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Results (3 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
5324.6-a1 5324.6-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\Z/3\Z$ $0.804718677$ $0.722336016$ 1.757617297 \( -\frac{531165637}{1362944} a + \frac{64260511}{681472} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( -45 a + 7\) , \( -280 a + 120\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-45a+7\right){x}-280a+120$
42592.18-c2 42592.18-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{3} \) $1$ $\mathsf{trivial}$ $0.489938282$ $1.197858769$ 3.549097701 \( -\frac{531165637}{1362944} a + \frac{64260511}{681472} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 17 a - 6\) , \( -14 a - 68\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(17a-6\right){x}-14a-68$
42592.6-d2 42592.6-d \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{3} \) $1$ $\mathsf{trivial}$ $0.034494406$ $1.197858769$ 7.496292234 \( -\frac{531165637}{1362944} a + \frac{64260511}{681472} \) \( \bigl[a\) , \( a\) , \( a\) , \( -17 a + 12\) , \( 52 a - 49\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-17a+12\right){x}+52a-49$
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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.