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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 \(\Q(\sqrt{37}) \) \( 1 \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $67.94515897$ 0.446804613 \( 4096 \) \( \bigl[0\) , \( -1\) , \( 1\) , \( 8 a - 28\) , \( -19 a + 67\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}+\left(8a-28\right){x}-19a+67$
1.1-a2 1.1-a \(\Q(\sqrt{37}) \) \( 1 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $2.717806358$ 0.446804613 \( 38477541376 \) \( \bigl[0\) , \( -1\) , \( 1\) , \( 1688 a - 5978\) , \( 65277 a - 231171\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}+\left(1688a-5978\right){x}+65277a-231171$
9.1-a1 9.1-a \(\Q(\sqrt{37}) \) \( 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $24.86632948$ 1.021999846 \( \frac{1331}{27} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( 5 a + 14\) , \( 73 a + 185\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(5a+14\right){x}+73a+185$
9.1-a2 9.1-a \(\Q(\sqrt{37}) \) \( 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $12.43316474$ 1.021999846 \( -\frac{21580736655842}{531441} a + \frac{8491991437009}{59049} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -345 a - 876\) , \( -4855 a - 12339\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-345a-876\right){x}-4855a-12339$
9.1-a3 9.1-a \(\Q(\sqrt{37}) \) \( 3^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $24.86632948$ 1.021999846 \( \frac{12008989}{729} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -115 a - 291\) , \( 1052 a + 2673\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-115a-291\right){x}+1052a+2673$
9.1-a4 9.1-a \(\Q(\sqrt{37}) \) \( 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $12.43316474$ 1.021999846 \( \frac{21580736655842}{531441} a + \frac{54847186277239}{531441} \) \( \bigl[1\) , \( 1\) , \( a\) , \( 344 a - 1220\) , \( 4854 a - 17193\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(344a-1220\right){x}+4854a-17193$
9.2-a1 9.2-a \(\Q(\sqrt{37}) \) \( 3^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.102786295$ $30.43428306$ 1.028554772 \( 4096 \) \( \bigl[0\) , \( -a\) , \( 1\) , \( -2 a - 3\) , \( 5 a + 13\bigr] \) ${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-2a-3\right){x}+5a+13$
9.2-a2 9.2-a \(\Q(\sqrt{37}) \) \( 3^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.513931478$ $6.086856612$ 1.028554772 \( 38477541376 \) \( \bigl[0\) , \( -a\) , \( 1\) , \( -492 a - 1263\) , \( -9865 a - 25061\bigr] \) ${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-492a-1263\right){x}-9865a-25061$
9.3-a1 9.3-a \(\Q(\sqrt{37}) \) \( 3^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.102786295$ $30.43428306$ 1.028554772 \( 4096 \) \( \bigl[0\) , \( a - 1\) , \( 1\) , \( 2 a - 5\) , \( -5 a + 18\bigr] \) ${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a-5\right){x}-5a+18$
9.3-a2 9.3-a \(\Q(\sqrt{37}) \) \( 3^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.513931478$ $6.086856612$ 1.028554772 \( 38477541376 \) \( \bigl[0\) , \( a - 1\) , \( 1\) , \( 492 a - 1755\) , \( 9865 a - 34926\bigr] \) ${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(492a-1755\right){x}+9865a-34926$
11.1-a1 11.1-a \(\Q(\sqrt{37}) \) \( 11 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $10.72865780$ 1.763780478 \( -\frac{2087}{11} a - \frac{5405}{11} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( a + 5\) , \( a + 2\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a+5\right){x}+a+2$
11.1-b1 11.1-b \(\Q(\sqrt{37}) \) \( 11 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $9.664500298$ 1.588834061 \( \frac{12970510}{1331} a - \frac{45933551}{1331} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -2 a - 5\) , \( 289 a + 734\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a-5\right){x}+289a+734$
11.2-a1 11.2-a \(\Q(\sqrt{37}) \) \( 11 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $10.72865780$ 1.763780478 \( \frac{2087}{11} a - \frac{7492}{11} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 4 a + 11\) , \( 4 a + 10\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(4a+11\right){x}+4a+10$
