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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
38.1-a1 38.1-a \(\Q(\sqrt{38}) \) \( 2 \cdot 19 \) $1$ $\Z/3\Z$ $1.083080177$ $32.17041206$ 2.512134654 \( -\frac{413493625}{152} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -16\) , \( 22\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-16{x}+22$
38.1-a2 38.1-a \(\Q(\sqrt{38}) \) \( 2 \cdot 19 \) $1$ $\mathsf{trivial}$ $9.747721593$ $0.397165580$ 2.512134654 \( -\frac{69173457625}{2550136832} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -86\) , \( -2456\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-86{x}-2456$
38.1-a3 38.1-a \(\Q(\sqrt{38}) \) \( 2 \cdot 19 \) $1$ $\Z/3\Z$ $3.249240531$ $3.574490228$ 2.512134654 \( \frac{94196375}{3511808} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 9\) , \( 90\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+9{x}+90$
38.1-b1 38.1-b \(\Q(\sqrt{38}) \) \( 2 \cdot 19 \) $2$ $\mathsf{trivial}$ $1.315712904$ $1.446313524$ 7.408717326 \( -\frac{413493625}{152} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 6899 a - 42446\) , \( 772258 a - 4760315\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(6899a-42446\right){x}+772258a-4760315$
38.1-b2 38.1-b \(\Q(\sqrt{38}) \) \( 2 \cdot 19 \) $2$ $\mathsf{trivial}$ $0.146190322$ $1.446313524$ 7.408717326 \( -\frac{69173457625}{2550136832} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 37979 a - 234036\) , \( -80443562 a + 495887623\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(37979a-234036\right){x}-80443562a+495887623$
38.1-b3 38.1-b \(\Q(\sqrt{38}) \) \( 2 \cdot 19 \) $2$ $\mathsf{trivial}$ $0.146190322$ $1.446313524$ 7.408717326 \( \frac{94196375}{3511808} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -4201 a + 25979\) , \( 2939458 a - 18119833\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4201a+25979\right){x}+2939458a-18119833$
38.1-c1 38.1-c \(\Q(\sqrt{38}) \) \( 2 \cdot 19 \) $0$ $\mathsf{trivial}$ $1$ $5.550558930$ 1.800839115 \( -\frac{37966934881}{4952198} \) \( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -31079 a - 191599\) , \( 7993701 a + 49276473\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-31079a-191599\right){x}+7993701a+49276473$
38.1-c2 38.1-c \(\Q(\sqrt{38}) \) \( 2 \cdot 19 \) $0$ $\mathsf{trivial}$ $1$ $5.550558930$ 1.800839115 \( -\frac{1}{608} \) \( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( a - 9\) , \( -39009 a - 240477\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a-9\right){x}-39009a-240477$
38.1-d1 38.1-d \(\Q(\sqrt{38}) \) \( 2 \cdot 19 \) $1$ $\mathsf{trivial}$ $14.18215134$ $0.671163407$ 6.176445005 \( -\frac{37966934881}{4952198} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -70\) , \( -279\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-70{x}-279$
38.1-d2 38.1-d \(\Q(\sqrt{38}) \) \( 2 \cdot 19 \) $1$ $\Z/5\Z$ $2.836430269$ $16.77908518$ 6.176445005 \( -\frac{1}{608} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+1$
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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.