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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
6.1-a1 6.1-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1.424700212$ 1.039746854 \( \frac{773243804465483}{78364164096} a - \frac{2224704505657277}{78364164096} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -10 a - 173\) , \( -27 a + 899\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-10a-173\right){x}-27a+899$
6.1-a2 6.1-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 3 \) $0$ $\Z/2\Z$ $1$ $0.712350106$ 1.039746854 \( \frac{413197302910024471}{2928229434235008} a - \frac{374086572953648785}{2928229434235008} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -90 a - 13\) , \( -683 a + 3107\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-90a-13\right){x}-683a+3107$
6.1-a3 6.1-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 3 \) $0$ $\Z/4\Z$ $1$ $1.424700212$ 1.039746854 \( -\frac{291660246420647}{587068342272} a + \frac{520440745417985}{587068342272} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( 6 a - 22\) , \( 14 a - 31\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+\left(a+1\right){x}^2+\left(6a-22\right){x}+14a-31$
6.1-a4 6.1-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 3 \) $0$ $\Z/4\Z$ $1$ $9.972901485$ 1.039746854 \( \frac{9841}{48} a + \frac{43625}{48} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( a - 2\) , \( -1\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+\left(a+1\right){x}^2+\left(a-2\right){x}-1$
6.1-a5 6.1-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $9.972901485$ 1.039746854 \( -\frac{15457}{36} a + \frac{95803}{36} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -3\) , \( -a - 3\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2-3{x}-a-3$
6.1-a6 6.1-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 3 \) $0$ $\Z/2\Z$ $1$ $9.972901485$ 1.039746854 \( \frac{57217}{6} a + \frac{106031}{6} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -a - 1\) , \( a + 4\bigr] \) ${y}^2+a{x}{y}={x}^3-{x}^2+\left(-a-1\right){x}+a+4$
6.1-a7 6.1-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 3 \) $0$ $\Z/2\Z$ $1$ $4.986450742$ 1.039746854 \( -\frac{238419887}{162} a + \frac{349824755}{162} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 10 a + 7\) , \( 11 a - 103\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(10a+7\right){x}+11a-103$
6.1-a8 6.1-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 3 \) $0$ $\Z/2\Z$ $1$ $1.424700212$ 1.039746854 \( -\frac{133689253600013}{279936} a + \frac{73951848116651}{279936} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -206 a + 609\) , \( 1402 a + 5610\bigr] \) ${y}^2+a{x}{y}={x}^3-{x}^2+\left(-206a+609\right){x}+1402a+5610$
6.4-a1 6.4-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 3 \) $0$ $\Z/2\Z$ $1$ $1.424700212$ 1.039746854 \( \frac{133689253600013}{279936} a - \frac{9956234247227}{46656} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 206 a + 403\) , \( -1402 a + 7012\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a-1\right){x}^2+\left(206a+403\right){x}-1402a+7012$
6.4-a2 6.4-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1.424700212$ 1.039746854 \( -\frac{773243804465483}{78364164096} a - \frac{241910116865299}{13060694016} \) \( \bigl[a\) , \( a\) , \( a\) , \( 8 a - 178\) , \( -154 a + 999\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+a{x}^2+\left(8a-178\right){x}-154a+999$
6.4-a3 6.4-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 3 \) $0$ $\Z/2\Z$ $1$ $0.712350106$ 1.039746854 \( -\frac{413197302910024471}{2928229434235008} a + \frac{6518454992729281}{488038239039168} \) \( \bigl[a\) , \( a\) , \( a\) , \( 88 a - 98\) , \( 582 a + 1991\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+a{x}^2+\left(88a-98\right){x}+582a+1991$
6.4-a4 6.4-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 3 \) $0$ $\Z/4\Z$ $1$ $1.424700212$ 1.039746854 \( \frac{291660246420647}{587068342272} a + \frac{38130083166223}{97844723712} \) \( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -4 a - 17\) , \( -9 a\bigr] \) ${y}^2+{x}{y}={x}^3+\left(-a-1\right){x}^2+\left(-4a-17\right){x}-9a$
