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Results (4 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
17.1-a1 17.1-a \(\Q(\sqrt{21}) \) \( 17 \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $45.16448385$ 1.095077597 \( \frac{20811}{17} a - \frac{19591}{17} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -7\) , \( -2 a + 2\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}-7{x}-2a+2$
17.1-a2 17.1-a \(\Q(\sqrt{21}) \) \( 17 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $5.018275983$ 1.095077597 \( \frac{2723256379739}{4913} a + \frac{4878142779916}{4913} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -15 a + 33\) , \( 10 a - 33\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-15a+33\right){x}+10a-33$
17.1-b1 17.1-b \(\Q(\sqrt{21}) \) \( 17 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.092314733$ $19.62917645$ 0.790848774 \( \frac{20811}{17} a - \frac{19591}{17} \) \( \bigl[a\) , \( -a\) , \( 1\) , \( -a + 1\) , \( 0\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-a+1\right){x}$
17.1-b2 17.1-b \(\Q(\sqrt{21}) \) \( 17 \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.276944199$ $19.62917645$ 0.790848774 \( \frac{2723256379739}{4913} a + \frac{4878142779916}{4913} \) \( \bigl[a\) , \( -a\) , \( 1\) , \( -11 a - 14\) , \( 26 a + 50\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-11a-14\right){x}+26a+50$
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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.