11.2-b1 11.2-b \(\Q(\sqrt{37}) \) \( 11 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $9.664500298$ 1.588834061 \( -\frac{12970510}{1331} a - \frac{32963041}{1331} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 3 a + 2\) , \( -287 a + 1025\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(3a+2\right){x}-287a+1025$
12.1-a1 12.1-a \(\Q(\sqrt{37}) \) \( 2^{2} \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $9.251314477$ 1.520906731 \( \frac{13801}{4374} a + \frac{503422}{2187} \) \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 4 a + 15\) , \( 7 a + 9\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4a+15\right){x}+7a+9$
12.1-b1 12.1-b \(\Q(\sqrt{37}) \) \( 2^{2} \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.310673886$ 1.276861808 \( \frac{1293877682358550987489}{6} a - \frac{2291057091849561691514}{3} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( 1312 a - 4655\) , \( 44197 a - 156565\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(1312a-4655\right){x}+44197a-156565$
12.1-b2 12.1-b \(\Q(\sqrt{37}) \) \( 2^{2} \cdot 3 \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $7.766847163$ 1.276861808 \( \frac{19793521}{7776} a - \frac{74116909}{7776} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( 2 a - 5\) , \( a - 7\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(2a-5\right){x}+a-7$
12.2-a1 12.2-a \(\Q(\sqrt{37}) \) \( 2^{2} \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $9.251314477$ 1.520906731 \( -\frac{13801}{4374} a + \frac{113405}{486} \) \( \bigl[a\) , \( a\) , \( 0\) , \( 3 a + 8\) , \( 2 a + 5\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(3a+8\right){x}+2a+5$
12.2-b1 12.2-b \(\Q(\sqrt{37}) \) \( 2^{2} \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.310673886$ 1.276861808 \( -\frac{1293877682358550987489}{6} a - \frac{1096078833780190798513}{2} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -1313 a - 3342\) , \( -44198 a - 112367\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1313a-3342\right){x}-44198a-112367$
12.2-b2 12.2-b \(\Q(\sqrt{37}) \) \( 2^{2} \cdot 3 \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $7.766847163$ 1.276861808 \( -\frac{19793521}{7776} a - \frac{1508983}{216} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -3 a - 2\) , \( -2 a - 5\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a-2\right){x}-2a-5$
16.1-a1 16.1-a \(\Q(\sqrt{37}) \) \( 2^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $10.44146158$ 1.716565710 \( -1523712 a + 5398528 \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 24 a - 85\) , \( 120 a - 425\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(24a-85\right){x}+120a-425$
16.1-a2 16.1-a \(\Q(\sqrt{37}) \) \( 2^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $10.44146158$ 1.716565710 \( 1523712 a + 3874816 \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -24 a - 61\) , \( -120 a - 305\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-24a-61\right){x}-120a-305$
21.1-a1 21.1-a \(\Q(\sqrt{37}) \) \( 3 \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.525790352$ $17.24649447$ 1.490776659 \( -\frac{48155111}{3087} a + \frac{18937350}{343} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 14 a - 43\) , \( -41 a + 150\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(14a-43\right){x}-41a+150$
21.1-a2 21.1-a \(\Q(\sqrt{37}) \) \( 3 \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.175263450$ $17.24649447$ 1.490776659 \( -\frac{26608457}{5103} a + \frac{10488103}{567} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -a + 6\) , \( a + 7\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+6\right){x}+a+7$
21.1-a3 21.1-a \(\Q(\sqrt{37}) \) \( 3 \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.087631725$ $8.623247237$ 1.490776659 \( \frac{82104162493}{26040609} a + \frac{23195606656}{2893401} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -11 a - 19\) , \( 24 a + 66\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-11a-19\right){x}+24a+66$