6.4-a5 6.4-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 3 \) $0$ $\Z/4\Z$ $1$ $9.972901485$ 1.039746854 \( -\frac{9841}{48} a + \frac{8911}{8} \) \( \bigl[1\) , \( -a - 1\) , \( 0\) , \( a - 2\) , \( 1\bigr] \) ${y}^2+{x}{y}={x}^3+\left(-a-1\right){x}^2+\left(a-2\right){x}+1$
6.4-a6 6.4-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $9.972901485$ 1.039746854 \( \frac{15457}{36} a + \frac{13391}{6} \) \( \bigl[a\) , \( a\) , \( a\) , \( -2 a + 2\) , \( 3\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+a{x}^2+\left(-2a+2\right){x}+3$
6.4-a7 6.4-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 3 \) $0$ $\Z/2\Z$ $1$ $9.972901485$ 1.039746854 \( -\frac{57217}{6} a + 27208 \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( a - 2\) , \( -a + 5\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a-1\right){x}^2+\left(a-2\right){x}-a+5$
6.4-a8 6.4-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 3 \) $0$ $\Z/2\Z$ $1$ $4.986450742$ 1.039746854 \( \frac{238419887}{162} a + \frac{18567478}{27} \) \( \bigl[a\) , \( a\) , \( a\) , \( -12 a + 22\) , \( 8 a - 45\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+a{x}^2+\left(-12a+22\right){x}+8a-45$
26.1-a1 26.1-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 13 \) $0$ $\Z/3\Z$ $1$ $3.545248488$ 0.492823607 \( \frac{16964307415}{17576} a - \frac{7085161553}{17576} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 4 a + 4\) , \( a - 30\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(4a+4\right){x}+a-30$
26.1-a2 26.1-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 13 \) $0$ $\Z/3\Z$ $1$ $1.181749496$ 0.492823607 \( \frac{2187264503235295}{5429503678976} a - \frac{3398685237054473}{5429503678976} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 9 a - 21\) , \( 26 a - 58\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(9a-21\right){x}+26a-58$
26.1-a3 26.1-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 13 \) $0$ $\Z/3\Z$ $1$ $10.63574546$ 0.492823607 \( \frac{703}{26} a - \frac{2345}{26} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(-a-1\right){x}$
26.1-a4 26.1-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 13 \) $0$ $\mathsf{trivial}$ $1$ $0.393916498$ 0.492823607 \( \frac{305308359952290279703}{294876348416} a + \frac{525859732378041384175}{294876348416} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 824 a - 2026\) , \( 19455 a - 22260\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(824a-2026\right){x}+19455a-22260$
26.4-a1 26.4-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 13 \) $0$ $\Z/3\Z$ $1$ $1.181749496$ 0.492823607 \( -\frac{2187264503235295}{5429503678976} a - \frac{605710366909589}{2714751839488} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -10 a - 11\) , \( -26 a - 32\bigr] \) ${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-10a-11\right){x}-26a-32$
26.4-a2 26.4-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 13 \) $0$ $\Z/3\Z$ $1$ $10.63574546$ 0.492823607 \( -\frac{703}{26} a - \frac{821}{13} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -1\) , \( 0\bigr] \) ${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2-{x}$
26.4-a3 26.4-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 13 \) $0$ $\Z/3\Z$ $1$ $3.545248488$ 0.492823607 \( -\frac{16964307415}{17576} a + \frac{4939572931}{8788} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -5 a + 9\) , \( -a - 29\bigr] \) ${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-5a+9\right){x}-a-29$
26.4-a4 26.4-a \(\Q(\sqrt{-23}) \) \( 2 \cdot 13 \) $0$ $\mathsf{trivial}$ $1$ $0.393916498$ 0.492823607 \( -\frac{305308359952290279703}{294876348416} a + \frac{415584046165165831939}{147438174208} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -825 a - 1201\) , \( -19455 a - 2805\bigr] \) ${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-825a-1201\right){x}-19455a-2805$
