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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
15488.20-a1 15488.20-a \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $0.440423686$ $0.901434118$ 2.400908571 \( \frac{249748466395}{428717762} a + \frac{268677287127}{428717762} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 4 a - 53\) , \( 50 a + 95\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(4a-53\right){x}+50a+95$
15488.20-a2 15488.20-a \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $0.440423686$ $3.605736472$ 2.400908571 \( \frac{36743275}{1936} a + \frac{2964983}{1936} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -a + 7\) , \( -3 a - 1\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-a+7\right){x}-3a-1$
15488.20-a3 15488.20-a \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.220211843$ $1.802868236$ 2.400908571 \( -\frac{67141725}{58564} a + \frac{157233167}{58564} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -6 a + 17\) , \( 12 a + 9\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-6a+17\right){x}+12a+9$
15488.20-a4 15488.20-a \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $0.440423686$ $0.901434118$ 2.400908571 \( -\frac{92394174795}{29282} a + \frac{21793731097}{29282} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -96 a + 247\) , \( 774 a + 643\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-96a+247\right){x}+774a+643$
15488.20-b1 15488.20-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $2.229437542$ $0.876401577$ 2.953992798 \( \frac{16131562657}{184549376} a - \frac{8531119419}{184549376} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 14 a - 26\) , \( 60 a - 212\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(14a-26\right){x}+60a-212$
15488.20-b2 15488.20-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.557359385$ $0.876401577$ 2.953992798 \( \frac{16280859}{937024} a + \frac{1479117671}{937024} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -5 a + 62\) , \( 3 a - 62\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-5a+62\right){x}+3a-62$
15488.20-b3 15488.20-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $0.278679692$ $0.876401577$ 2.953992798 \( -\frac{34401807041}{1714871048} a + \frac{3239379833499}{1714871048} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 47 a - 26\) , \( -43 a - 38\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(47a-26\right){x}-43a-38$
15488.20-b4 15488.20-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $1.114718771$ $0.438200788$ 2.953992798 \( \frac{320710739562017}{1714871048} a + \frac{130944650574757}{1714871048} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 35 a + 662\) , \( 5075 a - 3358\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(35a+662\right){x}+5075a-3358$
15488.20-b5 15488.20-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $1.114718771$ $0.876401577$ 2.953992798 \( -\frac{78156424101}{495616} a + \frac{112033106855}{495616} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 116 a\) , \( -130 a - 782\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+116a{x}-130a-782$
15488.20-b6 15488.20-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $2.229437542$ $0.438200788$ 2.953992798 \( -\frac{32518499729401}{704} a + \frac{722188386307}{704} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 1876 a\) , \( -9282 a - 47246\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+1876a{x}-9282a-47246$
15488.20-c1 15488.20-c \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.338242877$ 1.022750326 \( \frac{31504873455125}{519691042816} a + \frac{50524809992625}{259845521408} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 17 a + 209\) , \( 128 a - 3204\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(17a+209\right){x}+128a-3204$
15488.20-c2 15488.20-c \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.338242877$ 1.022750326 \( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -148 a - 29\) , \( -567 a - 2768\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-148a-29\right){x}-567a-2768$
15488.20-c3 15488.20-c \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.338242877$ 1.022750326 \( \frac{1133731711875}{959512576} a + \frac{6924008747375}{959512576} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -92 a + 619\) , \( -3344 a + 181\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-92a+619\right){x}-3344a+181$
15488.20-c4 15488.20-c \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.338242877$ 1.022750326 \( -\frac{1133731711875}{959512576} a + \frac{4028870229625}{479756288} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -437 a + 119\) , \( 3199 a - 3493\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-437a+119\right){x}+3199a-3493$
15488.20-c5 15488.20-c \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.169121438$ 1.022750326 \( \frac{915988506230265125}{54875873536} a + \frac{2123510665930979625}{54875873536} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -1372 a + 9579\) , \( -237584 a + 17845\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-1372a+9579\right){x}-237584a+17845$
15488.20-c6 15488.20-c \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.169121438$ 1.022750326 \( -\frac{915988506230265125}{54875873536} a + \frac{1519749586080622375}{27437936768} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -6757 a + 1799\) , \( 217839 a - 268149\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6757a+1799\right){x}+217839a-268149$
15488.20-d1 15488.20-d \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1.033734412$ 1.562859530 \( \frac{46830231}{234256} a + \frac{377324919}{234256} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -32 a + 7\) , \( -26 a + 65\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-32a+7\right){x}-26a+65$
15488.20-d2 15488.20-d \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1.033734412$ 1.562859530 \( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -5 a + 46\) , \( 27 a + 42\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-5a+46\right){x}+27a+42$
15488.20-d3 15488.20-d \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.516867206$ 1.562859530 \( \frac{56046918875913}{857435524} a + \frac{9320189138181}{214358881} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 5 a + 416\) , \( -2371 a + 1428\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(5a+416\right){x}-2371a+1428$
15488.20-d4 15488.20-d \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.516867206$ 1.562859530 \( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -292 a - 13\) , \( 2282 a - 1707\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-292a-13\right){x}+2282a-1707$
15488.20-d5 15488.20-d \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $1.033734412$ 1.562859530 \( \frac{14003310699}{30976} a + \frac{5238465399}{30976} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -23 a + 148\) , \( -429 a + 66\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-23a+148\right){x}-429a+66$
15488.20-d6 15488.20-d \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $1.033734412$ 1.562859530 \( -\frac{14003310699}{30976} a + \frac{9620888049}{15488} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -104 a + 31\) , \( 364 a - 481\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-104a+31\right){x}+364a-481$
15488.20-e1 15488.20-e \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $0.208093150$ $2.443829262$ 6.150771644 \( -\frac{150031}{2816} a + \frac{4541269}{2816} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 4 a - 8\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(4a-8\right){x}$
15488.20-e2 15488.20-e \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.416186300$ $2.443829262$ 6.150771644 \( \frac{119091}{1936} a + \frac{3575519}{1936} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -5 a - 2\) , \( 3 a - 2\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-5a-2\right){x}+3a-2$
15488.20-e3 15488.20-e \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $0.832372600$ $2.443829262$ 6.150771644 \( -\frac{1085152369}{58564} a + \frac{6871492395}{58564} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 5 a - 19\) , \( -23 a + 35\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(5a-19\right){x}-23a+35$
15488.20-e4 15488.20-e \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $0.832372600$ $1.221914631$ 6.150771644 \( \frac{9255981777}{58564} a + \frac{40892213717}{58564} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -65 a - 22\) , \( 311 a - 134\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-65a-22\right){x}+311a-134$
15488.20-f1 15488.20-f \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/4\Z$ $2.418339135$ $1.737958760$ 6.354298938 \( \frac{34643161}{176} a - \frac{7276683}{176} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -22 a - 22\) , \( 67 a + 11\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-22a-22\right){x}+67a+11$
15488.20-f2 15488.20-f \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $1.209169567$ $1.737958760$ 6.354298938 \( \frac{704969}{484} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 10 a - 15\) , \( -4 a - 19\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(10a-15\right){x}-4a-19$
15488.20-f3 15488.20-f \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $2.418339135$ $0.868979380$ 6.354298938 \( \frac{59776471}{29282} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -40 a + 55\) , \( 6 a - 33\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-40a+55\right){x}+6a-33$
15488.20-f4 15488.20-f \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $1$ $\Z/2\Z$ $2.418339135$ $1.737958760$ 6.354298938 \( -\frac{34643161}{176} a + \frac{13683239}{88} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 16 a + 28\) , \( -29 a + 91\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(16a+28\right){x}-29a+91$
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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.