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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
4.1-a1 4.1-a \(\Q(\sqrt{217}) \) \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $35.74821466$ 2.426746937 \( -\frac{7861875}{64} a - \frac{26985875}{32} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -4575 a + 35985\) , \( -2480637 a + 19511351\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-4575a+35985\right){x}-2480637a+19511351$
4.1-a2 4.1-a \(\Q(\sqrt{217}) \) \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $35.74821466$ 2.426746937 \( \frac{7861875}{64} a - \frac{61833625}{64} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 4575 a + 31410\) , \( 2480637 a + 17030714\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(4575a+31410\right){x}+2480637a+17030714$
4.1-a3 4.1-a \(\Q(\sqrt{217}) \) \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $35.74821466$ 2.426746937 \( -\frac{1779679887375}{8} a + \frac{13998000969625}{8} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -89895 a - 617170\) , \( 37511019 a + 257530398\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-89895a-617170\right){x}+37511019a+257530398$
4.1-a4 4.1-a \(\Q(\sqrt{217}) \) \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $35.74821466$ 2.426746937 \( \frac{1779679887375}{8} a + \frac{6109160541125}{4} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 89895 a - 707065\) , \( -37511019 a + 295041417\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(89895a-707065\right){x}-37511019a+295041417$
4.1-b1 4.1-b \(\Q(\sqrt{217}) \) \( 2^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $32.05257343$ 6.527611391 \( -\frac{2193}{8} a - \frac{2459}{4} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -5894 a - 40465\) , \( 851278 a + 5844415\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-5894a-40465\right){x}+851278a+5844415$
4.1-b2 4.1-b \(\Q(\sqrt{217}) \) \( 2^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $32.05257343$ 6.527611391 \( \frac{2193}{8} a - \frac{7111}{8} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 5894 a - 46359\) , \( -851278 a + 6695693\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(5894a-46359\right){x}-851278a+6695693$
4.1-c1 4.1-c \(\Q(\sqrt{217}) \) \( 2^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $14.29159922$ 2.910530915 \( -\frac{2193}{8} a - \frac{2459}{4} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -7682232 a + 60424288\) , \( -18970234890 a + 149209622415\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-7682232a+60424288\right){x}-18970234890a+149209622415$
4.1-c2 4.1-c \(\Q(\sqrt{217}) \) \( 2^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $14.29159922$ 2.910530915 \( \frac{2193}{8} a - \frac{7111}{8} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 7682232 a + 52742056\) , \( 18970234890 a + 130239387525\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(7682232a+52742056\right){x}+18970234890a+130239387525$
4.1-d1 4.1-d \(\Q(\sqrt{217}) \) \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.098105599$ 0.346081958 \( -\frac{7861875}{64} a - \frac{26985875}{32} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -76876685 a - 527793801\) , \( -996242529392 a - 6839663167426\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-76876685a-527793801\right){x}-996242529392a-6839663167426$
4.1-d2 4.1-d \(\Q(\sqrt{217}) \) \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.098105599$ 0.346081958 \( \frac{7861875}{64} a - \frac{61833625}{64} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 76876685 a - 604670486\) , \( 996242529392 a - 7835905696818\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(76876685a-604670486\right){x}+996242529392a-7835905696818$
4.1-d3 4.1-d \(\Q(\sqrt{217}) \) \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.098105599$ 0.346081958 \( -\frac{1779679887375}{8} a + \frac{13998000969625}{8} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 1230190055 a - 9676010586\) , \( 63741468271084 a - 501355964650234\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(1230190055a-9676010586\right){x}+63741468271084a-501355964650234$
4.1-d4 4.1-d \(\Q(\sqrt{217}) \) \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.098105599$ 0.346081958 \( \frac{1779679887375}{8} a + \frac{6109160541125}{4} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -1230190055 a - 8445820531\) , \( -63741468271084 a - 437614496379150\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-1230190055a-8445820531\right){x}-63741468271084a-437614496379150$
6.1-a1 6.1-a \(\Q(\sqrt{217}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.801985746$ $29.66850780$ 3.230445974 \( \frac{30385}{6} a + \frac{208607}{6} \) \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -a + 18\) , \( -5 a + 9\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+18\right){x}-5a+9$
