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Results (6 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
33.2-b5 33.2-b \(\Q(\sqrt{3}) \) \( 3 \cdot 11 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $15.45625621$ 1.115459211 \( \frac{1324878680}{363} a + \frac{2299866043}{363} \) \( \bigl[1\) , \( a\) , \( 0\) , \( -4\) , \( -4 a - 1\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}-4{x}-4a-1$
33.2-c5 33.2-c \(\Q(\sqrt{3}) \) \( 3 \cdot 11 \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $26.61641567$ 0.480218586 \( \frac{1324878680}{363} a + \frac{2299866043}{363} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -4\) , \( 4 a + 1\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}-4{x}+4a+1$
1089.2-e5 1089.2-e \(\Q(\sqrt{3}) \) \( 3^{2} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.633323250$ 1.337525213 \( \frac{1324878680}{363} a + \frac{2299866043}{363} \) \( \bigl[a\) , \( -a\) , \( a + 1\) , \( -384 a - 684\) , \( 5634 a + 9709\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-384a-684\right){x}+5634a+9709$
1089.2-i5 1089.2-i \(\Q(\sqrt{3}) \) \( 3^{2} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.690588852$ 0.776706099 \( \frac{1324878680}{363} a + \frac{2299866043}{363} \) \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -384 a - 683\) , \( -5635 a - 9711\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-384a-683\right){x}-5635a-9711$
1584.1-b5 1584.1-b \(\Q(\sqrt{3}) \) \( 2^{4} \cdot 3^{2} \cdot 11 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.952045376$ 1.704364192 \( \frac{1324878680}{363} a + \frac{2299866043}{363} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -2 a - 60\) , \( -22 a - 176\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-2a-60\right){x}-22a-176$
1584.1-o5 1584.1-o \(\Q(\sqrt{3}) \) \( 2^{4} \cdot 3^{2} \cdot 11 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.220630836$ $11.61313845$ 2.958592720 \( \frac{1324878680}{363} a + \frac{2299866043}{363} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -2 a - 60\) , \( 22 a + 176\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a-60\right){x}+22a+176$
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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.