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Results (4 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
36.1-a3 36.1-a \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 3^{2} \) $0$ $\Z/2\Z\oplus\Z/10\Z$ $1$ $7.710672559$ 1.069277895 \( \frac{476379541}{236196} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 48 a - 115\) , \( -96 a + 218\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(48a-115\right){x}-96a+218$
108.1-a3 108.1-a \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 3^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $4.010392437$ 1.112282735 \( \frac{476379541}{236196} \) \( \bigl[a\) , \( a\) , \( a\) , \( 82 a - 195\) , \( -239 a + 538\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(82a-195\right){x}-239a+538$
108.2-a3 108.2-a \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 3^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $4.010392437$ 1.112282735 \( \frac{476379541}{236196} \) \( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -79 a - 111\) , \( 46 a + 57\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-79a-111\right){x}+46a+57$
324.1-f3 324.1-f \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 3^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $2.085842366$ 1.157017170 \( \frac{476379541}{236196} \) \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 439 a - 1025\) , \( 2431 a - 5613\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(439a-1025\right){x}+2431a-5613$
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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.