21.1-a4 21.1-a \(\Q(\sqrt{37}) \) \( 3 \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.262895176$ $8.623247237$ 1.490776659 \( \frac{271552460437}{9529569} a + \frac{76675641283}{1058841} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 4 a - 8\) , \( -109 a + 390\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(4a-8\right){x}-109a+390$
21.1-b1 21.1-b \(\Q(\sqrt{37}) \) \( 3 \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $18.09657311$ 1.487529146 \( -\frac{1449791608112}{33480783} a - \frac{325818657413}{3720087} \) \( \bigl[a\) , \( a\) , \( 0\) , \( 197 a - 683\) , \( -2535 a + 8988\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(197a-683\right){x}-2535a+8988$
21.1-b2 21.1-b \(\Q(\sqrt{37}) \) \( 3 \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $18.09657311$ 1.487529146 \( \frac{1020689116688854}{107163} a + \frac{293830214716873}{11907} \) \( \bigl[a\) , \( a\) , \( 0\) , \( 3082 a - 10903\) , \( -163227 a + 578055\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(3082a-10903\right){x}-163227a+578055$
21.1-c1 21.1-c \(\Q(\sqrt{37}) \) \( 3 \cdot 7 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $21.12141524$ 0.434042409 \( -\frac{33776}{63} a + \frac{17839}{7} \) \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 9 a - 28\) , \( 22 a - 86\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(9a-28\right){x}+22a-86$
21.1-c2 21.1-c \(\Q(\sqrt{37}) \) \( 3 \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.56070762$ 0.434042409 \( -\frac{6273137672}{3969} a + \frac{2470185541}{441} \) \( \bigl[1\) , \( -a - 1\) , \( a\) , \( -104 a - 262\) , \( -618 a - 1572\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-104a-262\right){x}-618a-1572$
21.1-c3 21.1-c \(\Q(\sqrt{37}) \) \( 3 \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.280353810$ 0.434042409 \( -\frac{957961400352382}{63} a + \frac{376945173009773}{7} \) \( \bigl[1\) , \( -a - 1\) , \( a\) , \( -574 a - 1457\) , \( 13253 a + 33679\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-574a-1457\right){x}+13253a+33679$
21.1-c4 21.1-c \(\Q(\sqrt{37}) \) \( 3 \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.640176905$ 0.434042409 \( \frac{27348970029058}{15752961} a + \frac{7718451347197}{1750329} \) \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 119 a - 418\) , \( 1678 a - 5950\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(119a-418\right){x}+1678a-5950$
21.4-a1 21.4-a \(\Q(\sqrt{37}) \) \( 3 \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.262895176$ $8.623247237$ 1.490776659 \( -\frac{271552460437}{9529569} a + \frac{961633231984}{9529569} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -5 a - 3\) , \( 109 a + 281\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a-3\right){x}+109a+281$
21.4-a2 21.4-a \(\Q(\sqrt{37}) \) \( 3 \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.087631725$ $8.623247237$ 1.490776659 \( -\frac{82104162493}{26040609} a + \frac{290864622397}{26040609} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 11 a - 30\) , \( -24 a + 90\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(11a-30\right){x}-24a+90$
21.4-a3 21.4-a \(\Q(\sqrt{37}) \) \( 3 \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.175263450$ $17.24649447$ 1.490776659 \( \frac{26608457}{5103} a + \frac{67784470}{5103} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( a + 5\) , \( -a + 8\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+5\right){x}-a+8$
21.4-a4 21.4-a \(\Q(\sqrt{37}) \) \( 3 \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.525790352$ $17.24649447$ 1.490776659 \( \frac{48155111}{3087} a + \frac{122281039}{3087} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -15 a - 28\) , \( 41 a + 109\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-15a-28\right){x}+41a+109$
