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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
1.1-a1 1.1-a \(\Q(\sqrt{209}) \) \( 1 \) 0 $\mathsf{trivial}$ $-19$ $N(\mathrm{U}(1))$ $1$ $17.56070946$ 1.214699673 \( -884736 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 12880 a - 99542\) , \( -2141323 a + 16549035\bigr] \) ${y}^2+{y}={x}^{3}+\left(12880a-99542\right){x}-2141323a+16549035$
1.1-a2 1.1-a \(\Q(\sqrt{209}) \) \( 1 \) 0 $\mathsf{trivial}$ $-19$ $N(\mathrm{U}(1))$ $1$ $17.56070946$ 1.214699673 \( -884736 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( -12880 a - 86662\) , \( 2141323 a + 14407712\bigr] \) ${y}^2+{y}={x}^{3}+\left(-12880a-86662\right){x}+2141323a+14407712$
2.1-a1 2.1-a \(\Q(\sqrt{209}) \) \( 2 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.048108188$ $34.45290976$ 2.751585456 \( -\frac{1714092597}{4096} a - \frac{11539289943}{4096} \) \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 333486 a - 2577189\) , \( -412096662 a + 3184854795\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(333486a-2577189\right){x}-412096662a+3184854795$
2.1-b1 2.1-b \(\Q(\sqrt{209}) \) \( 2 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $18.51817441$ 2.561857817 \( \frac{2361203}{4} a - \frac{18549919}{4} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -166349 a - 1119240\) , \( -101485499 a - 682836650\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-166349a-1119240\right){x}-101485499a-682836650$
2.1-b2 2.1-b \(\Q(\sqrt{209}) \) \( 2 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $18.51817441$ 2.561857817 \( -\frac{102557}{1024} a + \frac{1072561}{1024} \) \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -6449241 a + 49842606\) , \( -1496864675 a + 11568393744\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6449241a+49842606\right){x}-1496864675a+11568393744$
2.1-c1 2.1-c \(\Q(\sqrt{209}) \) \( 2 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.529462610$ $13.03498084$ 1.909556628 \( \frac{2361203}{4} a - \frac{18549919}{4} \) \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 1502 a - 11391\) , \( 84221 a - 650261\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1502a-11391\right){x}+84221a-650261$
2.1-c2 2.1-c \(\Q(\sqrt{209}) \) \( 2 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.105892522$ $13.03498084$ 1.909556628 \( -\frac{102557}{1024} a + \frac{1072561}{1024} \) \( \bigl[a + 1\) , \( 0\) , \( a\) , \( 8 a + 57\) , \( 19 a + 137\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(8a+57\right){x}+19a+137$
2.1-d1 2.1-d \(\Q(\sqrt{209}) \) \( 2 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $2.835776404$ 0.392309511 \( -\frac{1714092597}{4096} a - \frac{11539289943}{4096} \) \( \bigl[a + 1\) , \( 1\) , \( a\) , \( -1797 a - 12082\) , \( -124118 a - 835100\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-1797a-12082\right){x}-124118a-835100$
2.2-a1 2.2-a \(\Q(\sqrt{209}) \) \( 2 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.048108188$ $34.45290976$ 2.751585456 \( \frac{1714092597}{4096} a - \frac{3313345635}{1024} \) \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -333486 a - 2243755\) , \( 412430147 a + 2775001836\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-333486a-2243755\right){x}+412430147a+2775001836$
2.2-b1 2.2-b \(\Q(\sqrt{209}) \) \( 2 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $18.51817441$ 2.561857817 \( -\frac{2361203}{4} a - 4047179 \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 166348 a - 1285588\) , \( 101485499 a - 784322149\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(166348a-1285588\right){x}+101485499a-784322149$
2.2-b2 2.2-b \(\Q(\sqrt{209}) \) \( 2 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $18.51817441$ 2.561857817 \( \frac{102557}{1024} a + \frac{242501}{256} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 6449267 a + 43393366\) , \( 1546707281 a + 10406890251\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6449267a+43393366\right){x}+1546707281a+10406890251$
2.2-c1 2.2-c \(\Q(\sqrt{209}) \) \( 2 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.529462610$ $13.03498084$ 1.909556628 \( -\frac{2361203}{4} a - 4047179 \) \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -1476 a - 9940\) , \( -95638 a - 643494\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1476a-9940\right){x}-95638a-643494$