6.1-b1 6.1-b \(\Q(\sqrt{217}) \) \( 2 \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $30.54717750$ 2.073677529 \( \frac{30385}{6} a + \frac{208607}{6} \) \( \bigl[1\) , \( a\) , \( a\) , \( -83592993998 a - 573904350815\) , \( 35287915421569989 a + 242267769386884299\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-83592993998a-573904350815\right){x}+35287915421569989a+242267769386884299$
6.2-a1 6.2-a \(\Q(\sqrt{217}) \) \( 2 \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $16.22987535$ 8.814045832 \( \frac{1333879}{13122} a + \frac{368465}{486} \) \( \bigl[a + 1\) , \( 0\) , \( a\) , \( 1454820719431 a + 9988013356524\) , \( 857134272549098597 a + 5884621003953910568\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(1454820719431a+9988013356524\right){x}+857134272549098597a+5884621003953910568$
6.2-b1 6.2-b \(\Q(\sqrt{217}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $2.451506314$ $9.778072031$ 6.509031491 \( \frac{1333879}{13122} a + \frac{368465}{486} \) \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 7 a + 83\) , \( 20 a + 171\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(7a+83\right){x}+20a+171$
6.3-a1 6.3-a \(\Q(\sqrt{217}) \) \( 2 \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $16.22987535$ 8.814045832 \( -\frac{1333879}{13122} a + \frac{5641217}{6561} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -1454820719433 a + 11442834075956\) , \( -857134272549098598 a + 6741755276503009165\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1454820719433a+11442834075956\right){x}-857134272549098598a+6741755276503009165$
6.3-b1 6.3-b \(\Q(\sqrt{217}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $2.451506314$ $9.778072031$ 6.509031491 \( -\frac{1333879}{13122} a + \frac{5641217}{6561} \) \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -7 a + 36\) , \( -14 a + 101\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7a+36\right){x}-14a+101$
6.4-a1 6.4-a \(\Q(\sqrt{217}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.801985746$ $29.66850780$ 3.230445974 \( -\frac{30385}{6} a + 39832 \) \( \bigl[1\) , \( a\) , \( a\) , \( 18\) , \( 4 a + 5\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+18{x}+4a+5$
6.4-b1 6.4-b \(\Q(\sqrt{217}) \) \( 2 \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $30.54717750$ 2.073677529 \( -\frac{30385}{6} a + 39832 \) \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 83592993997 a - 657497344813\) , \( -35287915421569990 a + 277555684808454288\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(83592993997a-657497344813\right){x}-35287915421569990a+277555684808454288$
7.1-a1 7.1-a \(\Q(\sqrt{217}) \) \( 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.009166008$ 0.136079961 \( -\frac{658503}{117649} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 945951 a - 7440340\) , \( -23919915394 a + 188141136092\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(945951a-7440340\right){x}-23919915394a+188141136092$
7.1-a2 7.1-a \(\Q(\sqrt{217}) \) \( 7 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $32.07332806$ 0.136079961 \( -\frac{34063182558}{49} a + \frac{267922691739}{49} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 173213478909 a - 1362403677925\) , \( -106496592842533228 a + 837644683825909912\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(173213478909a-1362403677925\right){x}-106496592842533228a+837644683825909912$
7.1-a3 7.1-a \(\Q(\sqrt{217}) \) \( 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $16.03666403$ 0.136079961 \( \frac{34965783}{343} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 3555471 a - 27965415\) , \( -9820546524 a + 77243115188\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(3555471a-27965415\right){x}-9820546524a+77243115188$
7.1-a4 7.1-a \(\Q(\sqrt{217}) \) \( 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $8.018332017$ 0.136079961 \( \frac{34063182558}{49} a + \frac{233859509181}{49} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 129 a - 1015\) , \( 656 a - 5160\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(129a-1015\right){x}+656a-5160$
7.1-b1 7.1-b \(\Q(\sqrt{217}) \) \( 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.009166008$ 0.136079961 \( -\frac{658503}{117649} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -945951 a - 6494389\) , \( 23919915394 a + 164221220698\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-945951a-6494389\right){x}+23919915394a+164221220698$
7.1-b2 7.1-b \(\Q(\sqrt{217}) \) \( 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $8.018332017$ 0.136079961 \( -\frac{34063182558}{49} a + \frac{267922691739}{49} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -129 a - 886\) , \( -656 a - 4504\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-129a-886\right){x}-656a-4504$
