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Results (4 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
134199.7-a1 134199.7-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 13 \cdot 31 \cdot 37 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.181400004$ $1.743707208$ 2.378701242 \( \frac{3074077600}{581529} a - \frac{339172305263}{581529} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( -55 a + 26\) , \( 91 a - 120\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-55a+26\right){x}+91a-120$
134199.7-a2 134199.7-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 13 \cdot 31 \cdot 37 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.181400004$ $0.435926802$ 2.378701242 \( \frac{38041716070089006}{935643136987} a - \frac{750025198610512667}{8420788232883} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( -385 a + 626\) , \( 3265 a + 2700\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-385a+626\right){x}+3265a+2700$
134199.7-a3 134199.7-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 13 \cdot 31 \cdot 37 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.590700002$ $0.871853604$ 2.378701242 \( -\frac{21975427845360}{37575108649} a + \frac{112219616857967}{112725325947} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( -55 a + 41\) , \( 166 a - 96\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-55a+41\right){x}+166a-96$
134199.7-a4 134199.7-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 13 \cdot 31 \cdot 37 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.295350001$ $0.435926802$ 2.378701242 \( \frac{1669618709134603634}{877529309726667} a + \frac{1751461029196170083}{877529309726667} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( 275 a - 304\) , \( 1627 a - 1416\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(275a-304\right){x}+1627a-1416$
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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.