2.2-c2 2.2-c \(\Q(\sqrt{209}) \) \( 2 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.105892522$ $13.03498084$ 1.909556628 \( \frac{102557}{1024} a + \frac{242501}{256} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -10 a + 66\) , \( -20 a + 156\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a+66\right){x}-20a+156$
2.2-d1 2.2-d \(\Q(\sqrt{209}) \) \( 2 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $2.835776404$ 0.392309511 \( \frac{1714092597}{4096} a - \frac{3313345635}{1024} \) \( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 1797 a - 13879\) , \( 122321 a - 945339\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1797a-13879\right){x}+122321a-945339$
4.1-a1 4.1-a \(\Q(\sqrt{209}) \) \( 2^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.299859083$ $19.84955375$ 2.470279326 \( -\frac{27}{8} \) \( \bigl[1\) , \( -1\) , \( a\) , \( -403 a - 2708\) , \( -267565 a - 1800300\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-403a-2708\right){x}-267565a-1800300$
4.1-b1 4.1-b \(\Q(\sqrt{209}) \) \( 2^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.299859083$ $19.84955375$ 2.470279326 \( -\frac{27}{8} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( 402 a - 3111\) , \( 267564 a - 2067865\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(402a-3111\right){x}+267564a-2067865$
4.1-c1 4.1-c \(\Q(\sqrt{209}) \) \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.636252383$ 4.102951284 \( -\frac{24345866052441}{1073741824} a - \frac{160359237040419}{1073741824} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 25 a - 196\) , \( -132 a + 1019\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(25a-196\right){x}-132a+1019$
4.1-c2 4.1-c \(\Q(\sqrt{209}) \) \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.636252383$ 4.102951284 \( -\frac{239886134047017}{32768} a + \frac{463484975124303}{8192} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 109626655 a - 847240411\) , \( 1679777810708 a - 12982021956321\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(109626655a-847240411\right){x}+1679777810708a-12982021956321$
4.1-c3 4.1-c \(\Q(\sqrt{209}) \) \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.636252383$ 4.102951284 \( \frac{24345866052441}{1073741824} a - \frac{46176275773215}{268435456} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -25 a - 171\) , \( 132 a + 887\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-25a-171\right){x}+132a+887$
4.1-c4 4.1-c \(\Q(\sqrt{209}) \) \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.636252383$ 4.102951284 \( \frac{239886134047017}{32768} a + \frac{1614053766450195}{32768} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -109626655 a - 737613756\) , \( -1679777810708 a - 11302244145613\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-109626655a-737613756\right){x}-1679777810708a-11302244145613$
4.1-d1 4.1-d \(\Q(\sqrt{209}) \) \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $8.606301134$ 0.297655148 \( -\frac{24345866052441}{1073741824} a - \frac{160359237040419}{1073741824} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -1485209680 a - 9993108793\) , \( 83988775088712 a + 565111430507277\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-1485209680a-9993108793\right){x}+83988775088712a+565111430507277$
4.1-d2 4.1-d \(\Q(\sqrt{209}) \) \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $8.606301134$ 0.297655148 \( -\frac{239886134047017}{32768} a + \frac{463484975124303}{8192} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 950 a + 6392\) , \( -42668 a - 287088\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(950a+6392\right){x}-42668a-287088$
4.1-d3 4.1-d \(\Q(\sqrt{209}) \) \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $8.606301134$ 0.297655148 \( \frac{24345866052441}{1073741824} a - \frac{46176275773215}{268435456} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 1485209680 a - 11478318473\) , \( -83988775088712 a + 649100205595989\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(1485209680a-11478318473\right){x}-83988775088712a+649100205595989$
4.1-d4 4.1-d \(\Q(\sqrt{209}) \) \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $8.606301134$ 0.297655148 \( \frac{239886134047017}{32768} a + \frac{1614053766450195}{32768} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -950 a + 7342\) , \( 42668 a - 329756\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-950a+7342\right){x}+42668a-329756$
