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Results (5 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
2.1-a2 2.1-a \(\Q(\sqrt{113}) \) \( 2 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $25.42172449$ 1.195737336 \( \frac{32125}{4} a + \frac{158187}{4} \) \( \bigl[1\) , \( -a - 1\) , \( a\) , \( 8\) , \( -a - 8\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+8{x}-a-8$
16.5-a2 16.5-a \(\Q(\sqrt{113}) \) \( 2^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.562112878$ $10.27635668$ 3.443559771 \( \frac{32125}{4} a + \frac{158187}{4} \) \( \bigl[a\) , \( 0\) , \( a\) , \( -916 a - 4411\) , \( -37061 a - 178450\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-916a-4411\right){x}-37061a-178450$
32.3-h2 32.3-h \(\Q(\sqrt{113}) \) \( 2^{5} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.354829174$ $22.97376349$ 3.067412879 \( \frac{32125}{4} a + \frac{158187}{4} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -20 a + 138\) , \( -153 a + 936\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-20a+138\right){x}-153a+936$
64.6-a2 64.6-a \(\Q(\sqrt{113}) \) \( 2^{6} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $7.458691788$ $7.266481497$ 5.098560907 \( \frac{32125}{4} a + \frac{158187}{4} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -30 a - 129\) , \( -315 a - 1505\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-30a-129\right){x}-315a-1505$
64.6-d2 64.6-d \(\Q(\sqrt{113}) \) \( 2^{6} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $8.987936888$ 0.845513979 \( \frac{32125}{4} a + \frac{158187}{4} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -12678 a + 73711\) , \( -1815474 a + 10557107\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-12678a+73711\right){x}-1815474a+10557107$
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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.