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Results (6 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
224.2-a1 224.2-a \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $1.956842684$ 1.479234028 \( \frac{4096655365}{28} a - \frac{2878658051}{14} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -22 a + 87\) , \( -162 a - 91\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-22a+87\right){x}-162a-91$
224.2-a2 224.2-a \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.913685369$ 1.479234028 \( -\frac{13647889}{14} a - \frac{40536829}{7} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -3 a - 12\) , \( 23\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a-12\right){x}+23$
224.2-a3 224.2-a \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $3.913685369$ 1.479234028 \( -\frac{1145925}{112} a - \frac{72257}{56} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -2 a + 7\) , \( -2 a - 3\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-2a+7\right){x}-2a-3$
224.2-a4 224.2-a \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7 \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $3.913685369$ 1.479234028 \( -\frac{138325}{1792} a - \frac{317937}{896} \) \( \bigl[a\) , \( a\) , \( a\) , \( -2\) , \( -2 a + 3\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}-2{x}-2a+3$
224.2-a5 224.2-a \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.956842684$ 1.479234028 \( -\frac{5786513}{4802} a + \frac{263001}{343} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -8 a - 1\) , \( 10 a + 3\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-8a-1\right){x}+10a+3$
224.2-a6 224.2-a \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.913685369$ 1.479234028 \( \frac{361845}{196} a - \frac{43727}{98} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 2 a - 1\) , \( 2 a - 1\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(2a-1\right){x}+2a-1$
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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.