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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-a2 75.1-a \(\Q(\sqrt{57}) \) \( 3 \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 2.699915346 \( -\frac{1}{15} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( -251 a - 819\) , \( -680263 a - 2227808\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-251a-819\right){x}-680263a-2227808$
75.1-b2 75.1-b \(\Q(\sqrt{57}) \) \( 3 \cdot 5^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.027768762$ $31.38702211$ 1.068189016 \( -\frac{1}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$
225.1-a2 225.1-a \(\Q(\sqrt{57}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.006926864$ $10.32626388$ 2.754442525 \( -\frac{1}{15} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -3 a - 3\) , \( 675 a + 2214\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a-3\right){x}+675a+2214$
225.1-b2 225.1-b \(\Q(\sqrt{57}) \) \( 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.006926864$ $10.32626388$ 2.754442525 \( -\frac{1}{15} \) \( \bigl[1\) , \( a\) , \( 0\) , \( 3 a - 6\) , \( -675 a + 2889\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(3a-6\right){x}-675a+2889$
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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.