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Results (10 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
10092.1-a1 10092.1-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 29^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.027321701$ $1.233279083$ 2.023214005 \( -\frac{19968681097}{712704} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 56 a\) , \( -192\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+56a{x}-192$
10092.1-b1 10092.1-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 29^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.138093174$ $3.667475200$ 2.339207566 \( -\frac{13997521}{1566} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( 4 a\) , \( -7\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+4a{x}-7$
10092.1-c1 10092.1-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 29^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $4.198874530$ 2.424221340 \( \frac{12167}{1392} \) \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -1\) , \( -2\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}-{x}-2$
10092.1-c2 10092.1-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 29^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.049718632$ 2.424221340 \( \frac{13430356633}{4243686} \) \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -50 a + 49\) , \( 86\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-50a+49\right){x}+86$
10092.1-c3 10092.1-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 29^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.099437265$ 2.424221340 \( \frac{822656953}{30276} \) \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -20 a + 19\) , \( -34\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-20a+19\right){x}-34$
10092.1-c4 10092.1-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 29^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.049718632$ 2.424221340 \( \frac{3279392280793}{4698} \) \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -310 a + 309\) , \( -2122\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-310a+309\right){x}-2122$
10092.1-d1 10092.1-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 29^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.141523007$ 2.287833704 \( -\frac{30526075007211889}{103499257854} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -6511 a + 6511\) , \( -203353\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-6511a+6511\right){x}-203353$
10092.1-d2 10092.1-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 29^{2} \) 0 $\Z/7\Z$ $\mathrm{SU}(2)$ $1$ $0.990661053$ 2.287833704 \( -\frac{117649}{8118144} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -a + 1\) , \( 137\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-a+1\right){x}+137$
10092.1-e1 10092.1-e \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 29^{2} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $0.047800804$ 2.833374908 \( -\frac{50577879066661513}{621261297432576} \) \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -7705 a + 7704\) , \( 1226492\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-7705a+7704\right){x}+1226492$
10092.1-e2 10092.1-e \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 29^{2} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $0.015933601$ 2.833374908 \( \frac{36079072622241241607}{458176313589497856} \) \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 68840 a - 68841\) , \( -31810330\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(68840a-68841\right){x}-31810330$
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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.