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Results (12 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
22500.2-a1 22500.2-a \(\Q(\sqrt{-2}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{4} \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.119882568$ $2.388115705$ 4.858560858 \( \frac{5488}{81} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( 3\) , \( -9\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+3{x}-9$
22500.2-a2 22500.2-a \(\Q(\sqrt{-2}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{4} \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.119882568$ $2.388115705$ 4.858560858 \( \frac{131072}{9} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -13\) , \( 22\bigr] \) ${y}^2={x}^{3}-{x}^{2}-13{x}+22$
22500.2-b1 22500.2-b \(\Q(\sqrt{-2}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.200470374$ 2.546582227 \( -\frac{30866268160}{3} \) \( \bigl[0\) , \( -1\) , \( a\) , \( -303\) , \( 2135\bigr] \) ${y}^2+a{y}={x}^{3}-{x}^{2}-303{x}+2135$
22500.2-b2 22500.2-b \(\Q(\sqrt{-2}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $3.601411123$ 2.546582227 \( -\frac{40960}{27} \) \( \bigl[0\) , \( -1\) , \( a\) , \( -3\) , \( 5\bigr] \) ${y}^2+a{y}={x}^{3}-{x}^{2}-3{x}+5$
22500.2-c1 22500.2-c \(\Q(\sqrt{-2}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $5.655038515$ $0.550455002$ 4.402226540 \( \frac{20283392}{6075} a - \frac{5636096}{6075} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -100 a - 134\) , \( 724 a + 275\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-100a-134\right){x}+724a+275$
22500.2-c2 22500.2-c \(\Q(\sqrt{-2}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.827519257$ $0.550455002$ 4.402226540 \( -\frac{171491008}{295245} a - \frac{176375504}{295245} \) \( \bigl[a\) , \( a - 1\) , \( a\) , \( -26 a + 124\) , \( -407 a - 617\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-26a+124\right){x}-407a-617$
22500.2-d1 22500.2-d \(\Q(\sqrt{-2}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $5.655038515$ $0.550455002$ 4.402226540 \( -\frac{20283392}{6075} a - \frac{5636096}{6075} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 100 a - 134\) , \( -724 a + 275\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(100a-134\right){x}-724a+275$
22500.2-d2 22500.2-d \(\Q(\sqrt{-2}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.827519257$ $0.550455002$ 4.402226540 \( \frac{171491008}{295245} a - \frac{176375504}{295245} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 26 a + 124\) , \( 407 a - 617\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(26a+124\right){x}+407a-617$
22500.2-e1 22500.2-e \(\Q(\sqrt{-2}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.477623141$ 2.701844495 \( \frac{5488}{81} \) \( \bigl[a\) , \( 0\) , \( a\) , \( 74\) , \( -1198\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+74{x}-1198$
22500.2-e2 22500.2-e \(\Q(\sqrt{-2}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.477623141$ 2.701844495 \( \frac{131072}{9} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -333\) , \( 2088\bigr] \) ${y}^2={x}^{3}+{x}^{2}-333{x}+2088$
22500.2-f1 22500.2-f \(\Q(\sqrt{-2}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.240094074$ 4.583848008 \( -\frac{30866268160}{3} \) \( \bigl[0\) , \( 1\) , \( a\) , \( -7583\) , \( 251651\bigr] \) ${y}^2+a{y}={x}^{3}+{x}^{2}-7583{x}+251651$
22500.2-f2 22500.2-f \(\Q(\sqrt{-2}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{4} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $0.720282224$ 4.583848008 \( -\frac{40960}{27} \) \( \bigl[0\) , \( 1\) , \( a\) , \( -83\) , \( 401\bigr] \) ${y}^2+a{y}={x}^{3}+{x}^{2}-83{x}+401$
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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.