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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-a1 36.1-a \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 3^{2} \) $0$ $\Z/2\Z$ $1$ $0.308426902$ 1.069277895 \( -\frac{4395631034341}{3145728} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 1023 a - 2390\) , \( 24243 a - 55924\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(1023a-2390\right){x}+24243a-55924$
36.1-a2 36.1-a \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 3^{2} \) $0$ $\Z/10\Z$ $1$ $7.710672559$ 1.069277895 \( \frac{5735339}{3888} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -12 a + 25\) , \( -12 a + 26\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-12a+25\right){x}-12a+26$
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 \( \frac{476379541}{236196} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 48 a - 115\) , \( -96 a + 218\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(48a-115\right){x}-96a+218$
36.1-a4 36.1-a \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 3^{2} \) $0$ $\Z/10\Z$ $1$ $3.855336279$ 1.069277895 \( -\frac{1025795879759761}{3486784401} a + \frac{5304841542920801}{6973568802} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -420 a - 565\) , \( -6327 a - 8227\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-420a-565\right){x}-6327a-8227$
36.1-a5 36.1-a \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 3^{2} \) $0$ $\Z/10\Z$ $1$ $3.855336279$ 1.069277895 \( \frac{1025795879759761}{3486784401} a + \frac{1084416594467093}{2324522934} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 418 a - 985\) , \( 6326 a - 14554\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(418a-985\right){x}+6326a-14554$
36.1-a6 36.1-a \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 3^{2} \) $0$ $\Z/2\Z$ $1$ $0.154213451$ 1.069277895 \( -\frac{1373276865151726904870180471}{1296} a + \frac{2108232339288241560240379517}{864} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -14305 a - 26645\) , \( -1473236 a - 2202528\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-14305a-26645\right){x}-1473236a-2202528$
36.1-a7 36.1-a \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 3^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.308426902$ 1.069277895 \( \frac{18013780041269221}{9216} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 16383 a - 38230\) , \( 1551027 a - 3576436\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(16383a-38230\right){x}+1551027a-3576436$
36.1-a8 36.1-a \(\Q(\sqrt{13}) \) \( 2^{2} \cdot 3^{2} \) $0$ $\Z/2\Z$ $1$ $0.154213451$ 1.069277895 \( \frac{1373276865151726904870180471}{1296} a + \frac{3578143287561270870980777609}{2592} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 14303 a - 40950\) , \( 1473235 a - 3675764\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(14303a-40950\right){x}+1473235a-3675764$
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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.