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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
1.1-a1 1.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 1 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.925503519$ 0.283435452 \( -4572291148814851641920 a^{3} + 10462525154672292268320 a^{2} + 3492919624948937785472 a - 7992658002021083838208 \) \( \bigl[\frac{1}{2} a^{3} - a\) , \( -a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( \frac{85}{2} a^{3} + \frac{51}{2} a^{2} - 284 a - 304\) , \( \frac{951}{2} a^{3} + \frac{589}{2} a^{2} - 2911 a - 2650\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(\frac{85}{2}a^{3}+\frac{51}{2}a^{2}-284a-304\right){x}+\frac{951}{2}a^{3}+\frac{589}{2}a^{2}-2911a-2650$
1.1-a2 1.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 1 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.925503519$ 0.283435452 \( 4572291148814851641920 a^{3} + 10462525154672292268320 a^{2} - 3492919624948937785472 a - 7992658002021083838208 \) \( \bigl[\frac{1}{2} a^{3} - a\) , \( a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( -43 a^{3} + \frac{51}{2} a^{2} + 284 a - 304\) , \( -\frac{951}{2} a^{3} + \frac{589}{2} a^{2} + 2910 a - 2650\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-43a^{3}+\frac{51}{2}a^{2}+284a-304\right){x}-\frac{951}{2}a^{3}+\frac{589}{2}a^{2}+2910a-2650$
1.1-a3 1.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 1 \) 0 $\Z/14\Z$ $\mathrm{SU}(2)$ $1$ $2222.133950$ 0.283435452 \( 820352 a^{3} - 717600 a^{2} - 4294784 a + 3756992 \) \( \bigl[\frac{1}{2} a^{3} - a\) , \( \frac{1}{2} a^{3} - 2 a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a\) , \( \frac{1}{2} a^{2} + a - 1\) , \( 0\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-2a\right){x}^{2}+\left(\frac{1}{2}a^{2}+a-1\right){x}$
1.1-a4 1.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 1 \) 0 $\Z/14\Z$ $\mathrm{SU}(2)$ $1$ $2222.133950$ 0.283435452 \( -820352 a^{3} - 717600 a^{2} + 4294784 a + 3756992 \) \( \bigl[\frac{1}{2} a^{3} - a\) , \( -\frac{1}{2} a^{3} + 2 a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a\) , \( -a^{3} + \frac{1}{2} a^{2} - 1\) , \( -a^{3} + a\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a\right){x}^{2}+\left(-a^{3}+\frac{1}{2}a^{2}-1\right){x}-a^{3}+a$
1.1-a5 1.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 1 \) 0 $\Z/14\Z$ $\mathrm{SU}(2)$ $1$ $2222.133950$ 0.283435452 \( 313664 a^{3} + 717600 a^{2} - 241280 a - 548608 \) \( \bigl[a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( \frac{1}{2} a^{2} + a - 1\) , \( \frac{1}{2} a^{3} - a^{2} + 1\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} + 1\bigr] \) ${y}^2+a{x}{y}+\left(\frac{1}{2}a^{2}+a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){x}^{2}+\left(\frac{1}{2}a^{3}-a^{2}+1\right){x}+\frac{1}{2}a^{3}-\frac{3}{2}a^{2}+1$
1.1-a6 1.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 1 \) 0 $\Z/14\Z$ $\mathrm{SU}(2)$ $1$ $2222.133950$ 0.283435452 \( -313664 a^{3} + 717600 a^{2} + 241280 a - 548608 \) \( \bigl[a\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a - 1\) , \( \frac{1}{2} a^{2} + a - 1\) , \( -a^{3} - a^{2} + a + 1\) , \( -a^{3} - \frac{3}{2} a^{2} + a + 1\bigr] \) ${y}^2+a{x}{y}+\left(\frac{1}{2}a^{2}+a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+2a-1\right){x}^{2}+\left(-a^{3}-a^{2}+a+1\right){x}-a^{3}-\frac{3}{2}a^{2}+a+1$
1.1-a7 1.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 1 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.925503519$ 0.283435452 \( 11970413633970086033024 a^{3} - 10462525154672292268320 a^{2} - 62677899506190812914304 a + 54782492926012669771712 \) \( \bigl[a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a\) , \( \frac{1}{2} a^{2} + a\) , \( \frac{25}{2} a^{3} - 25 a^{2} - 164 a - 151\) , \( -28 a^{3} - 421 a^{2} - 984 a - 681\bigr] \) ${y}^2+a{x}{y}+\left(\frac{1}{2}a^{2}+a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a\right){x}^{2}+\left(\frac{25}{2}a^{3}-25a^{2}-164a-151\right){x}-28a^{3}-421a^{2}-984a-681$
1.1-a8 1.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 1 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.925503519$ 0.283435452 \( -11970413633970086033024 a^{3} - 10462525154672292268320 a^{2} + 62677899506190812914304 a + 54782492926012669771712 \) \( \bigl[a\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a\) , \( \frac{1}{2} a^{2} + a\) , \( -13 a^{3} - 25 a^{2} + 164 a - 151\) , \( \frac{55}{2} a^{3} - 421 a^{2} + 984 a - 681\bigr] \) ${y}^2+a{x}{y}+\left(\frac{1}{2}a^{2}+a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+3a\right){x}^{2}+\left(-13a^{3}-25a^{2}+164a-151\right){x}+\frac{55}{2}a^{3}-421a^{2}+984a-681$
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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.