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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
15488.5-a1 15488.5-a \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $0.440423686$ $0.901434118$ 2.400908571 \( \frac{92394174795}{29282} a - \frac{35300221849}{14641} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( 96 a + 151\) , \( -774 a + 1417\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(96a+151\right){x}-774a+1417$
15488.5-a2 15488.5-a \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $0.440423686$ $0.901434118$ 2.400908571 \( -\frac{249748466395}{428717762} a + \frac{259212876761}{214358881} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( -4 a - 49\) , \( -50 a + 145\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-4a-49\right){x}-50a+145$
15488.5-a3 15488.5-a \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.220211843$ $1.802868236$ 2.400908571 \( \frac{67141725}{58564} a + \frac{45045721}{29282} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( 6 a + 11\) , \( -12 a + 21\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(6a+11\right){x}-12a+21$
15488.5-a4 15488.5-a \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $0.440423686$ $3.605736472$ 2.400908571 \( -\frac{36743275}{1936} a + \frac{19854129}{968} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( a + 6\) , \( 3 a - 4\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(a+6\right){x}+3a-4$
15488.5-b1 15488.5-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $2.229437542$ $0.438200788$ 2.953992798 \( \frac{32518499729401}{704} a - \frac{15898155671547}{352} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -1878 a + 1878\) , \( 9281 a - 56527\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1878a+1878\right){x}+9281a-56527$
15488.5-b2 15488.5-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $2.229437542$ $0.876401577$ 2.953992798 \( -\frac{16131562657}{184549376} a + \frac{3800221619}{92274688} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( -14 a - 10\) , \( -85 a - 123\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-14a-10\right){x}-85a-123$
15488.5-b3 15488.5-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.557359385$ $0.876401577$ 2.953992798 \( -\frac{16280859}{937024} a + \frac{747699265}{468512} \) \( \bigl[a\) , \( 0\) , \( a\) , \( 3 a + 59\) , \( -4 a - 58\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(3a+59\right){x}-4a-58$
15488.5-b4 15488.5-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $0.278679692$ $0.876401577$ 2.953992798 \( \frac{34401807041}{1714871048} a + \frac{1602489013229}{857435524} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( -47 a + 21\) , \( 43 a - 81\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-47a+21\right){x}+43a-81$
15488.5-b5 15488.5-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $1.114718771$ $0.876401577$ 2.953992798 \( \frac{78156424101}{495616} a + \frac{16938341377}{247808} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -118 a + 118\) , \( 129 a - 911\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-118a+118\right){x}+129a-911$
15488.5-b6 15488.5-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $1.114718771$ $0.438200788$ 2.953992798 \( -\frac{320710739562017}{1714871048} a + \frac{225827695068387}{857435524} \) \( \bigl[a\) , \( 0\) , \( a\) , \( -37 a + 699\) , \( -5076 a + 1718\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-37a+699\right){x}-5076a+1718$
15488.5-c1 15488.5-c \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.338242877$ 1.022750326 \( \frac{31504873455125}{519691042816} a + \frac{50524809992625}{259845521408} \) \( \bigl[a\) , \( 0\) , \( a\) , \( 146 a - 175\) , \( 566 a - 3334\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(146a-175\right){x}+566a-3334$
15488.5-c2 15488.5-c \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.338242877$ 1.022750326 \( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -19 a + 228\) , \( -129 a - 3075\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-19a+228\right){x}-129a-3075$
15488.5-c3 15488.5-c \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.338242877$ 1.022750326 \( \frac{1133731711875}{959512576} a + \frac{6924008747375}{959512576} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( 437 a - 316\) , \( -3079 a - 1167\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(437a-316\right){x}-3079a-1167$
15488.5-c4 15488.5-c \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.338242877$ 1.022750326 \( -\frac{1133731711875}{959512576} a + \frac{4028870229625}{479756288} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( 92 a + 527\) , \( 3344 a - 3163\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(92a+527\right){x}+3344a-3163$
15488.5-c5 15488.5-c \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.169121438$ 1.022750326 \( \frac{915988506230265125}{54875873536} a + \frac{2123510665930979625}{54875873536} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( 6757 a - 4956\) , \( -216039 a - 63823\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6757a-4956\right){x}-216039a-63823$
