137569} a^{3} - \frac{9306221858122368}{24137569} a^{2} - \frac{43762768311598592}{24137569} a + \frac{33332412617053120}{24137569} \) \( \bigl[a^{2} - 2\) , \( a^{3} - 2 a\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -15 a^{3} + 4 a^{2} + 38 a - 40\) , \( -65 a^{3} + 8 a^{2} + 170 a - 124\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}-2a\right){x}^{2}+\left(-15a^{3}+4a^{2}+38a-40\right){x}-65a^{3}+8a^{2}+170a-124$
17.1-b5 17.1-b \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/2\Z$ $1$ $14.66721799$ 0.729231279 \( \frac{6051196672537254728960}{4913} a^{3} - \frac{4631385425125526708608}{4913} a^{2} - \frac{20660077747963655657984}{4913} a + \frac{15812538931040685648832}{4913} \) \( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 3 a + 2\) , \( a^{3} - 3 a + 1\) , \( 18 a^{3} - 33 a^{2} - 10 a + 18\) , \( 90 a^{3} - 160 a^{2} - 59 a + 84\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+2\right){x}^{2}+\left(18a^{3}-33a^{2}-10a+18\right){x}+90a^{3}-160a^{2}-59a+84$
17.1-b6 17.1-b \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/2\Z$ $1$ $14.66721799$ 0.729231279 \( -\frac{7841209391842596488}{4913} a^{3} + \frac{14486119363825311696}{4913} a^{2} + \frac{4596030288025128320}{4913} a - \frac{8483662774447771368}{4913} \) \( \bigl[a^{2} + a - 2\) , \( -a^{3} + 3 a + 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -27 a^{3} - 88 a^{2} + 8 a + 41\) , \( 237 a^{3} + 260 a^{2} - 168 a - 180\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+3a+1\right){x}^{2}+\left(-27a^{3}-88a^{2}+8a+41\right){x}+237a^{3}+260a^{2}-168a-180$
17.1-b7 17.1-b \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/6\Z$ $1$ $1188.044657$ 0.729231279 \( \frac{34031804264}{17} a^{3} + \frac{62883544896}{17} a^{2} - \frac{19935919648}{17} a - \frac{36835732008}{17} \) \( \bigl[a^{3} - 3 a\) , \( a + 1\) , \( a^{3} - 3 a + 1\) , \( 4 a^{3} + a^{2} - 10 a - 9\) , \( 9 a^{3} + 4 a^{2} - 27 a - 21\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4a^{3}+a^{2}-10a-9\right){x}+9a^{3}+4a^{2}-27a-21$
17.1-b8 17.1-b \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/2\Z$ $1$ $7.333608997$ 0.729231279 \( \frac{25337090011897879957000}{582622237229761} a^{3} + \frac{46831566314755966139568}{582622237229761} a^{2} - \frac{14823378335892769704832}{582622237229761} a - \frac{27446515898763049270664}{582622237229761} \) \( \bigl[a\) , \( a^{2} + a - 1\) , \( a^{3} - 2 a + 1\) , \( 28 a^{3} + 6 a^{2} - 79 a - 53\) , \( 52 a^{3} - 20 a^{2} - 119 a - 58\bigr] \) ${y}^2+a{x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(28a^{3}+6a^{2}-79a-53\right){x}+52a^{3}-20a^{2}-119a-58$
17.2-a1 17.2-a \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $610.8649797$ 1.687292068 \( \frac{68499872256}{83521} a^{3} + \frac{126928507008}{83521} a^{2} - \frac{40134547968}{83521} a - \frac{74168666944}{83521} \) \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( 1\) , \( a^{3} - 2 a + 1\) , \( 5 a^{3} + 4 a^{2} - 17 a - 14\) , \( 9 a^{3} + 7 a^{2} - 31 a - 25\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+{x}^{2}+\left(5a^{3}+4a^{2}-17a-14\right){x}+9a^{3}+7a^{2}-31a-25$
17.2-a2 17.2-a \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $610.8649797$ 1.687292068 \( -\frac{5305459200}{289} a^{3} + \frac{9552369536}{289} a^{2} + \frac{3373619712}{289} a - \frac{5376130368}{289} \) \( \bigl[a^{2} - 2\) , \( a^{2} - a - 2\) , \( a^{2} + a - 1\) , \( 17 a^{3} + 15 a^{2} - 60 a - 51\) , \( 54 a^{3} + 42 a^{2} - 186 a - 145\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(17a^{3}+15a^{2}-60a-51\right){x}+54a^{3}+42a^{2}-186a-145$
17.2-a3 17.2-a \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/2\Z$ $1$ $76.35812246$ 1.687292068 \( -\frac{8388075833640}{17} a^{3} - \frac{6438155264624}{17} a^{2} + \frac{28638682336544}{17} a + \frac{21981236916776}{17} \) \( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a^{2} + a - 1\) , \( 26 a^{3} + 20 a^{2} - 88 a - 68\) , \( 108 a^{3} + 83 a^{2} - 369 a - 283\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-3\right){x}^{2}+\left(26a^{3}+20a^{2}-88a-68\right){x}+108a^{3}+83a^{2}-369a-283$
17.2-a4 17.2-a \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/2\Z$ $1$ $305.4324898$ 1.687292068 \( -\frac{57784725759971544}{17} a^{3} + \frac{106772250842960368}{17} a^{2} + \frac{33849508652174560}{17} a - \frac{62545736458709272}{17} \) \( \bigl[a^{2} + a - 2\) , \( -a^{2} - a + 2\) , \( a^{2} + a - 1\) , \( 44 a^{3} + 32 a^{2} - 152 a - 113\) , \( 463 a^{3} + 364 a^{2} - 1582 a - 1245\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(44a^{3}+32a^{2}-152a-113\right){x}+463a^{3}+364a^{2}-1582a-1245$
