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Results (24 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
3584.7-a1 3584.7-a \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.691848366$ 1.045976412 \( \frac{4096655365}{28} a - \frac{2878658051}{14} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -468 a + 384\) , \( -2140 a + 7060\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-468a+384\right){x}-2140a+7060$
3584.7-a2 3584.7-a \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $1.383696732$ 1.045976412 \( -\frac{13647889}{14} a - \frac{40536829}{7} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 55 a - 105\) , \( 282 a - 254\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(55a-105\right){x}+282a-254$
3584.7-a3 3584.7-a \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.383696732$ 1.045976412 \( -\frac{1145925}{112} a - \frac{72257}{56} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -28 a + 24\) , \( -44 a + 132\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-28a+24\right){x}-44a+132$
3584.7-a4 3584.7-a \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.383696732$ 1.045976412 \( -\frac{138325}{1792} a - \frac{317937}{896} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 11 a - 10\) , \( 33 a + 6\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(11a-10\right){x}+33a+6$
3584.7-a5 3584.7-a \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.691848366$ 1.045976412 \( -\frac{5786513}{4802} a + \frac{263001}{343} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -5 a - 90\) , \( 99 a - 466\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-5a-90\right){x}+99a-466$
3584.7-a6 3584.7-a \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.383696732$ 1.045976412 \( \frac{361845}{196} a - \frac{43727}{98} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 15 a + 10\) , \( 3 a - 50\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(15a+10\right){x}+3a-50$
3584.7-b1 3584.7-b \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.261235310$ 1.709333224 \( -\frac{4}{7} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 0\) , \( 4 a - 12\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+4a-12$
3584.7-b2 3584.7-b \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.261235310$ 1.709333224 \( -\frac{59930}{7} a + \frac{346862}{7} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 14 a - 3\) , \( -13 a - 14\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(14a-3\right){x}-13a-14$
3584.7-b3 3584.7-b \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2.261235310$ 1.709333224 \( \frac{59930}{7} a + \frac{286932}{7} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 2 a + 17\) , \( 29 a - 18\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(2a+17\right){x}+29a-18$
3584.7-b4 3584.7-b \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.130617655$ 1.709333224 \( \frac{3543122}{49} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 40 a + 40\) , \( 84 a - 252\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(40a+40\right){x}+84a-252$
3584.7-c1 3584.7-c \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.611837523$ $1.538008342$ 2.845350462 \( \frac{91484}{49} a - \frac{488028}{49} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 20 a - 24\) , \( -44 a + 4\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(20a-24\right){x}-44a+4$
3584.7-c2 3584.7-c \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.611837523$ $6.152033368$ 2.845350462 \( -\frac{21696}{7} a - \frac{9088}{7} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+{x}$
3584.7-c3 3584.7-c \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.305918761$ $3.076016684$ 2.845350462 \( \frac{3408}{7} a - 1360 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4\) , \( -4 a - 4\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}-4{x}-4a-4$
3584.7-c4 3584.7-c \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.611837523$ $1.538008342$ 2.845350462 \( -\frac{12673028}{7} a + \frac{25007348}{7} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -20 a - 64\) , \( -140 a - 188\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-20a-64\right){x}-140a-188$
3584.7-d1 3584.7-d \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.347763164$ 2.037626376 \( \frac{39051258}{7} a - \frac{25340662}{7} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 86 a - 43\) , \( -261 a - 150\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(86a-43\right){x}-261a-150$
3584.7-d2 3584.7-d \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.695526328$ 2.037626376 \( -\frac{24238}{49} a + \frac{44442}{49} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( a - 6\) , \( -6 a + 4\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(a-6\right){x}-6a+4$
3584.7-d3 3584.7-d \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.695526328$ 2.037626376 \( \frac{10452}{7} a + \frac{13028}{7} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 6 a - 3\) , \( -5 a + 2\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(6a-3\right){x}-5a+2$
3584.7-d4 3584.7-d \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.695526328$ 2.037626376 \( -\frac{88712}{7} a + \frac{116960}{7} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 4 a - 12\) , \( -4 a + 12\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(4a-12\right){x}-4a+12$
3584.7-e1 3584.7-e \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.839949937$ 2.146800363 \( \frac{432}{7} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -a - 1\) , \( -2 a + 6\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}-2a+6$
3584.7-e2 3584.7-e \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.709987484$ 2.146800363 \( \frac{11090466}{2401} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 59 a + 59\) , \( 138 a - 414\bigr] \) ${y}^2={x}^{3}+\left(59a+59\right){x}+138a-414$
3584.7-e3 3584.7-e \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.419974968$ 2.146800363 \( \frac{740772}{49} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 19 a + 19\) , \( -30 a + 90\bigr] \) ${y}^2={x}^{3}+\left(19a+19\right){x}-30a+90$
3584.7-e4 3584.7-e \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.839949937$ 2.146800363 \( -\frac{516132}{7} a + \frac{464076}{7} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -a - 13\) , \( 2 a + 18\bigr] \) ${y}^2={x}^{3}+\left(-a-13\right){x}+2a+18$
3584.7-e5 3584.7-e \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.839949937$ 2.146800363 \( \frac{516132}{7} a - \frac{52056}{7} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -10 a + 2\) , \( -13 a + 15\bigr] \) ${y}^2={x}^{3}+\left(-10a+2\right){x}-13a+15$
3584.7-e6 3584.7-e \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.709987484$ 2.146800363 \( \frac{1443468546}{7} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 299 a + 299\) , \( -1990 a + 5970\bigr] \) ${y}^2={x}^{3}+\left(299a+299\right){x}-1990a+5970$
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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.