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Results (4 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
75.1-a4 75.1-a \(\Q(\sqrt{57}) \) \( 3 \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 2.699915346 \( \frac{111284641}{50625} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( -121051 a - 396429\) , \( 20377967 a + 66736152\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-121051a-396429\right){x}+20377967a+66736152$
75.1-b4 75.1-b \(\Q(\sqrt{57}) \) \( 3 \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $4.111075049$ $7.846755528$ 1.068189016 \( \frac{111284641}{50625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$
225.1-a4 225.1-a \(\Q(\sqrt{57}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $4.027707458$ $5.163131942$ 2.754442525 \( \frac{111284641}{50625} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -1203 a - 3933\) , \( -19185 a - 62826\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1203a-3933\right){x}-19185a-62826$
225.1-b4 225.1-b \(\Q(\sqrt{57}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $4.027707458$ $5.163131942$ 2.754442525 \( \frac{111284641}{50625} \) \( \bigl[1\) , \( a\) , \( 0\) , \( 1203 a - 5136\) , \( 19185 a - 82011\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(1203a-5136\right){x}+19185a-82011$
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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.