15488.5-c6 15488.5-c \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.169121438$ 1.022750326 \( -\frac{915988506230265125}{54875873536} a + \frac{1519749586080622375}{27437936768} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( 1372 a + 8207\) , \( 237584 a - 219739\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(1372a+8207\right){x}+237584a-219739$
15488.5-d1 15488.5-d \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1.033734412$ 1.562859530 \( \frac{46830231}{234256} a + \frac{377324919}{234256} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 6 a + 42\) , \( -33 a + 29\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a+42\right){x}-33a+29$
15488.5-d2 15488.5-d \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1.033734412$ 1.562859530 \( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 33 a - 24\) , \( -7 a + 65\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(33a-24\right){x}-7a+65$
15488.5-d3 15488.5-d \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.516867206$ 1.562859530 \( \frac{56046918875913}{857435524} a + \frac{9320189138181}{214358881} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 293 a - 304\) , \( -2575 a + 881\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(293a-304\right){x}-2575a+881$
15488.5-d4 15488.5-d \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.516867206$ 1.562859530 \( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -4 a + 422\) , \( 2375 a - 1363\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a+422\right){x}+2375a-1363$
15488.5-d5 15488.5-d \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $1.033734412$ 1.562859530 \( \frac{14003310699}{30976} a + \frac{5238465399}{30976} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 105 a - 72\) , \( -469 a - 43\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(105a-72\right){x}-469a-43$
15488.5-d6 15488.5-d \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $1.033734412$ 1.562859530 \( -\frac{14003310699}{30976} a + \frac{9620888049}{15488} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 24 a + 126\) , \( 405 a - 487\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(24a+126\right){x}+405a-487$
15488.5-e1 15488.5-e \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $0.208093150$ $2.443829262$ 6.150771644 \( \frac{150031}{2816} a + \frac{2195619}{1408} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -4 a - 4\) , \( 0\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a-4\right){x}$
15488.5-e2 15488.5-e \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.416186300$ $2.443829262$ 6.150771644 \( -\frac{119091}{1936} a + \frac{1847305}{968} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 5 a - 7\) , \( -3 a + 1\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(5a-7\right){x}-3a+1$
15488.5-e3 15488.5-e \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $0.832372600$ $2.443829262$ 6.150771644 \( \frac{1085152369}{58564} a + \frac{2893170013}{29282} \) \( \bigl[a\) , \( -a\) , \( a\) , \( -7 a - 12\) , \( 22 a + 13\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-7a-12\right){x}+22a+13$
15488.5-e4 15488.5-e \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $0.832372600$ $1.221914631$ 6.150771644 \( -\frac{9255981777}{58564} a + \frac{25074097747}{29282} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 65 a - 87\) , \( -311 a + 177\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(65a-87\right){x}-311a+177$
15488.5-f1 15488.5-f \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $2.418339135$ $1.737958760$ 6.354298938 \( \frac{34643161}{176} a - \frac{7276683}{176} \) \( \bigl[a\) , \( a\) , \( a\) , \( -16 a + 45\) , \( 73 a + 50\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-16a+45\right){x}+73a+50$
15488.5-f2 15488.5-f \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $1.209169567$ $1.737958760$ 6.354298938 \( \frac{704969}{484} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -10 a - 4\) , \( 0\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a-4\right){x}$
15488.5-f3 15488.5-f \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $2.418339135$ $0.868979380$ 6.354298938 \( \frac{59776471}{29282} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 40 a + 16\) , \( 10 a - 124\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(40a+16\right){x}+10a-124$
15488.5-f4 15488.5-f \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/4\Z$ $2.418339135$ $1.737958760$ 6.354298938 \( -\frac{34643161}{176} a + \frac{13683239}{88} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 20 a - 42\) , \( -68 a + 79\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(20a-42\right){x}-68a+79$
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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.