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Results (6 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
218.3-a3 218.3-a \(\Q(\sqrt{-7}) \) \( 2 \cdot 109 \) $0$ $\Z/3\Z$ $1$ $2.538206648$ 0.639567958 \( \frac{175486627225}{663054848} a + \frac{290993664997}{331527424} \) \( \bigl[a\) , \( 0\) , \( 1\) , \( -5 a\) , \( a - 5\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-5a{x}+a-5$
6976.13-b3 6976.13-b \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 109 \) $1$ $\mathsf{trivial}$ $0.490565254$ $0.897391566$ 2.662255488 \( \frac{175486627225}{663054848} a + \frac{290993664997}{331527424} \) \( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( -9 a - 45\) , \( 74 a - 18\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-9a-45\right){x}+74a-18$
13952.3-h3 13952.3-h \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 109 \) $1$ $\mathsf{trivial}$ $0.079771726$ $1.794783133$ 5.844343151 \( \frac{175486627225}{663054848} a + \frac{290993664997}{331527424} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 4 a + 10\) , \( -2 a - 11\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(4a+10\right){x}-2a-11$
17658.3-a3 17658.3-a \(\Q(\sqrt{-7}) \) \( 2 \cdot 3^{4} \cdot 109 \) $1$ $\Z/3\Z$ $0.663087980$ $0.846068882$ 5.089077913 \( \frac{175486627225}{663054848} a + \frac{290993664997}{331527424} \) \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -40 a + 1\) , \( 12 a + 129\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-40a+1\right){x}+12a+129$
23762.4-a3 23762.4-a \(\Q(\sqrt{-7}) \) \( 2 \cdot 109^{2} \) $0$ $\mathsf{trivial}$ $1$ $0.243116104$ 3.308013011 \( \frac{175486627225}{663054848} a + \frac{290993664997}{331527424} \) \( \bigl[a\) , \( -a\) , \( 1\) , \( -398 a + 638\) , \( 4480 a - 1733\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-398a+638\right){x}+4480a-1733$
27904.9-b3 27904.9-b \(\Q(\sqrt{-7}) \) \( 2^{8} \cdot 109 \) $0$ $\mathsf{trivial}$ $1$ $0.634551662$ 2.878055814 \( \frac{175486627225}{663054848} a + \frac{290993664997}{331527424} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -70 a - 1\) , \( 7 a + 305\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-70a-1\right){x}+7a+305$
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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.