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Results (7 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
3249.1-a1 3249.1-a \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 19^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.085998375$ 1.216200686 \( -\frac{9358714467168256}{22284891} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -4390\) , \( -113432\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}-4390{x}-113432$
3249.1-a2 3249.1-a \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 19^{2} \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $2.149959381$ 1.216200686 \( \frac{841232384}{1121931} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( 20\) , \( -32\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+20{x}-32$
3249.1-b1 3249.1-b \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 19^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.711524088$ 1.665775316 \( \frac{67419143}{390963} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 8\) , \( 29\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+8{x}+29$
3249.1-b2 3249.1-b \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 19^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $18.84609635$ 1.665775316 \( \frac{389017}{57} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-2{x}-1$
3249.1-b3 3249.1-b \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 19^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $18.84609635$ 1.665775316 \( \frac{30664297}{3249} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -7\) , \( 5\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-7{x}+5$
3249.1-b4 3249.1-b \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 19^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $18.84609635$ 1.665775316 \( \frac{115714886617}{1539} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -102\) , \( 385\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-102{x}+385$
3249.1-c1 3249.1-c \(\Q(\sqrt{2}) \) \( 3^{2} \cdot 19^{2} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.020501072$ $30.86363048$ 1.789652000 \( -\frac{1404928}{171} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -2\) , \( 2\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}-2{x}+2$
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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.