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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
71.3-a1 71.3-a \(\Q(\zeta_{7})^+\) \( 71 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.289607277$ 0.587429871 \( -\frac{925759129064909928}{1804229351} a^{2} + \frac{385959155459705697}{1804229351} a + \frac{2310445605654755654}{1804229351} \) \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( 4 a^{2} - 10 a - 44\) , \( -32 a^{2} - 61 a - 73\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(4a^{2}-10a-44\right){x}-32a^{2}-61a-73$
71.3-a2 71.3-a \(\Q(\zeta_{7})^+\) \( 71 \) 0 $\Z/10\Z$ $\mathrm{SU}(2)$ $1$ $411.2009097$ 0.587429871 \( \frac{2121}{71} a^{2} - \frac{713073}{71} a + \frac{1242209}{71} \) \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( -a^{2} + 1\) , \( 0\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-a^{2}+1\right){x}$
71.3-a3 71.3-a \(\Q(\zeta_{7})^+\) \( 71 \) 0 $\Z/10\Z$ $\mathrm{SU}(2)$ $1$ $205.6004548$ 0.587429871 \( \frac{841196669387}{5041} a^{2} - \frac{1885779500418}{5041} a + \frac{672641959002}{5041} \) \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( -11 a^{2} - 5 a + 6\) , \( 18 a^{2} + 12 a - 9\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-11a^{2}-5a+6\right){x}+18a^{2}+12a-9$
71.3-a4 71.3-a \(\Q(\zeta_{7})^+\) \( 71 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.644803638$ 0.587429871 \( \frac{1128735985778740212430417}{3255243551009881201} a^{2} + \frac{808193592087701284035551}{3255243551009881201} a - \frac{697032567862883246911701}{3255243551009881201} \) \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( -221 a^{2} - 190 a + 81\) , \( -2926 a^{2} - 2384 a + 1532\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-221a^{2}-190a+81\right){x}-2926a^{2}-2384a+1532$
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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.