27.2-a1 27.2-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) $0$ $\Z/2\Z$ $1$ $3.179173933$ 0.662903589 \( \frac{27256702}{81} a - \frac{57582961}{81} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -2 a + 13\) , \( -11 a - 20\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(-2a+13\right){x}-11a-20$
27.2-a2 27.2-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) $0$ $\Z/4\Z$ $1$ $3.179173933$ 0.662903589 \( -\frac{27256702}{81} a - \frac{10108753}{27} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -10 a + 60\) , \( 93 a + 58\bigr] \) ${y}^2+a{x}{y}={x}^3+a{x}^2+\left(-10a+60\right){x}+93a+58$
27.2-a3 27.2-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $3.179173933$ 0.662903589 \( -\frac{2924207}{81} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -16 a + 13\) , \( 34 a - 88\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-16a+13\right){x}+34a-88$
27.2-a4 27.2-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $3.179173933$ 0.662903589 \( \frac{1950520}{6561} a + \frac{58507}{2187} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 1\) , \( a - 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+{x}+a-2$
27.2-a5 27.2-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $3.179173933$ 0.662903589 \( -\frac{1950520}{6561} a + \frac{2126041}{6561} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -2 a + 12\) , \( -a - 26\bigr] \) ${y}^2+a{x}{y}={x}^3+a{x}^2+\left(-2a+12\right){x}-a-26$
27.2-a6 27.2-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) $0$ $\Z/2\Z$ $1$ $1.589586966$ 0.662903589 \( \frac{67902559538}{43046721} a + \frac{66394340881}{43046721} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -17 a - 78\) , \( -130 a - 80\bigr] \) ${y}^2+a{x}{y}={x}^3+a{x}^2+\left(-17a-78\right){x}-130a-80$
27.2-a7 27.2-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) $0$ $\Z/2\Z$ $1$ $1.589586966$ 0.662903589 \( -\frac{67902559538}{43046721} a + \frac{44765633473}{14348907} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 10 a - 14\) , \( 13 a + 34\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(10a-14\right){x}+13a+34$
27.2-a8 27.2-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) $0$ $\Z/2\Z$ $1$ $1.589586966$ 0.662903589 \( \frac{12214672127}{9} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -241 a + 148\) , \( 1654 a - 4948\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-241a+148\right){x}+1654a-4948$
27.3-a1 27.3-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) $0$ $\Z/4\Z$ $1$ $3.179173933$ 0.662903589 \( \frac{27256702}{81} a - \frac{57582961}{81} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 10 a + 47\) , \( -32 a + 94\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a+1\right){x}^2+\left(10a+47\right){x}-32a+94$
27.3-a2 27.3-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) $0$ $\Z/2\Z$ $1$ $3.179173933$ 0.662903589 \( -\frac{27256702}{81} a - \frac{10108753}{27} \) \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 4 a + 11\) , \( 14 a - 20\bigr] \) ${y}^2+{x}{y}={x}^3+\left(a+1\right){x}^2+\left(4a+11\right){x}+14a-20$
27.3-a3 27.3-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $3.179173933$ 0.662903589 \( -\frac{2924207}{81} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 14 a - 1\) , \( -35 a - 53\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+\left(14a-1\right){x}-35a-53$
27.3-a4 27.3-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $3.179173933$ 0.662903589 \( \frac{1950520}{6561} a + \frac{58507}{2187} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 2 a + 7\) , \( 14 a - 36\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a+1\right){x}^2+\left(2a+7\right){x}+14a-36$
27.3-a5 27.3-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $3.179173933$ 0.662903589 \( -\frac{1950520}{6561} a + \frac{2126041}{6561} \) \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 2 a + 1\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^3+\left(a+1\right){x}^2+\left(2a+1\right){x}$
