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Results (8 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
72.1-a2 72.1-a \(\Q(\sqrt{2}) \) \( 2^{3} \cdot 3^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2.325279868$ 0.822110581 \( \frac{207646}{6561} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 3\) , \( -23\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+3{x}-23$
144.1-b2 144.1-b \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 3^{2} \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $5.683508517$ 1.004711853 \( \frac{207646}{6561} \) \( \bigl[a\) , \( 0\) , \( a\) , \( 3\) , \( 22\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+3{x}+22$
648.1-a2 648.1-a \(\Q(\sqrt{2}) \) \( 2^{3} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.894502839$ 1.339615804 \( \frac{207646}{6561} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 35\) , \( 607\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+35{x}+607$
1296.1-b2 1296.1-b \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 3^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.079273864$ $0.775093289$ 2.366086572 \( \frac{207646}{6561} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( 36\) , \( -572\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+36{x}-572$
2304.1-c2 2304.1-c \(\Q(\sqrt{2}) \) \( 2^{8} \cdot 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.141888207$ $1.817673508$ 2.752945917 \( \frac{207646}{6561} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 32 a + 48\) , \( 900 a + 1260\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(32a+48\right){x}+900a+1260$
2304.1-s2 2304.1-s \(\Q(\sqrt{2}) \) \( 2^{8} \cdot 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.141888207$ $1.817673508$ 2.752945917 \( \frac{207646}{6561} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 32 a + 48\) , \( -900 a - 1260\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(32a+48\right){x}-900a-1260$
3528.2-d2 3528.2-d \(\Q(\sqrt{2}) \) \( 2^{3} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.578217810$ $1.374032019$ 3.066752947 \( \frac{207646}{6561} \) \( \bigl[a\) , \( -a\) , \( a\) , \( -16 a + 35\) , \( -495 a + 562\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-16a+35\right){x}-495a+562$
3528.3-d2 3528.3-d \(\Q(\sqrt{2}) \) \( 2^{3} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.578217810$ $1.374032019$ 3.066752947 \( \frac{207646}{6561} \) \( \bigl[a\) , \( a\) , \( a\) , \( 16 a + 35\) , \( 495 a + 562\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(16a+35\right){x}+495a+562$
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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.