17.2-a5 17.2-a \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/2\Z$ $1$ $152.7162449$ 1.687292068 \( \frac{2038265836077624}{289} a^{3} + \frac{3766223840964720}{289} a^{2} - \frac{1193988845046000}{289} a - \frac{2206202569644280}{289} \) \( \bigl[a^{3} - 3 a\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( a^{3} - 3 a + 1\) , \( -11 a^{3} - 14 a^{2} + 19 a + 14\) , \( -22 a^{3} - 36 a^{2} + 23 a + 27\bigr] \) ${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+3\right){x}^{2}+\left(-11a^{3}-14a^{2}+19a+14\right){x}-22a^{3}-36a^{2}+23a+27$
17.2-a6 17.2-a \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/2\Z$ $1$ $152.7162449$ 1.687292068 \( -\frac{113010507685176}{6975757441} a^{3} - \frac{82992167336432}{6975757441} a^{2} + \frac{372591802841328}{6975757441} a + \frac{292134350112776}{6975757441} \) \( \bigl[a\) , \( -a^{3} + 3 a + 1\) , \( 1\) , \( 3 a^{3} + 2 a^{2} - 12 a - 8\) , \( -3 a^{3} - 3 a^{2} + 9 a + 7\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a^{3}+3a+1\right){x}^{2}+\left(3a^{3}+2a^{2}-12a-8\right){x}-3a^{3}-3a^{2}+9a+7$
17.2-b1 17.2-b \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/2\Z$ $1$ $14.66721799$ 0.729231279 \( \frac{18927597887502661144}{4913} a^{3} - \frac{14486119363825311696}{4913} a^{2} - \frac{64624003054350579920}{4913} a + \frac{49460814680853475416}{4913} \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a + 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( 71 a^{3} + 86 a^{2} - 241 a - 307\) , \( -545 a^{3} - 262 a^{2} + 1871 a + 864\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(71a^{3}+86a^{2}-241a-307\right){x}-545a^{3}-262a^{2}+1871a+864$
17.2-b2 17.2-b \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/6\Z$ $1$ $1188.044657$ 0.729231279 \( \frac{4110080}{17} a^{3} + \frac{4283264}{17} a^{2} - \frac{5993984}{17} a + \frac{235456}{17} \) \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( a^{3} + a^{2} - 2 a - 1\) , \( a^{2} - 1\) , \( 2 a^{3} + 4 a^{2} - 2 a - 3\) , \( a^{3} + 2 a^{2} + a\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-2a-1\right){x}^{2}+\left(2a^{3}+4a^{2}-2a-3\right){x}+a^{3}+2a^{2}+a$
17.2-b3 17.2-b \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ $1$ $2376.089315$ 0.729231279 \( -\frac{9703168}{289} a^{3} - \frac{7079808}{289} a^{2} + \frac{32808448}{289} a + \frac{25407424}{289} \) \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( 1\) , \( a^{3} - 2 a + 1\) , \( -3 a^{3} + 2 a^{2} + 11 a - 7\) , \( -a^{3} + a^{2} + 4 a - 3\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+{x}^{2}+\left(-3a^{3}+2a^{2}+11a-7\right){x}-a^{3}+a^{2}+4a-3$
17.2-b4 17.2-b \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/2\Z$ $1$ $14.66721799$ 0.729231279 \( \frac{2506487730351891471104}{4913} a^{3} + \frac{4631385425125526708608}{4913} a^{2} - \frac{1468266518518419684352}{4913} a - \frac{2713002769461421185600}{4913} \) \( \bigl[a^{2} - 2\) , \( a^{3} + a^{2} - 2 a - 3\) , \( a^{2} + a - 1\) , \( 2 a^{3} - 52 a^{2} + 5 a + 29\) , \( 112 a^{3} - 458 a^{2} - 64 a + 266\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-2a-3\right){x}^{2}+\left(2a^{3}-52a^{2}+5a+29\right){x}+112a^{3}-458a^{2}-64a+266$
17.2-b5 17.2-b \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $29.33443598$ 0.729231279 \( \frac{6050416701310208}{24137569} a^{3} + \frac{9306221858122368}{24137569} a^{2} - \frac{5580466233834496}{24137569} a - \frac{3892474815436352}{24137569} \) \( \bigl[a^{2} - 2\) , \( -a^{3} + 4 a\) , \( a^{2} + a - 1\) , \( 6 a^{3} - 5 a^{2} - 34 a - 22\) , \( 24 a^{3} - 9 a^{2} - 138 a - 90\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(6a^{3}-5a^{2}-34a-22\right){x}+24a^{3}-9a^{2}-138a-90$
17.2-b6 17.2-b \(\Q(\zeta_{16})^+\) \( 17 \) $0$ $\Z/6\Z$ $1$ $594.0223287$ 0.729231279 \( -\frac{245431085672}{83521} a^{3} + \frac{453481639872}{83521} a^{2} + \frac{143774643536}{83521} a - \frac{265495846472}{83521} \) \( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( 8 a^{3} + 7 a^{2} - 31 a - 23\) , \( 6 a^{3} + 5 a^{2} - 23 a - 18\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-1\right){x}^{2}+\left(8a^{3}+7a^{2}-31a-23\right){x}+6a^{3}+5a^{2}-23a-18$
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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.