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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
17.2-a1 17.2-a \(\Q(\zeta_{9})^+\) \( 17 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $219.1378571$ 0.507263558 \( \frac{42561684}{4913} a^{2} + \frac{127953099}{4913} a + \frac{43312806}{4913} \) \( \bigl[a^{2} - 1\) , \( -a + 1\) , \( a^{2} + a - 2\) , \( -30 a^{2} + 43 a + 21\) , \( 103 a^{2} - 160 a - 66\bigr] \) ${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-30a^{2}+43a+21\right){x}+103a^{2}-160a-66$
153.2-a6 153.2-a \(\Q(\zeta_{9})^+\) \( 3^{2} \cdot 17 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $18.78534723$ 1.043630401 \( \frac{42561684}{4913} a^{2} + \frac{127953099}{4913} a + \frac{43312806}{4913} \) \( \bigl[a + 1\) , \( -a\) , \( a^{2} + a - 1\) , \( -10 a^{2} + 9 a + 12\) , \( -15 a^{2} + 24 a + 3\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}-a{x}^{2}+\left(-10a^{2}+9a+12\right){x}-15a^{2}+24a+3$
289.6-b1 289.6-b \(\Q(\zeta_{9})^+\) \( 17^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.204671540$ $14.29370058$ 1.434934525 \( \frac{42561684}{4913} a^{2} + \frac{127953099}{4913} a + \frac{43312806}{4913} \) \( \bigl[a^{2} + a - 1\) , \( a + 1\) , \( a\) , \( -149 a^{2} + 223 a + 123\) , \( -1345 a^{2} + 2090 a + 839\bigr] \) ${y}^2+\left(a^{2}+a-1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-149a^{2}+223a+123\right){x}-1345a^{2}+2090a+839$
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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.