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Results (17 matches)

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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
57122.3-a1 57122.3-a \(\Q(\sqrt{-1}) \) \( 2 \cdot 13^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.188700458$ $0.674452303$ 3.206887051 \( -\frac{38575685889}{16384} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -389\) , \( -2859\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-389{x}-2859$
57122.3-a2 57122.3-a \(\Q(\sqrt{-1}) \) \( 2 \cdot 13^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.169814351$ $4.721166125$ 3.206887051 \( \frac{351}{4} \) \( \bigl[i\) , \( 1\) , \( 0\) , \( 1\) , \( -1\bigr] \) ${y}^2+i{x}{y}={x}^{3}+{x}^{2}+{x}-1$
57122.3-b1 57122.3-b \(\Q(\sqrt{-1}) \) \( 2 \cdot 13^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.383448027$ $0.043086807$ 3.814935003 \( -\frac{1064019559329}{125497034} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -35944\) , \( -2868878\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-35944{x}-2868878$
57122.3-b2 57122.3-b \(\Q(\sqrt{-1}) \) \( 2 \cdot 13^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.197635432$ $0.301607655$ 3.814935003 \( -\frac{2146689}{1664} \) \( \bigl[i\) , \( 1\) , \( 0\) , \( -454\) , \( -5812\bigr] \) ${y}^2+i{x}{y}={x}^{3}+{x}^{2}-454{x}-5812$
57122.3-c1 57122.3-c \(\Q(\sqrt{-1}) \) \( 2 \cdot 13^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $6.410813447$ $0.042120063$ 4.320381952 \( -\frac{1680914269}{32768} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -54421\) , \( 4945517\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-54421{x}+4945517$
57122.3-c2 57122.3-c \(\Q(\sqrt{-1}) \) \( 2 \cdot 13^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.282162689$ $0.210600319$ 4.320381952 \( \frac{1331}{8} \) \( \bigl[i\) , \( -1\) , \( 0\) , \( 504\) , \( 13112\bigr] \) ${y}^2+i{x}{y}={x}^{3}-{x}^{2}+504{x}+13112$
57122.3-d1 57122.3-d \(\Q(\sqrt{-1}) \) \( 2 \cdot 13^{4} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.023317478$ $0.547560830$ 6.128514177 \( -\frac{1680914269}{32768} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -322\) , \( 2127\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-322{x}+2127$
57122.3-d2 57122.3-d \(\Q(\sqrt{-1}) \) \( 2 \cdot 13^{4} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.023317478$ $2.737804153$ 6.128514177 \( \frac{1331}{8} \) \( \bigl[i\) , \( -1\) , \( i\) , \( 4\) , \( 5\bigr] \) ${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}+4{x}+5$
57122.3-e1 57122.3-e \(\Q(\sqrt{-1}) \) \( 2 \cdot 13^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.041832015$ $0.389201187$ 5.209942410 \( -\frac{941069729}{13312} a + \frac{158887857}{1664} \) \( \bigl[1\) , \( -i - 1\) , \( i + 1\) , \( -741 i + 37\) , \( -4890 i + 5590\bigr] \) ${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-741i+37\right){x}-4890i+5590$
57122.3-e2 57122.3-e \(\Q(\sqrt{-1}) \) \( 2 \cdot 13^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.209160076$ $0.389201187$ 5.209942410 \( \frac{362248343231}{1485172} a + \frac{42997188354}{371293} \) \( \bigl[i\) , \( -1\) , \( 1\) , \( 526 i - 666\) , \( 7787 i - 4864\bigr] \) ${y}^2+i{x}{y}+{y}={x}^{3}-{x}^{2}+\left(526i-666\right){x}+7787i-4864$
57122.3-f1 57122.3-f \(\Q(\sqrt{-1}) \) \( 2 \cdot 13^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.041832015$ $0.389201187$ 5.209942410 \( \frac{941069729}{13312} a + \frac{158887857}{1664} \) \( \bigl[i\) , \( -i + 1\) , \( i + 1\) , \( 740 i + 38\) , \( -4890 i - 5590\bigr] \) ${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(740i+38\right){x}-4890i-5590$
57122.3-f2 57122.3-f \(\Q(\sqrt{-1}) \) \( 2 \cdot 13^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.209160076$ $0.389201187$ 5.209942410 \( -\frac{362248343231}{1485172} a + \frac{42997188354}{371293} \) \( \bigl[i\) , \( -1\) , \( 1\) , \( -527 i - 666\) , \( -7787 i - 4864\bigr] \) ${y}^2+i{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-527i-666\right){x}-7787i-4864$
57122.3-g1 57122.3-g \(\Q(\sqrt{-1}) \) \( 2 \cdot 13^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.051880946$ 1.452666500 \( -\frac{38575685889}{16384} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -65773\) , \( -6478507\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-65773{x}-6478507$
57122.3-g2 57122.3-g \(\Q(\sqrt{-1}) \) \( 2 \cdot 13^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.363166625$ 1.452666500 \( \frac{351}{4} \) \( \bigl[i\) , \( 1\) , \( i\) , \( 138\) , \( -2643\bigr] \) ${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+138{x}-2643$
57122.3-h1 57122.3-h \(\Q(\sqrt{-1}) \) \( 2 \cdot 13^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.068994933$ 4.967635186 \( -\frac{10730978619193}{6656} \) \( \bigl[i\) , \( 0\) , \( 0\) , \( -77659\) , \( 8336303\bigr] \) ${y}^2+i{x}{y}={x}^{3}-77659{x}+8336303$
57122.3-h2 57122.3-h \(\Q(\sqrt{-1}) \) \( 2 \cdot 13^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.206984799$ 4.967635186 \( -\frac{10218313}{17576} \) \( \bigl[i\) , \( 0\) , \( 0\) , \( -764\) , \( 16264\bigr] \) ${y}^2+i{x}{y}={x}^{3}-764{x}+16264$
57122.3-h3 57122.3-h \(\Q(\sqrt{-1}) \) \( 2 \cdot 13^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.620954398$ 4.967635186 \( \frac{12167}{26} \) \( \bigl[i\) , \( 0\) , \( 0\) , \( 81\) , \( -467\bigr] \) ${y}^2+i{x}{y}={x}^{3}+81{x}-467$
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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.