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Results (22 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
3872.14-a1 3872.14-a \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.292255878$ $2.457844850$ 2.171994331 \( \frac{704969}{484} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -6 a + 2\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-6a+2\right){x}$
3872.14-a2 3872.14-a \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $1$ $\Z/2\Z$ $0.146127939$ $1.228922425$ 2.171994331 \( \frac{59776471}{29282} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 24 a - 8\) , \( -18 a - 26\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(24a-8\right){x}-18a-26$
3872.14-a3 3872.14-a \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $1$ $\Z/2\Z$ $0.584511757$ $2.457844850$ 2.171994331 \( -\frac{34643161}{176} a + \frac{13683239}{88} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 3 a - 24\) , \( -22 a + 46\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3a-24\right){x}-22a+46$
3872.14-a4 3872.14-a \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $1$ $\Z/2\Z$ $0.584511757$ $2.457844850$ 2.171994331 \( \frac{34643161}{176} a - \frac{7276683}{176} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -2 a + 22\) , \( 26 a - 14\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-2a+22\right){x}+26a-14$
3872.14-b1 3872.14-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1.461921226$ 2.210217144 \( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 12 a - 20\) , \( 11 a - 9\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(12a-20\right){x}+11a-9$
3872.14-b2 3872.14-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $1.461921226$ 2.210217144 \( \frac{46830231}{234256} a + \frac{377324919}{234256} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 9 a + 13\) , \( 9 a + 13\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(9a+13\right){x}+9a+13$
3872.14-b3 3872.14-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/4\Z$ $1$ $0.730960613$ 2.210217144 \( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 69 a + 153\) , \( 753 a - 1067\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(69a+153\right){x}+753a-1067$
3872.14-b4 3872.14-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.730960613$ 2.210217144 \( \frac{56046918875913}{857435524} a + \frac{9320189138181}{214358881} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 102 a - 210\) , \( -765 a + 847\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(102a-210\right){x}-765a+847$
3872.14-b5 3872.14-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $1.461921226$ 2.210217144 \( -\frac{14003310699}{30976} a + \frac{9620888049}{15488} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 33 a + 37\) , \( 111 a - 245\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(33a+37\right){x}+111a-245$
3872.14-b6 3872.14-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/4\Z$ $1$ $1.461921226$ 2.210217144 \( \frac{14003310699}{30976} a + \frac{5238465399}{30976} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 42 a - 62\) , \( -163 a + 81\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(42a-62\right){x}-163a+81$
3872.14-c1 3872.14-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/4\Z$ $1$ $0.619709498$ 2.810738089 \( -\frac{32518499729401}{704} a + \frac{722188386307}{704} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -471 a - 938\) , \( -9387 a - 9491\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-471a-938\right){x}-9387a-9491$
3872.14-c2 3872.14-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/4\Z$ $1$ $1.239418997$ 2.810738089 \( \frac{16131562657}{184549376} a - \frac{8531119419}{184549376} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -11 a + 6\) , \( 5 a - 73\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-11a+6\right){x}+5a-73$
3872.14-c3 3872.14-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1.239418997$ 2.810738089 \( \frac{16280859}{937024} a + \frac{1479117671}{937024} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 17 a - 31\) , \( -13 a - 33\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(17a-31\right){x}-13a-33$
3872.14-c4 3872.14-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $1.239418997$ 2.810738089 \( -\frac{34401807041}{1714871048} a + \frac{3239379833499}{1714871048} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -18 a - 12\) , \( -36 a + 19\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-18a-12\right){x}-36a+19$
3872.14-c5 3872.14-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $1.239418997$ 2.810738089 \( -\frac{78156424101}{495616} a + \frac{112033106855}{495616} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -31 a - 58\) , \( -147 a - 163\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-31a-58\right){x}-147a-163$
3872.14-c6 3872.14-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.619709498$ 2.810738089 \( \frac{320710739562017}{1714871048} a + \frac{130944650574757}{1714871048} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 157 a - 351\) , \( 1387 a - 2265\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(157a-351\right){x}+1387a-2265$
3872.14-d1 3872.14-d \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/4\Z$ $1$ $0.478347664$ 2.892774765 \( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 30 a + 86\) , \( -500 a - 580\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(30a+86\right){x}-500a-580$
3872.14-d2 3872.14-d \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.478347664$ 2.892774765 \( \frac{31504873455125}{519691042816} a + \frac{50524809992625}{259845521408} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 46 a - 113\) , \( -353 a - 833\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(46a-113\right){x}-353a-833$
3872.14-d3 3872.14-d \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.478347664$ 2.892774765 \( -\frac{1133731711875}{959512576} a + \frac{4028870229625}{479756288} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 138 a + 159\) , \( 623 a - 1831\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(138a+159\right){x}+623a-1831$
3872.14-d4 3872.14-d \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $0.478347664$ 2.892774765 \( \frac{1133731711875}{959512576} a + \frac{6924008747375}{959512576} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 178 a - 265\) , \( -1275 a + 703\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(178a-265\right){x}-1275a+703$
3872.14-d5 3872.14-d \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.239173832$ 2.892774765 \( -\frac{915988506230265125}{54875873536} a + \frac{1519749586080622375}{27437936768} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 2138 a + 2479\) , \( 46031 a - 123975\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2138a+2479\right){x}+46031a-123975$
3872.14-d6 3872.14-d \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/4\Z$ $1$ $0.239173832$ 2.892774765 \( \frac{915988506230265125}{54875873536} a + \frac{2123510665930979625}{54875873536} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 2738 a - 4105\) , \( -87547 a + 61119\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2738a-4105\right){x}-87547a+61119$
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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.