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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
1083.1-a1 1083.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 19^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.637562893$ $2.262154252$ 3.233482749 \( \frac{67419143}{390963} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( -43 a + 118\) , \( 659 a - 1842\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-43a+118\right){x}+659a-1842$
1083.1-a2 1083.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 19^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.637562893$ $36.19446804$ 3.233482749 \( \frac{389017}{57} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 7 a - 22\) , \( -11 a + 28\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(7a-22\right){x}-11a+28$
1083.1-a3 1083.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 19^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $3.275125787$ $9.048617011$ 3.233482749 \( \frac{30664297}{3249} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 32 a - 92\) , \( 158 a - 444\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(32a-92\right){x}+158a-444$
1083.1-a4 1083.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 19^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $6.550251574$ $2.262154252$ 3.233482749 \( \frac{115714886617}{1539} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -509 a - 914\) , \( -9754 a - 17480\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-509a-914\right){x}-9754a-17480$
1083.1-b1 1083.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 19^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.085998375$ 3.377949122 \( -\frac{9358714467168256}{22284891} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -4390\) , \( -113432\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}-4390{x}-113432$
1083.1-b2 1083.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 19^{2} \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $2.149959381$ 3.377949122 \( \frac{841232384}{1121931} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( 20\) , \( -32\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+20{x}-32$
1083.1-c1 1083.1-c \(\Q(\sqrt{21}) \) \( 3 \cdot 19^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $3.679988085$ 3.212156944 \( -\frac{1404928}{171} \) \( \bigl[0\) , \( -a\) , \( 1\) , \( 12 a - 31\) , \( 43 a - 121\bigr] \) ${y}^2+{y}={x}^{3}-a{x}^{2}+\left(12a-31\right){x}+43a-121$
1083.1-d1 1083.1-d \(\Q(\sqrt{21}) \) \( 3 \cdot 19^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.037574592$ $30.86363048$ 1.012258976 \( -\frac{1404928}{171} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -2\) , \( 2\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}-2{x}+2$
1083.1-e1 1083.1-e \(\Q(\sqrt{21}) \) \( 3 \cdot 19^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.190603013$ $3.435258684$ 2.857653421 \( -\frac{9358714467168256}{22284891} \) \( \bigl[0\) , \( a\) , \( 1\) , \( 21952 a - 61463\) , \( -2700411 a + 7538465\bigr] \) ${y}^2+{y}={x}^{3}+a{x}^{2}+\left(21952a-61463\right){x}-2700411a+7538465$
1083.1-e2 1083.1-e \(\Q(\sqrt{21}) \) \( 3 \cdot 19^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.953015065$ $3.435258684$ 2.857653421 \( \frac{841232384}{1121931} \) \( \bigl[0\) , \( a\) , \( 1\) , \( -98 a + 277\) , \( -861 a + 2405\bigr] \) ${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-98a+277\right){x}-861a+2405$
1083.1-f1 1083.1-f \(\Q(\sqrt{21}) \) \( 3 \cdot 19^{2} \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.460486004$ $4.711524088$ 3.787548392 \( \frac{67419143}{390963} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 8\) , \( 29\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+8{x}+29$
1083.1-f2 1083.1-f \(\Q(\sqrt{21}) \) \( 3 \cdot 19^{2} \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.460486004$ $18.84609635$ 3.787548392 \( \frac{389017}{57} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-2{x}-1$
1083.1-f3 1083.1-f \(\Q(\sqrt{21}) \) \( 3 \cdot 19^{2} \) $2$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.460486004$ $18.84609635$ 3.787548392 \( \frac{30664297}{3249} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -7\) , \( 5\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-7{x}+5$
1083.1-f4 1083.1-f \(\Q(\sqrt{21}) \) \( 3 \cdot 19^{2} \) $2$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.460486004$ $18.84609635$ 3.787548392 \( \frac{115714886617}{1539} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -102\) , \( 385\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-102{x}+385$
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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.