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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
10.1-a1 10.1-a 4.4.16448.1 \( 2 \cdot 5 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.005502615$ $2194.334899$ 3.765958694 \( \frac{100210679}{2500} a^{3} - \frac{90943874}{625} a^{2} - \frac{18207153}{625} a + \frac{79650407}{1250} \) \( \bigl[a^{3} - 3 a^{2} - 3 a + 3\) , \( a^{3} - 3 a^{2} - 4 a + 2\) , \( a^{3} - 3 a^{2} - 3 a + 2\) , \( 66 a^{3} - 99 a^{2} - 441 a - 230\) , \( -516 a^{3} + 750 a^{2} + 3510 a + 1912\bigr] \) ${y}^2+\left(a^{3}-3a^{2}-3a+3\right){x}{y}+\left(a^{3}-3a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-3a^{2}-4a+2\right){x}^{2}+\left(66a^{3}-99a^{2}-441a-230\right){x}-516a^{3}+750a^{2}+3510a+1912$
10.1-b1 10.1-b 4.4.16448.1 \( 2 \cdot 5 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.021941483$ $724.7407107$ 1.983864792 \( \frac{100210679}{2500} a^{3} - \frac{90943874}{625} a^{2} - \frac{18207153}{625} a + \frac{79650407}{1250} \) \( \bigl[a^{3} - 2 a^{2} - 4 a - 1\) , \( -2 a^{3} + 5 a^{2} + 7 a - 1\) , \( 2 a^{3} - 5 a^{2} - 8 a + 2\) , \( -a^{3} + 4 a^{2} - 3 a - 3\) , \( 3 a^{3} - 32 a - 27\bigr] \) ${y}^2+\left(a^{3}-2a^{2}-4a-1\right){x}{y}+\left(2a^{3}-5a^{2}-8a+2\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+7a-1\right){x}^{2}+\left(-a^{3}+4a^{2}-3a-3\right){x}+3a^{3}-32a-27$
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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.