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Results (10 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
99.3-a5 99.3-a \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 11 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.697318412$ 0.600092679 \( \frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 8 a\) , \( 19 a + 22\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+8a{x}+19a+22$
891.5-c5 891.5-c \(\Q(\sqrt{-2}) \) \( 3^{4} \cdot 11 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.565772804$ 1.600247146 \( \frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 84 a - 6\) , \( -444 a - 593\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(84a-6\right){x}-444a-593$
1584.3-b5 1584.3-b \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 3^{2} \cdot 11 \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $0.345223109$ $0.848659206$ 2.485990333 \( \frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 38 a - 1\) , \( 119 a + 177\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(38a-1\right){x}+119a+177$
3267.4-b5 3267.4-b \(\Q(\sqrt{-2}) \) \( 3^{3} \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.883508368$ $0.295465210$ 1.574051365 \( \frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -291 a - 132\) , \( -3667 a + 2142\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-291a-132\right){x}-3667a+2142$
3267.7-c5 3267.7-c \(\Q(\sqrt{-2}) \) \( 3^{3} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.295465210$ 2.507105449 \( \frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( 168 a + 361\) , \( 2627 a - 4644\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(168a+361\right){x}+2627a-4644$
14256.5-h5 14256.5-h \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 3^{4} \cdot 11 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.415762837$ $0.282886402$ 4.531140880 \( \frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 333 a - 17\) , \( -3865 a - 4056\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(333a-17\right){x}-3865a-4056$
28611.7-c5 28611.7-c \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 11 \cdot 17^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.126723656$ $0.411660182$ 7.871409715 \( \frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) \( \bigl[1\) , \( 0\) , \( a + 1\) , \( 15 a + 221\) , \( -1485 a + 473\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(15a+221\right){x}-1485a+473$
28611.9-c5 28611.9-c \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 11 \cdot 17^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.411660182$ 1.164350825 \( \frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 3 a - 222\) , \( -54 a - 2241\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(3a-222\right){x}-54a-2241$
35937.11-c5 35937.11-c \(\Q(\sqrt{-2}) \) \( 3^{3} \cdot 11^{3} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.201450673$ $0.295465210$ 4.040464655 \( \frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) \( \bigl[a + 1\) , \( -a\) , \( a\) , \( -283 a + 165\) , \( 553 a - 5868\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-283a+165\right){x}+553a-5868$
35937.7-d5 35937.7-d \(\Q(\sqrt{-2}) \) \( 3^{3} \cdot 11^{3} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $2.595855749$ $0.295465210$ 4.338722729 \( \frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) \( \bigl[1\) , \( a\) , \( 1\) , \( 147 a - 380\) , \( -2722 a + 4365\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(147a-380\right){x}-2722a+4365$
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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.