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Results (5 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
9.1-a5 9.1-a \(\Q(\sqrt{13}) \) \( 3^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $27.39950531$ 0.474953467 \( -\frac{1567304375}{729} a + \frac{1203684625}{243} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -5\) , \( -3 a - 1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}-5{x}-3a-1$
27.1-a5 27.1-a \(\Q(\sqrt{13}) \) \( 3^{3} \) 0 $\Z/2\Z\oplus\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $18.79661701$ 0.868873929 \( -\frac{1567304375}{729} a + \frac{1203684625}{243} \) \( \bigl[a\) , \( 0\) , \( a\) , \( -4 a - 15\) , \( a + 10\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-4a-15\right){x}+a+10$
27.2-a5 27.2-a \(\Q(\sqrt{13}) \) \( 3^{3} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.265539006$ 0.868873929 \( -\frac{1567304375}{729} a + \frac{1203684625}{243} \) \( \bigl[1\) , \( -a\) , \( 1\) , \( 6 a - 20\) , \( 20 a - 46\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(6a-20\right){x}+20a-46$
81.1-a5 81.1-a \(\Q(\sqrt{13}) \) \( 3^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.298286986$ 1.192130317 \( -\frac{1567304375}{729} a + \frac{1203684625}{243} \) \( \bigl[a + 1\) , \( -1\) , \( a\) , \( 2 a - 45\) , \( 39 a - 61\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(2a-45\right){x}+39a-61$
1521.1-h5 1521.1-h \(\Q(\sqrt{13}) \) \( 3^{2} \cdot 13^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.576390951$ 0.991912381 \( -\frac{1567304375}{729} a + \frac{1203684625}{243} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -163 a - 218\) , \( 828 a + 1070\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-163a-218\right){x}+828a+1070$
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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.