27.3-a6 27.3-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) $0$ $\Z/2\Z$ $1$ $1.589586966$ 0.662903589 \( \frac{67902559538}{43046721} a + \frac{66394340881}{43046721} \) \( \bigl[1\) , \( a + 1\) , \( 0\) , \( -8 a - 4\) , \( -22 a + 43\bigr] \) ${y}^2+{x}{y}={x}^3+\left(a+1\right){x}^2+\left(-8a-4\right){x}-22a+43$
27.3-a7 27.3-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) $0$ $\Z/2\Z$ $1$ $1.589586966$ 0.662903589 \( -\frac{67902559538}{43046721} a + \frac{44765633473}{14348907} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 17 a - 98\) , \( 53 a - 309\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a+1\right){x}^2+\left(17a-98\right){x}+53a-309$
27.3-a8 27.3-a \(\Q(\sqrt{-23}) \) \( 3^{3} \) $0$ $\Z/2\Z$ $1$ $1.589586966$ 0.662903589 \( \frac{12214672127}{9} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 239 a - 91\) , \( -1655 a - 3293\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+\left(239a-91\right){x}-1655a-3293$
32.3-a1 32.3-a \(\Q(\sqrt{-23}) \) \( 2^{5} \) $1$ $\mathsf{trivial}$ $0.019902703$ $8.580110917$ 0.854579154 \( 512 a + 256 \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4\) , \( -a - 1\bigr] \) ${y}^2={x}^3+\left(a-1\right){x}^2-4{x}-a-1$
32.4-a1 32.4-a \(\Q(\sqrt{-23}) \) \( 2^{5} \) $1$ $\mathsf{trivial}$ $0.019902703$ $8.580110917$ 0.854579154 \( -512 a + 768 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -4\) , \( a - 2\bigr] \) ${y}^2={x}^3-a{x}^2-4{x}+a-2$
36.4-a1 36.4-a \(\Q(\sqrt{-23}) \) \( 2^{2} \cdot 3^{2} \) $1$ $\Z/2\Z$ $0.159931548$ $2.500359038$ 0.667056446 \( \frac{520033}{32} a - \frac{141195}{64} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -26 a + 15\) , \( -25 a + 239\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(-26a+15\right){x}-25a+239$
36.4-a2 36.4-a \(\Q(\sqrt{-23}) \) \( 2^{2} \cdot 3^{2} \) $1$ $\Z/6\Z$ $0.479794644$ $7.501077115$ 0.667056446 \( -\frac{7739}{2} a - \frac{8427}{4} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -a\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2-a{x}$
36.4-a3 36.4-a \(\Q(\sqrt{-23}) \) \( 2^{2} \cdot 3^{2} \) $1$ $\Z/6\Z$ $0.959589288$ $7.501077115$ 0.667056446 \( \frac{21797}{16} a - \frac{5757}{8} \) \( \bigl[a\) , \( 0\) , \( a\) , \( -a\) , \( -a + 1\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3-a{x}-a+1$
36.4-a4 36.4-a \(\Q(\sqrt{-23}) \) \( 2^{2} \cdot 3^{2} \) $1$ $\Z/2\Z$ $0.319863096$ $2.500359038$ 0.667056446 \( -\frac{1982707}{4096} a + \frac{3848079}{2048} \) \( \bigl[a\) , \( 0\) , \( a\) , \( 4 a + 30\) , \( 21 a - 27\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(4a+30\right){x}+21a-27$
36.6-a1 36.6-a \(\Q(\sqrt{-23}) \) \( 2^{2} \cdot 3^{2} \) $1$ $\Z/6\Z$ $0.479794644$ $7.501077115$ 0.667056446 \( \frac{7739}{2} a - \frac{23905}{4} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( -a + 5\) , \( 3 a + 3\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(-a+5\right){x}+3a+3$
36.6-a2 36.6-a \(\Q(\sqrt{-23}) \) \( 2^{2} \cdot 3^{2} \) $1$ $\Z/6\Z$ $0.959589288$ $7.501077115$ 0.667056446 \( -\frac{21797}{16} a + \frac{10283}{16} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -a - 1\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-a{x}^2+\left(-a-1\right){x}$
36.6-a3 36.6-a \(\Q(\sqrt{-23}) \) \( 2^{2} \cdot 3^{2} \) $1$ $\Z/2\Z$ $0.319863096$ $2.500359038$ 0.667056446 \( \frac{1982707}{4096} a + \frac{5713451}{4096} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -6 a + 34\) , \( -22 a - 6\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-a{x}^2+\left(-6a+34\right){x}-22a-6$
36.6-a4 36.6-a \(\Q(\sqrt{-23}) \) \( 2^{2} \cdot 3^{2} \) $1$ $\Z/2\Z$ $0.159931548$ $2.500359038$ 0.667056446 \( -\frac{520033}{32} a + \frac{898871}{64} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( 24 a - 5\) , \( 43 a + 67\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(24a-5\right){x}+43a+67$
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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.