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Results (14 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
15876.3-a1 15876.3-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.058798633$ $3.000417687$ 2.444553594 \( -\frac{2271}{2} a + 945 \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 3 a\) , \( -3 a + 4\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+3a{x}-3a+4$
15876.3-a2 15876.3-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.411590433$ $0.428631098$ 2.444553594 \( \frac{15883557}{128} a + \frac{1611225}{64} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 3 a - 630\) , \( -129 a - 6044\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(3a-630\right){x}-129a-6044$
15876.3-b1 15876.3-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.229687320$ 1.419920610 \( \frac{17268549}{2} a - \frac{246587109}{2} \) \( \bigl[a\) , \( a\) , \( 1\) , \( 72 a - 214\) , \( 493 a - 1159\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(72a-214\right){x}+493a-1159$
15876.3-b2 15876.3-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.229687320$ 1.419920610 \( -\frac{17268549}{2} a - 114659280 \) \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -194 a + 11\) , \( -1163 a + 589\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-194a+11\right){x}-1163a+589$
15876.3-b3 15876.3-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.229687320$ 1.419920610 \( -\frac{132651}{2} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( 76 a - 29\) , \( -153 a - 106\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(76a-29\right){x}-153a-106$
15876.3-b4 15876.3-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.229687320$ 1.419920610 \( -\frac{1167051}{512} \) \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 36 a - 14\) , \( 65 a + 55\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(36a-14\right){x}+65a+55$
15876.3-b5 15876.3-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.229687320$ 1.419920610 \( \frac{9261}{8} \) \( \bigl[1\) , \( -1\) , \( a\) , \( -32 a + 12\) , \( 32 a + 18\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-32a+12\right){x}+32a+18$
15876.3-c1 15876.3-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.749014438$ 1.729774751 \( -\frac{1192725}{1372} a + \frac{287307}{2744} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -76 a + 32\) , \( -378 a + 254\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-76a+32\right){x}-378a+254$
15876.3-c2 15876.3-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.749014438$ 1.729774751 \( \frac{50481832659}{80707214} a + \frac{5130085995}{40353607} \) \( \bigl[a\) , \( a\) , \( 0\) , \( 72 a - 27\) , \( -299 a + 106\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(72a-27\right){x}-299a+106$
15876.3-c3 15876.3-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.749014438$ 1.729774751 \( -\frac{457190997}{1792} a + \frac{1524555639}{3584} \) \( \bigl[a\) , \( a\) , \( 0\) , \( 167 a - 277\) , \( 1305 a - 1549\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(167a-277\right){x}+1305a-1549$
15876.3-c4 15876.3-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.749014438$ 1.729774751 \( -\frac{43477641}{14} a + \frac{34139475}{14} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -179 a + 374\) , \( 1805 a + 621\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-179a+374\right){x}+1805a+621$
15876.3-c5 15876.3-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.749014438$ 1.729774751 \( -\frac{13989364197}{7} a + \frac{30175519239}{14} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 535 a - 758\) , \( 6903 a - 6086\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(535a-758\right){x}+6903a-6086$
15876.3-d1 15876.3-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.328226405$ $1.964234452$ 2.977804628 \( -\frac{2271}{2} a + 945 \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -7 a + 11\) , \( -3 a + 25\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-7a+11\right){x}-3a+25$
15876.3-d2 15876.3-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.046889486$ $1.964234452$ 2.977804628 \( \frac{15883557}{128} a + \frac{1611225}{64} \) \( \bigl[a\) , \( -1\) , \( a + 1\) , \( 20 a + 14\) , \( -46 a + 65\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(20a+14\right){x}-46a+65$
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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.