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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
121.1-b1 121.1-b \(\Q(\zeta_{11})^+\) \( 11^{2} \) $1$ $\Z/11\Z$ $-11$ $N(\mathrm{U}(1))$ $0.089785156$ $28099.20145$ 1.72316863 \( -32768 \) \( \bigl[0\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 1\) , \( a^{3} + a^{2} - 2 a - 2\) , \( 9 a^{4} - 16 a^{3} - 23 a^{2} + 45 a - 10\) , \( -38 a^{4} + 67 a^{3} + 96 a^{2} - 188 a + 43\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+3a+1\right){x}^{2}+\left(9a^{4}-16a^{3}-23a^{2}+45a-10\right){x}-38a^{4}+67a^{3}+96a^{2}-188a+43$
121.1-b2 121.1-b \(\Q(\zeta_{11})^+\) \( 11^{2} \) $1$ $\mathsf{trivial}$ $-11$ $N(\mathrm{U}(1))$ $0.987636717$ $21.11134594$ 1.72316863 \( -32768 \) \( \bigl[0\) , \( -a^{4} + 4 a^{2} + a - 2\) , \( a^{4} - 4 a^{2} + 3\) , \( -4 a^{4} + 9 a^{3} - a^{2} - 3 a\) , \( -13 a^{4} + 34 a^{3} - 6 a^{2} - 25 a + 5\bigr] \) ${y}^2+\left(a^{4}-4a^{2}+3\right){y}={x}^{3}+\left(-a^{4}+4a^{2}+a-2\right){x}^{2}+\left(-4a^{4}+9a^{3}-a^{2}-3a\right){x}-13a^{4}+34a^{3}-6a^{2}-25a+5$
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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.