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Results (8 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
225.2-a1 225.2-a \(\Q(\sqrt{21}) \) \( 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.866387513$ 2.443674873 \( \frac{3309568}{81} a - \frac{3604480}{27} \) \( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( -7 a - 88\) , \( 194 a + 73\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7a-88\right){x}+194a+73$
225.2-b1 225.2-b \(\Q(\sqrt{21}) \) \( 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $5.475537501$ 2.389720482 \( 0 \) \( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -4\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-4$
225.2-b2 225.2-b \(\Q(\sqrt{21}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $16.42661250$ 2.389720482 \( 0 \) \( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( 9 a + 16\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+9a+16$
225.2-c1 225.2-c \(\Q(\sqrt{21}) \) \( 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $2.305063867$ 1.006012348 \( \frac{3309568}{81} a - \frac{3604480}{27} \) \( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( 379 a - 1058\) , \( -6209 a + 17319\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(379a-1058\right){x}-6209a+17319$
225.2-d1 225.2-d \(\Q(\sqrt{21}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $-7$ $N(\mathrm{U}(1))$ $0.247061726$ $17.87331837$ 1.927218749 \( -3375 \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 15 a - 42\) , \( -63 a + 176\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(15a-42\right){x}-63a+176$
225.2-d2 225.2-d \(\Q(\sqrt{21}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $-7$ $N(\mathrm{U}(1))$ $1.729432086$ $2.553331196$ 1.927218749 \( -3375 \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -3\) , \( -3 a - 8\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-3{x}-3a-8$
225.2-d3 225.2-d \(\Q(\sqrt{21}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $-28$ $N(\mathrm{U}(1))$ $0.123530863$ $17.87331837$ 1.927218749 \( 16581375 \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 255 a - 717\) , \( -3441 a + 9611\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(255a-717\right){x}-3441a+9611$
225.2-d4 225.2-d \(\Q(\sqrt{21}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $-28$ $N(\mathrm{U}(1))$ $0.864716043$ $2.553331196$ 1.927218749 \( 16581375 \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -15 a - 78\) , \( -117 a - 353\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-15a-78\right){x}-117a-353$
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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.