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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
11.2-a2 11.2-a 4.4.7625.1 \( 11 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $868.2216528$ 1.242855680 \( \frac{3618522395}{484} a^{3} - \frac{772470125}{44} a^{2} - \frac{21109482815}{484} a + \frac{10734680853}{121} \) \( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{5}{4} a - 5\) , \( a^{2} - 2 a - 6\) , \( a + 1\) , \( \frac{15}{4} a^{3} + \frac{13}{4} a^{2} - \frac{135}{4} a - 43\) , \( \frac{29}{4} a^{3} + \frac{23}{4} a^{2} - \frac{229}{4} a - 70\bigr] \) ${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{5}{4}a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(\frac{15}{4}a^{3}+\frac{13}{4}a^{2}-\frac{135}{4}a-43\right){x}+\frac{29}{4}a^{3}+\frac{23}{4}a^{2}-\frac{229}{4}a-70$
11.2-b4 11.2-b 4.4.7625.1 \( 11 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1462.878091$ 2.094103896 \( \frac{3618522395}{484} a^{3} - \frac{772470125}{44} a^{2} - \frac{21109482815}{484} a + \frac{10734680853}{121} \) \( \bigl[\frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{5}{4} a\) , \( \frac{1}{4} a^{3} - \frac{5}{4} a^{2} + \frac{3}{4} a + 5\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{1}{4} a + 1\) , \( -3 a^{3} + 10 a^{2} + 14 a - 50\) , \( \frac{31}{4} a^{3} - \frac{75}{4} a^{2} - \frac{175}{4} a + 88\bigr] \) ${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{5}{4}a\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{1}{4}a+1\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{5}{4}a^{2}+\frac{3}{4}a+5\right){x}^{2}+\left(-3a^{3}+10a^{2}+14a-50\right){x}+\frac{31}{4}a^{3}-\frac{75}{4}a^{2}-\frac{175}{4}a+88$
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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.