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Results (16 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
147.1-a1 147.1-a \(\Q(\sqrt{3}) \) \( 3 \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.203505108$ 0.939949835 \( -\frac{796905901939896846693217}{21} a + 65727691000542993279720 \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 3395 a - 6664\) , \( 153951 a - 275173\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(3395a-6664\right){x}+153951a-275173$
147.1-a2 147.1-a \(\Q(\sqrt{3}) \) \( 3 \cdot 7^{2} \) $0$ $\Z/4\Z$ $1$ $0.814020435$ 0.939949835 \( -\frac{4354703137}{17294403} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \) ${y}^2+{x}{y}={x}^{3}-34{x}-217$
147.1-a3 147.1-a \(\Q(\sqrt{3}) \) \( 3 \cdot 7^{2} \) $0$ $\Z/4\Z$ $1$ $13.02432697$ 0.939949835 \( \frac{103823}{63} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -56 a + 97\) , \( 0\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-56a+97\right){x}$
147.1-a4 147.1-a \(\Q(\sqrt{3}) \) \( 3 \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $13.02432697$ 0.939949835 \( \frac{7189057}{3969} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \) ${y}^2+{x}{y}={x}^{3}-4{x}-1$
147.1-a5 147.1-a \(\Q(\sqrt{3}) \) \( 3 \cdot 7^{2} \) $0$ $\Z/8\Z$ $1$ $13.02432697$ 0.939949835 \( \frac{6570725617}{45927} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \) ${y}^2+{x}{y}={x}^{3}-39{x}+90$
147.1-a6 147.1-a \(\Q(\sqrt{3}) \) \( 3 \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $3.256081743$ 0.939949835 \( \frac{13027640977}{21609} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \) ${y}^2+{x}{y}={x}^{3}-49{x}-136$
147.1-a7 147.1-a \(\Q(\sqrt{3}) \) \( 3 \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.814020435$ 0.939949835 \( \frac{53297461115137}{147} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \) ${y}^2+{x}{y}={x}^{3}-784{x}-8515$
147.1-a8 147.1-a \(\Q(\sqrt{3}) \) \( 3 \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.203505108$ 0.939949835 \( \frac{796905901939896846693217}{21} a + 65727691000542993279720 \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -3395 a - 6664\) , \( -153951 a - 275173\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-3395a-6664\right){x}-153951a-275173$
147.1-b1 147.1-b \(\Q(\sqrt{3}) \) \( 3 \cdot 7^{2} \) $1$ $\Z/4\Z$ $5.970393669$ $7.303763884$ 1.573508462 \( -\frac{796905901939896846693217}{21} a + 65727691000542993279720 \) \( \bigl[a\) , \( -1\) , \( 0\) , \( 3395 a - 6664\) , \( -153951 a + 275173\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(3395a-6664\right){x}-153951a+275173$
147.1-b2 147.1-b \(\Q(\sqrt{3}) \) \( 3 \cdot 7^{2} \) $1$ $\Z/4\Z$ $0.746299208$ $3.651881942$ 1.573508462 \( -\frac{4354703137}{17294403} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -34\) , \( 217\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-34{x}+217$
147.1-b3 147.1-b \(\Q(\sqrt{3}) \) \( 3 \cdot 7^{2} \) $1$ $\Z/2\Z$ $0.373149604$ $14.60752776$ 1.573508462 \( \frac{103823}{63} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -54 a + 96\) , \( -55 a + 96\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-54a+96\right){x}-55a+96$
147.1-b4 147.1-b \(\Q(\sqrt{3}) \) \( 3 \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.746299208$ $14.60752776$ 1.573508462 \( \frac{7189057}{3969} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -4\) , \( 1\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-4{x}+1$
147.1-b5 147.1-b \(\Q(\sqrt{3}) \) \( 3 \cdot 7^{2} \) $1$ $\Z/2\Z$ $1.492598417$ $3.651881942$ 1.573508462 \( \frac{6570725617}{45927} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -39\) , \( -90\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-39{x}-90$
147.1-b6 147.1-b \(\Q(\sqrt{3}) \) \( 3 \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $1.492598417$ $14.60752776$ 1.573508462 \( \frac{13027640977}{21609} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -49\) , \( 136\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-49{x}+136$
147.1-b7 147.1-b \(\Q(\sqrt{3}) \) \( 3 \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $2.985196834$ $14.60752776$ 1.573508462 \( \frac{53297461115137}{147} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -784\) , \( 8515\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-784{x}+8515$
147.1-b8 147.1-b \(\Q(\sqrt{3}) \) \( 3 \cdot 7^{2} \) $1$ $\Z/4\Z$ $5.970393669$ $7.303763884$ 1.573508462 \( \frac{796905901939896846693217}{21} a + 65727691000542993279720 \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -3395 a - 6664\) , \( 153951 a + 275173\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-3395a-6664\right){x}+153951a+275173$
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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.