4.2-a1 4.2-a \(\Q(\sqrt{209}) \) \( 2^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.797684321$ $5.540110081$ 1.377807922 \( -45056 a - 303104 \) \( \bigl[0\) , \( -a - 1\) , \( a\) , \( 11\) , \( -a - 11\bigr] \) ${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+11{x}-a-11$
4.2-b1 4.2-b \(\Q(\sqrt{209}) \) \( 2^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.323850701$ $36.24219350$ 4.871216415 \( -45056 a - 303104 \) \( \bigl[0\) , \( -1\) , \( a\) , \( -37023561 a + 286133487\) , \( -1880699198318 a + 14534826052669\bigr] \) ${y}^2+a{y}={x}^{3}-{x}^{2}+\left(-37023561a+286133487\right){x}-1880699198318a+14534826052669$
4.3-a1 4.3-a \(\Q(\sqrt{209}) \) \( 2^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.797684321$ $5.540110081$ 1.377807922 \( 45056 a - 348160 \) \( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( 2 a + 10\) , \( a - 2\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+10\right){x}+a-2$
4.3-b1 4.3-b \(\Q(\sqrt{209}) \) \( 2^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.323850701$ $36.24219350$ 4.871216415 \( 45056 a - 348160 \) \( \bigl[0\) , \( -1\) , \( a + 1\) , \( 37023561 a + 249109926\) , \( 1880699198317 a + 12654126854351\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(37023561a+249109926\right){x}+1880699198317a+12654126854351$
10.1-a1 10.1-a \(\Q(\sqrt{209}) \) \( 2 \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $3.072924513$ 6.801876264 \( \frac{20383137018133}{610351562500} a - \frac{49963875368579}{152587890625} \) \( \bigl[a\) , \( -a\) , \( 1\) , \( 19297589 a - 149139785\) , \( -251996522818 a + 1947533996049\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(19297589a-149139785\right){x}-251996522818a+1947533996049$
10.1-b1 10.1-b \(\Q(\sqrt{209}) \) \( 2 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.971375992$ $16.34187476$ 2.228425904 \( -\frac{56211}{50} a + \frac{217211}{25} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( 12491185 a - 96537059\) , \( 61050477245 a - 471823494147\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(12491185a-96537059\right){x}+61050477245a-471823494147$
10.1-b2 10.1-b \(\Q(\sqrt{209}) \) \( 2 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.985687996$ $32.68374952$ 2.228425904 \( \frac{68921}{20} a + \frac{137842}{5} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -a + 17\) , \( -2 a - 8\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+17\right){x}-2a-8$
10.1-c1 10.1-c \(\Q(\sqrt{209}) \) \( 2 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $43.47954356$ 1.503771458 \( -\frac{56211}{50} a + \frac{217211}{25} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 3 a + 20\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+3a+20$
10.1-c2 10.1-c \(\Q(\sqrt{209}) \) \( 2 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $43.47954356$ 1.503771458 \( \frac{68921}{20} a + \frac{137842}{5} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 512138585 a - 3958020110\) , \( 13200346700953 a - 102017772594930\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(512138585a-3958020110\right){x}+13200346700953a-102017772594930$
10.1-d1 10.1-d \(\Q(\sqrt{209}) \) \( 2 \cdot 5 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.109314649$ $2.711568399$ 1.312217311 \( \frac{20383137018133}{610351562500} a - \frac{49963875368579}{152587890625} \) \( \bigl[a\) , \( 0\) , \( 1\) , \( -265 a - 1737\) , \( 31126 a + 209482\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-265a-1737\right){x}+31126a+209482$
10.4-a1 10.4-a \(\Q(\sqrt{209}) \) \( 2 \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $3.072924513$ 6.801876264 \( -\frac{20383137018133}{610351562500} a - \frac{179472364456183}{610351562500} \) \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -19297590 a - 129842196\) , \( 251996522818 a + 1695537473231\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-19297590a-129842196\right){x}+251996522818a+1695537473231$
10.4-b1 10.4-b \(\Q(\sqrt{209}) \) \( 2 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.985687996$ $32.68374952$ 2.228425904 \( -\frac{68921}{20} a + \frac{620289}{20} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( 16\) , \( a - 10\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+16{x}+a-10$
10.4-b2 10.4-b \(\Q(\sqrt{209}) \) \( 2 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.971375992$ $16.34187476$ 2.228425904 \( \frac{56211}{50} a + \frac{378211}{50} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -12491186 a - 84045873\) , \( -61050477246 a - 410773016901\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-12491186a-84045873\right){x}-61050477246a-410773016901$