7.1-b3 7.1-b \(\Q(\sqrt{217}) \) \( 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $16.03666403$ 0.136079961 \( \frac{34965783}{343} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -3555471 a - 24409944\) , \( 9820546524 a + 67422568664\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-3555471a-24409944\right){x}+9820546524a+67422568664$
7.1-b4 7.1-b \(\Q(\sqrt{217}) \) \( 7 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $32.07332806$ 0.136079961 \( \frac{34063182558}{49} a + \frac{233859509181}{49} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -173213478909 a - 1189190199016\) , \( 106496592842533228 a + 731148090983376684\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-173213478909a-1189190199016\right){x}+106496592842533228a+731148090983376684$
8.1-a1 8.1-a \(\Q(\sqrt{217}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.520883425$ $13.88937213$ 2.867996848 \( \frac{169942716001}{2097152} a - \frac{676100323303}{1048576} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -113 a - 696\) , \( 1555 a + 10865\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-113a-696\right){x}+1555a+10865$
8.1-a2 8.1-a \(\Q(\sqrt{217}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.506961141$ $13.88937213$ 2.867996848 \( \frac{13657}{128} a + \frac{53585}{64} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 2 a + 94\) , \( -a + 185\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a+94\right){x}-a+185$
8.1-b1 8.1-b \(\Q(\sqrt{217}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $12.50954182$ $1.087722570$ 1.847394612 \( \frac{169942716001}{2097152} a - \frac{676100323303}{1048576} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 1869574935893 a - 14705066746888\) , \( 3779122287683704783 a - 29724534929365231599\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1869574935893a-14705066746888\right){x}+3779122287683704783a-29724534929365231599$
8.1-b2 8.1-b \(\Q(\sqrt{217}) \) \( 2^{3} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $4.169847275$ $9.789503138$ 1.847394612 \( \frac{13657}{128} a + \frac{53585}{64} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -24740869992 a + 194598321582\) , \( 22630333034170967 a - 177997977712882799\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-24740869992a+194598321582\right){x}+22630333034170967a-177997977712882799$
8.2-a1 8.2-a \(\Q(\sqrt{217}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.520883425$ $13.88937213$ 2.867996848 \( -\frac{169942716001}{2097152} a - \frac{1182257930605}{2097152} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 114 a - 755\) , \( -1442 a + 11665\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(114a-755\right){x}-1442a+11665$
8.2-a2 8.2-a \(\Q(\sqrt{217}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.506961141$ $13.88937213$ 2.867996848 \( -\frac{13657}{128} a + \frac{120827}{128} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -a + 150\) , \( -a + 334\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-a+150\right){x}-a+334$
8.2-b1 8.2-b \(\Q(\sqrt{217}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $12.50954182$ $1.087722570$ 1.847394612 \( -\frac{169942716001}{2097152} a - \frac{1182257930605}{2097152} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -1869574935895 a - 12835491810995\) , \( -3779122287683704784 a - 25945412641681526816\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-1869574935895a-12835491810995\right){x}-3779122287683704784a-25945412641681526816$
8.2-b2 8.2-b \(\Q(\sqrt{217}) \) \( 2^{3} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $4.169847275$ $9.789503138$ 1.847394612 \( -\frac{13657}{128} a + \frac{120827}{128} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 24740869990 a + 169857451590\) , \( -22630333034170968 a - 155367644678711832\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(24740869990a+169857451590\right){x}-22630333034170968a-155367644678711832$
8.3-a1 8.3-a \(\Q(\sqrt{217}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.783342260$ $18.65119014$ 1.983618890 \( 122654 a - 964730 \) \( \bigl[0\) , \( -a + 1\) , \( a\) , \( 5238176497 a + 35962490874\) , \( -66537844035834579 a - 456812902144981867\bigr] \) ${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(5238176497a+35962490874\right){x}-66537844035834579a-456812902144981867$
8.3-b1 8.3-b \(\Q(\sqrt{217}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.389807035$ $6.932125642$ 1.308040105 \( 122654 a - 964730 \) \( \bigl[0\) , \( a - 1\) , \( a\) , \( 17 a - 118\) , \( 63 a - 499\bigr] \) ${y}^2+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(17a-118\right){x}+63a-499$
