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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
45.1-a1 45.1-a \(\Q(\zeta_{15})^+\) \( 3^{2} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.492249124$ 0.774245886 \( \frac{4733169839}{3515625} \) \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -35 a^{3} + 174 a^{2} - 140 a - 32\) , \( -328 a^{3} + 1241 a^{2} - 884 a - 245\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-3\right){x}^{2}+\left(-35a^{3}+174a^{2}-140a-32\right){x}-328a^{3}+1241a^{2}-884a-245$
45.1-b10 45.1-b \(\Q(\zeta_{15})^+\) \( 3^{2} \cdot 5 \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $3.848223270$ 0.917854808 \( \frac{4733169839}{3515625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$
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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.