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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
200.1-a1 200.1-a \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 5^{2} \) $0$ $\Z/4\Z$ $1$ $4.406960782$ 1.272179997 \( \frac{237276}{625} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 13 a + 25\) , \( -52 a - 91\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(13a+25\right){x}-52a-91$
200.1-b1 200.1-b \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 5^{2} \) $1$ $\Z/4\Z$ $0.683761292$ $8.151961419$ 1.609073952 \( \frac{237276}{625} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 12 a + 23\) , \( 75 a + 129\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(12a+23\right){x}+75a+129$
3600.1-c1 3600.1-c \(\Q(\sqrt{3}) \) \( 2^{4} \cdot 3^{2} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $3.460509320$ 1.997925987 \( \frac{237276}{625} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -a + 10\) , \( -8 a - 1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+10\right){x}-8a-1$
3600.1-k1 3600.1-k \(\Q(\sqrt{3}) \) \( 2^{4} \cdot 3^{2} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $3.460509320$ 1.997925987 \( \frac{237276}{625} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 12\) , \( 18 a\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+12{x}+18a$
5000.1-e1 5000.1-e \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 5^{4} \) $0$ $\Z/2\Z$ $1$ $0.881392156$ 2.035487995 \( \frac{237276}{625} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -326 a + 569\) , \( 8253 a - 14301\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-326a+569\right){x}+8253a-14301$
5000.1-f1 5000.1-f \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 5^{4} \) $1$ $\Z/2\Z$ $0.933393502$ $1.630392283$ 3.514440935 \( \frac{237276}{625} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -325 a + 571\) , \( -7684 a + 13325\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-325a+571\right){x}-7684a+13325$
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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.