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Results (3 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
107.1-A1 107.1-A 3.1.23.1 \( 107 \) 0 $\Z/9\Z$ $\mathrm{SU}(2)$ $1$ $72.11684248$ 0.371293855 \( -\frac{36864}{107} a^{2} + \frac{102400}{107} a + \frac{61440}{107} \) \( \bigl[0\) , \( a^{2} + a - 1\) , \( a^{2} + 1\) , \( a^{2} - a - 1\) , \( -a^{2}\bigr] \) ${y}^2+\left(a^{2}+1\right){y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(a^{2}-a-1\right){x}-a^{2}$
107.1-A2 107.1-A 3.1.23.1 \( 107 \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $8.012982497$ 0.371293855 \( -\frac{13431610740736}{1225043} a^{2} - \frac{34043228901376}{1225043} a - \frac{18044231077888}{1225043} \) \( \bigl[0\) , \( a^{2} - a + 1\) , \( a^{2} + a\) , \( -30 a^{2} - 11 a + 11\) , \( -101 a^{2} + 29 a + 80\bigr] \) ${y}^2+\left(a^{2}+a\right){y}={x}^{3}+\left(a^{2}-a+1\right){x}^{2}+\left(-30a^{2}-11a+11\right){x}-101a^{2}+29a+80$
107.1-A3 107.1-A 3.1.23.1 \( 107 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.890331388$ 0.371293855 \( -\frac{270815754742792058998784}{1838459212420154507} a^{2} + \frac{475186041093450994348032}{1838459212420154507} a - \frac{358714265350210784702464}{1838459212420154507} \) \( \bigl[0\) , \( -a^{2} - a\) , \( 1\) , \( -59 a^{2} + 100 a - 71\) , \( -274 a^{2} + 484 a - 422\bigr] \) ${y}^2+{y}={x}^{3}+\left(-a^{2}-a\right){x}^{2}+\left(-59a^{2}+100a-71\right){x}-274a^{2}+484a-422$
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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.