10.4-c1 10.4-c \(\Q(\sqrt{209}) \) \( 2 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $43.47954356$ 1.503771458 \( -\frac{68921}{20} a + \frac{620289}{20} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -512138585 a - 3445881525\) , \( -13200346700953 a - 88817425893977\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-512138585a-3445881525\right){x}-13200346700953a-88817425893977$
10.4-c2 10.4-c \(\Q(\sqrt{209}) \) \( 2 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $43.47954356$ 1.503771458 \( \frac{56211}{50} a + \frac{378211}{50} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( -3 a + 23\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-3a+23$
10.4-d1 10.4-d \(\Q(\sqrt{209}) \) \( 2 \cdot 5 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.109314649$ $2.711568399$ 1.312217311 \( -\frac{20383137018133}{610351562500} a - \frac{179472364456183}{610351562500} \) \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 264 a - 2002\) , \( -31126 a + 240608\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(264a-2002\right){x}-31126a+240608$
11.1-a1 11.1-a \(\Q(\sqrt{209}) \) \( 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $58.18256016$ $0.064435690$ 1.037304259 \( -\frac{52893159101157376}{11} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$
11.1-a2 11.1-a \(\Q(\sqrt{209}) \) \( 11 \) $1$ $\Z/5\Z$ $\mathrm{SU}(2)$ $11.63651203$ $1.610892258$ 1.037304259 \( -\frac{122023936}{161051} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$
11.1-a3 11.1-a \(\Q(\sqrt{209}) \) \( 11 \) $1$ $\Z/5\Z$ $\mathrm{SU}(2)$ $2.327302406$ $40.27230645$ 1.037304259 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}$
11.1-b1 11.1-b \(\Q(\sqrt{209}) \) \( 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $5.612837583$ $8.512583687$ 13.21997756 \( -\frac{52893159101157376}{11} \) \( \bigl[0\) , \( a + 1\) , \( 1\) , \( 4688891060561 a - 36237701385816\) , \( -14859019779017908422 a + 114836688394705117771\bigr] \) ${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4688891060561a-36237701385816\right){x}-14859019779017908422a+114836688394705117771$
11.1-b2 11.1-b \(\Q(\sqrt{209}) \) \( 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.122567516$ $8.512583687$ 13.21997756 \( -\frac{122023936}{161051} \) \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -6195627759 a - 41686761846\) , \( 1292706345403712 a + 8697866248261405\bigr] \) ${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6195627759a-41686761846\right){x}+1292706345403712a+8697866248261405$
11.1-b3 11.1-b \(\Q(\sqrt{209}) \) \( 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $5.612837583$ $8.512583687$ 13.21997756 \( -\frac{4096}{11} \) \( \bigl[0\) , \( a + 1\) , \( 1\) , \( 199858961 a - 1544593196\) , \( 9820121401118 a - 75893984805809\bigr] \) ${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(199858961a-1544593196\right){x}+9820121401118a-75893984805809$
16.4-a1 16.4-a \(\Q(\sqrt{209}) \) \( 2^{4} \) $1$ $\mathsf{trivial}$ $-11$ $N(\mathrm{U}(1))$ $0.404753223$ $38.24607426$ 2.141578668 \( -32768 \) \( \bigl[0\) , \( a - 1\) , \( a\) , \( -317 a - 2113\) , \( 7753 a + 52137\bigr] \) ${y}^2+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-317a-2113\right){x}+7753a+52137$
16.4-a2 16.4-a \(\Q(\sqrt{209}) \) \( 2^{4} \) $1$ $\mathsf{trivial}$ $-11$ $N(\mathrm{U}(1))$ $4.452285453$ $3.476915842$ 2.141578668 \( -32768 \) \( \bigl[0\) , \( -a\) , \( a\) , \( 931337 a - 7197740\) , \( 1351685914 a - 10446391276\bigr] \) ${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(931337a-7197740\right){x}+1351685914a-10446391276$
16.5-a1 16.5-a \(\Q(\sqrt{209}) \) \( 2^{4} \) $1$ $\mathsf{trivial}$ $-11$ $N(\mathrm{U}(1))$ $4.452285453$ $3.476915842$ 2.141578668 \( -32768 \) \( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( -931337 a - 6266403\) , \( -1351685915 a - 9094705362\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-931337a-6266403\right){x}-1351685915a-9094705362$
16.5-a2 16.5-a \(\Q(\sqrt{209}) \) \( 2^{4} \) $1$ $\mathsf{trivial}$ $-11$ $N(\mathrm{U}(1))$ $0.404753223$ $38.24607426$ 2.141578668 \( -32768 \) \( \bigl[0\) , \( -a\) , \( a + 1\) , \( 317 a - 2430\) , \( -7754 a + 59890\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(317a-2430\right){x}-7754a+59890$
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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.