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Results (9 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
400.1-a4 400.1-a \(\Q(\sqrt{-3}) \) \( 2^{4} \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $2.141031885$ 0.618062667 \( \frac{488095744}{125} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -41 a + 41\) , \( -116\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-41a+41\right){x}-116$
6400.1-h4 6400.1-h \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.141031885$ 1.854188003 \( \frac{488095744}{125} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -41\) , \( 116\bigr] \) ${y}^2={x}^{3}-{x}^{2}-41{x}+116$
10000.1-a4 10000.1-a \(\Q(\sqrt{-3}) \) \( 2^{4} \cdot 5^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.978663800$ $0.428206377$ 2.903402684 \( \frac{488095744}{125} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -1033\) , \( -12438\bigr] \) ${y}^2={x}^{3}-{x}^{2}-1033{x}-12438$
57600.1-g4 57600.1-g \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.586421166$ $1.236125335$ 3.691740124 \( \frac{488095744}{125} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 124\) , \( -572 a + 348\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+124\right){x}-572a+348$
57600.1-l4 57600.1-l \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.586421166$ $1.236125335$ 3.691740124 \( \frac{488095744}{125} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 125 a - 124\) , \( 572 a - 224\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(125a-124\right){x}+572a-224$
67600.1-a4 67600.1-a \(\Q(\sqrt{-3}) \) \( 2^{4} \cdot 5^{2} \cdot 13^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $7.906781553$ $0.593815403$ 5.421513801 \( \frac{488095744}{125} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 620 a - 289\) , \( -3888 a - 1642\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(620a-289\right){x}-3888a-1642$
67600.3-a4 67600.3-a \(\Q(\sqrt{-3}) \) \( 2^{4} \cdot 5^{2} \cdot 13^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $7.906781553$ $0.593815403$ 5.421513801 \( \frac{488095744}{125} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -620 a + 331\) , \( 3888 a - 5530\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-620a+331\right){x}+3888a-5530$
102400.1-a4 102400.1-a \(\Q(\sqrt{-3}) \) \( 2^{12} \cdot 5^{2} \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.269748285$ $1.070515942$ 4.001312284 \( \frac{488095744}{125} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 165 a\) , \( 763\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+165a{x}+763$
102400.1-t4 102400.1-t \(\Q(\sqrt{-3}) \) \( 2^{12} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.070515942$ 3.708376006 \( \frac{488095744}{125} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -165\) , \( -763\bigr] \) ${y}^2={x}^{3}-{x}^{2}-165{x}-763$
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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.