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Results (8 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 \(\Q(\sqrt{17}) \) \( 17 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $6.070512355$ $0.598363940$ 0.440490254 \( -\frac{97064067741644382786}{17} a + \frac{248634735746274843273}{17} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 330 a - 936\) , \( 4996 a - 13110\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(330a-936\right){x}+4996a-13110$
17.1-a2 17.1-a \(\Q(\sqrt{17}) \) \( 17 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.758814044$ $2.393455763$ 0.440490254 \( -\frac{35937}{83521} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-{x}-14$
17.1-a3 17.1-a \(\Q(\sqrt{17}) \) \( 17 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.379407022$ $38.29529222$ 0.440490254 \( -\frac{5821794}{17} a + \frac{14936697}{17} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 6 a + 9\) , \( 4 a + 6\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(6a+9\right){x}+4a+6$
17.1-a4 17.1-a \(\Q(\sqrt{17}) \) \( 17 \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $0.758814044$ $38.29529222$ 0.440490254 \( \frac{35937}{17} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-{x}$
17.1-a5 17.1-a \(\Q(\sqrt{17}) \) \( 17 \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1.517628088$ $9.573823055$ 0.440490254 \( \frac{20346417}{289} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-6{x}-4$
17.1-a6 17.1-a \(\Q(\sqrt{17}) \) \( 17 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.379407022$ $38.29529222$ 0.440490254 \( \frac{5821794}{17} a + \frac{9114903}{17} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -6 a + 15\) , \( -4 a + 10\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-6a+15\right){x}-4a+10$
17.1-a7 17.1-a \(\Q(\sqrt{17}) \) \( 17 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $3.035256177$ $2.393455763$ 0.440490254 \( \frac{82483294977}{17} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-91{x}-310$
17.1-a8 17.1-a \(\Q(\sqrt{17}) \) \( 17 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $6.070512355$ $0.598363940$ 0.440490254 \( \frac{97064067741644382786}{17} a + \frac{151570668004630460487}{17} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -330 a - 606\) , \( -4996 a - 8114\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-330a-606\right){x}-4996a-8114$
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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.