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Results (15 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
900.1-a1 900.1-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) $0$ $\Z/6\Z$ $1$ $2.819962089$ 1.085403914 \( -\frac{1860867}{320} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -8\) , \( 11\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-8{x}+11$
4900.1-a1 4900.1-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $0.403882379$ $1.846098533$ 1.721904841 \( -\frac{1860867}{320} \) \( \bigl[1\) , \( a\) , \( 1\) , \( -20 a + 12\) , \( -25 a + 46\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-20a+12\right){x}-25a+46$
4900.3-a1 4900.3-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $0.403882379$ $1.846098533$ 1.721904841 \( -\frac{1860867}{320} \) \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 20 a - 8\) , \( 25 a + 21\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(20a-8\right){x}+25a+21$
6400.1-d1 6400.1-d \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $1.221079403$ 1.409981044 \( -\frac{1860867}{320} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 42 a - 41\) , \( -119 a + 39\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(42a-41\right){x}-119a+39$
6400.1-f1 6400.1-f \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $1.221079403$ 1.409981044 \( -\frac{1860867}{320} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -40 a\) , \( 160 a - 80\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-40a{x}+160a-80$
22500.1-a1 22500.1-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{4} \) $1$ $\Z/2\Z$ $0.198498654$ $0.563992417$ 3.102497519 \( -\frac{1860867}{320} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -192 a + 192\) , \( 1216\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-192a+192\right){x}+1216$
36100.1-a1 36100.1-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 5^{2} \cdot 19^{2} \) $1$ $\Z/2\Z$ $0.204423358$ $1.120539309$ 3.174009553 \( -\frac{1860867}{320} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( -41 a + 53\) , \( -58 a - 93\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-41a+53\right){x}-58a-93$
36100.3-a1 36100.3-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 5^{2} \cdot 19^{2} \) $1$ $\Z/2\Z$ $0.204423358$ $1.120539309$ 3.174009553 \( -\frac{1860867}{320} \) \( \bigl[a\) , \( a\) , \( a\) , \( -54 a + 41\) , \( 57 a - 150\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-54a+41\right){x}+57a-150$
57600.1-d1 57600.1-d \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $0.949584851$ $0.704990522$ 3.092049343 \( -\frac{1860867}{320} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -123\) , \( -598\bigr] \) ${y}^2={x}^{3}-123{x}-598$
96100.1-b1 96100.1-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 5^{2} \cdot 31^{2} \) $0$ $\Z/2\Z$ $1$ $0.877249340$ 2.025920571 \( -\frac{1860867}{320} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( 28 a + 62\) , \( -324 a + 272\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(28a+62\right){x}-324a+272$
96100.3-b1 96100.3-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 5^{2} \cdot 31^{2} \) $0$ $\Z/2\Z$ $1$ $0.877249340$ 2.025920571 \( -\frac{1860867}{320} \) \( \bigl[a\) , \( a\) , \( 0\) , \( 90 a - 62\) , \( 324 a - 52\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(90a-62\right){x}+324a-52$
102400.1-h1 102400.1-h \(\Q(\sqrt{-3}) \) \( 2^{12} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $0.610539701$ 0.704990522 \( -\frac{1860867}{320} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -163 a\) , \( -954 a + 477\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-163a{x}-954a+477$
102400.1-k1 102400.1-k \(\Q(\sqrt{-3}) \) \( 2^{12} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $0.610539701$ 0.704990522 \( -\frac{1860867}{320} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 165 a - 164\) , \( 1118 a - 641\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(165a-164\right){x}+1118a-641$
122500.1-a1 122500.1-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 5^{4} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.369219706$ 1.705352776 \( -\frac{1860867}{320} \) \( \bigl[a\) , \( a\) , \( 1\) , \( 192 a - 513\) , \( -2745 a + 4764\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(192a-513\right){x}-2745a+4764$
122500.3-a1 122500.3-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 5^{4} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.369219706$ 1.705352776 \( -\frac{1860867}{320} \) \( \bigl[a\) , \( -1\) , \( 1\) , \( -321 a + 513\) , \( 2745 a + 2019\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-321a+513\right){x}+2745a+2019$
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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.