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Results (12 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
128.1-a2 128.1-a \(\Q(\sqrt{3}) \) \( 2^{7} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $11.09117728$ 1.600873547 \( 249872 a + 434912 \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -6 a - 9\) , \( -11 a - 19\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a-9\right){x}-11a-19$
128.1-d2 128.1-d \(\Q(\sqrt{3}) \) \( 2^{7} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.071050112$ $27.22522842$ 1.116800688 \( 249872 a + 434912 \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -6 a - 9\) , \( 11 a + 19\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a-9\right){x}+11a+19$
256.1-a2 256.1-a \(\Q(\sqrt{3}) \) \( 2^{8} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $27.22522842$ 1.964811619 \( 249872 a + 434912 \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 4 a - 8\) , \( -4 a + 8\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(4a-8\right){x}-4a+8$
256.1-b2 256.1-b \(\Q(\sqrt{3}) \) \( 2^{8} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $11.09117728$ 0.800436773 \( 249872 a + 434912 \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 4 a - 8\) , \( 4 a - 8\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(4a-8\right){x}+4a-8$
1024.1-a2 1024.1-a \(\Q(\sqrt{3}) \) \( 2^{10} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $17.06626753$ 2.463303538 \( 249872 a + 434912 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -8\) , \( 8 a + 8\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-8{x}+8a+8$
1024.1-b2 1024.1-b \(\Q(\sqrt{3}) \) \( 2^{10} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.690609244$ $8.846686439$ 3.527381188 \( 249872 a + 434912 \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -42 a - 73\) , \( -182 a - 315\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-42a-73\right){x}-182a-315$
1024.1-s2 1024.1-s \(\Q(\sqrt{3}) \) \( 2^{10} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $8.846686439$ 1.276909199 \( 249872 a + 434912 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -8\) , \( -8 a - 8\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}-8{x}-8a-8$
1024.1-t2 1024.1-t \(\Q(\sqrt{3}) \) \( 2^{10} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.199813625$ $17.06626753$ 1.968806443 \( 249872 a + 434912 \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -42 a - 73\) , \( 182 a + 315\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-42a-73\right){x}+182a+315$
1152.1-h2 1152.1-h \(\Q(\sqrt{3}) \) \( 2^{7} \cdot 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.172565561$ $13.93454908$ 2.776619808 \( 249872 a + 434912 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 12 a - 24\) , \( 24 a - 36\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(12a-24\right){x}+24a-36$
1152.1-j2 1152.1-j \(\Q(\sqrt{3}) \) \( 2^{7} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.223289230$ 2.085183990 \( 249872 a + 434912 \) \( \bigl[0\) , \( a\) , \( 0\) , \( 12 a - 24\) , \( -24 a + 36\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(12a-24\right){x}-24a+36$
2304.1-bc2 2304.1-bc \(\Q(\sqrt{3}) \) \( 2^{8} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.223289230$ 1.042591995 \( 249872 a + 434912 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -16 a - 30\) , \( -40 a - 70\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-16a-30\right){x}-40a-70$
2304.1-bf2 2304.1-bf \(\Q(\sqrt{3}) \) \( 2^{8} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $13.93454908$ 2.011278916 \( 249872 a + 434912 \) \( \bigl[0\) , \( a\) , \( 0\) , \( -16 a - 30\) , \( 40 a + 70\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-16a-30\right){x}+40a+70$
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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.