8.4-a1 8.4-a \(\Q(\sqrt{217}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.783342260$ $18.65119014$ 1.983618890 \( -122654 a - 842076 \) \( \bigl[0\) , \( a\) , \( a + 1\) , \( -5238176497 a + 41200667371\) , \( 66537844035834578 a - 523350746180816446\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-5238176497a+41200667371\right){x}+66537844035834578a-523350746180816446$
8.4-b1 8.4-b \(\Q(\sqrt{217}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.389807035$ $6.932125642$ 1.308040105 \( -122654 a - 842076 \) \( \bigl[0\) , \( -a\) , \( a + 1\) , \( -17 a - 101\) , \( -64 a - 436\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-17a-101\right){x}-64a-436$
12.1-a1 12.1-a \(\Q(\sqrt{217}) \) \( 2^{2} \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $13.44075155$ 1.824835336 \( \frac{166195231}{69984} a + \frac{1139844827}{69984} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( 2401258290 a - 18887000841\) , \( -1781930806827389 a + 14015705361500025\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2401258290a-18887000841\right){x}-1781930806827389a+14015705361500025$
12.1-b1 12.1-b \(\Q(\sqrt{217}) \) \( 2^{2} \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.078437573$ $11.87551769$ 1.770536432 \( \frac{166195231}{69984} a + \frac{1139844827}{69984} \) \( \bigl[1\) , \( -a\) , \( a + 1\) , \( -269 a - 1827\) , \( 7022 a + 48214\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-269a-1827\right){x}+7022a+48214$
12.1-c1 12.1-c \(\Q(\sqrt{217}) \) \( 2^{2} \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.419617984$ 0.328508743 \( \frac{862466072125}{429981696} a - \frac{3261071985131}{214990848} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( 5 a - 12\) , \( 8 a - 36\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5a-12\right){x}+8a-36$
12.1-c2 12.1-c \(\Q(\sqrt{217}) \) \( 2^{2} \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.419617984$ 0.328508743 \( -\frac{658839190694584165}{11019960576} a + \frac{2591060113241350883}{5509980288} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( 65 a - 512\) , \( 668 a - 5280\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(65a-512\right){x}+668a-5280$
12.1-d1 12.1-d \(\Q(\sqrt{217}) \) \( 2^{2} \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $4.725924539$ 3.849799944 \( \frac{36095551}{98304} a + \frac{247714811}{98304} \) \( \bigl[1\) , \( 0\) , \( a + 1\) , \( -97 a - 663\) , \( -1164 a - 8000\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-97a-663\right){x}-1164a-8000$
12.1-d2 12.1-d \(\Q(\sqrt{217}) \) \( 2^{2} \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $4.725924539$ 3.849799944 \( \frac{5784954706489}{864} a + \frac{39716374742807}{864} \) \( \bigl[1\) , \( 0\) , \( a + 1\) , \( -10256644 a + 80673218\) , \( -2022736447430 a + 15909752478878\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-10256644a+80673218\right){x}-2022736447430a+15909752478878$
12.1-e1 12.1-e \(\Q(\sqrt{217}) \) \( 2^{2} \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.152598850$ $11.35308701$ 2.822582225 \( \frac{36095551}{98304} a + \frac{247714811}{98304} \) \( \bigl[1\) , \( 1\) , \( a\) , \( 15849071845 a - 124660239549\) , \( -122912772997547574 a + 966765491060639043\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(15849071845a-124660239549\right){x}-122912772997547574a+966765491060639043$
12.1-e2 12.1-e \(\Q(\sqrt{217}) \) \( 2^{2} \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.457796550$ $11.35308701$ 2.822582225 \( \frac{5784954706489}{864} a + \frac{39716374742807}{864} \) \( \bigl[1\) , \( 1\) , \( a\) , \( -1275546 a - 8757206\) , \( 2127641751 a + 14607239178\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-1275546a-8757206\right){x}+2127641751a+14607239178$
12.1-f1 12.1-f \(\Q(\sqrt{217}) \) \( 2^{2} \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.014587921$ $9.455028562$ 7.865125872 \( \frac{1514638126999}{1836660096} a + \frac{5110717728563}{1836660096} \) \( \bigl[1\) , \( a\) , \( a\) , \( 315558654 a - 2482013931\) , \( -10476032628218 a + 82398814876539\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(315558654a-2482013931\right){x}-10476032628218a+82398814876539$
12.1-g1 12.1-g \(\Q(\sqrt{217}) \) \( 2^{2} \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $2.521591970$ 4.792950870 \( \frac{1514638126999}{1836660096} a + \frac{5110717728563}{1836660096} \) \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -345489 a - 2371916\) , \( -269827466 a - 1852489645\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-345489a-2371916\right){x}-269827466a-1852489645$
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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.