21.4-b1 21.4-b \(\Q(\sqrt{37}) \) \( 3 \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $18.09657311$ 1.487529146 \( \frac{1449791608112}{33480783} a - \frac{4382159524829}{33480783} \) \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -190 a - 482\) , \( 1853 a + 4709\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-190a-482\right){x}+1853a+4709$
21.4-b2 21.4-b \(\Q(\sqrt{37}) \) \( 3 \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $18.09657311$ 1.487529146 \( -\frac{1020689116688854}{107163} a + \frac{3665161049140711}{107163} \) \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -3075 a - 7817\) , \( 152325 a + 387119\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-3075a-7817\right){x}+152325a+387119$
21.4-c1 21.4-c \(\Q(\sqrt{37}) \) \( 3 \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.640176905$ 0.434042409 \( -\frac{27348970029058}{15752961} a + \frac{96815032153831}{15752961} \) \( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -118 a - 299\) , \( -1798 a - 4570\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-118a-299\right){x}-1798a-4570$
21.4-c2 21.4-c \(\Q(\sqrt{37}) \) \( 3 \cdot 7 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $21.12141524$ 0.434042409 \( \frac{33776}{63} a + \frac{126775}{63} \) \( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -8 a - 19\) , \( -32 a - 82\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-8a-19\right){x}-32a-82$
21.4-c3 21.4-c \(\Q(\sqrt{37}) \) \( 3 \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.56070762$ 0.434042409 \( \frac{6273137672}{3969} a + \frac{15958532197}{3969} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( 105 a - 366\) , \( 722 a - 2556\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(105a-366\right){x}+722a-2556$
21.4-c4 21.4-c \(\Q(\sqrt{37}) \) \( 3 \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.280353810$ 0.434042409 \( \frac{957961400352382}{63} a + \frac{2434545156735575}{63} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( 575 a - 2031\) , \( -12679 a + 44901\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(575a-2031\right){x}-12679a+44901$
25.1-a1 25.1-a \(\Q(\sqrt{37}) \) \( 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.076542676$ $26.47599750$ 1.332646934 \( \frac{3334144}{25} a + \frac{9547776}{25} \) \( \bigl[0\) , \( a\) , \( 1\) , \( 2 a - 4\) , \( a - 3\bigr] \) ${y}^2+{y}={x}^{3}+a{x}^{2}+\left(2a-4\right){x}+a-3$
25.1-b1 25.1-b \(\Q(\sqrt{37}) \) \( 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $7.639049474$ 2.511703995 \( \frac{89915392}{15625} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -224 a - 569\) , \( -2737 a - 6956\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+\left(-224a-569\right){x}-2737a-6956$
25.1-b2 25.1-b \(\Q(\sqrt{37}) \) \( 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $7.639049474$ 2.511703995 \( -\frac{504578899968}{25} a + \frac{357386780672}{5} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( 4 a - 47\) , \( 41 a - 83\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+\left(4a-47\right){x}+41a-83$
25.1-b3 25.1-b \(\Q(\sqrt{37}) \) \( 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $7.639049474$ 2.511703995 \( \frac{504578899968}{25} a + \frac{1282355003392}{25} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -4 a - 43\) , \( -41 a - 42\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+\left(-4a-43\right){x}-41a-42$
25.1-c1 25.1-c \(\Q(\sqrt{37}) \) \( 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.076542676$ $26.47599750$ 1.332646934 \( -\frac{3334144}{25} a + \frac{2576384}{5} \) \( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -2 a - 2\) , \( -a - 2\bigr] \) ${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-2\right){x}-a-2$
27.1-a1 27.1-a \(\Q(\sqrt{37}) \) \( 3^{3} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.694071006$ $9.335607421$ 1.299999940 \( \frac{1331}{27} \) \( \bigl[a\) , \( a\) , \( a + 1\) , \( 3 a + 6\) , \( 16 a + 40\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(3a+6\right){x}+16a+40$
27.1-a2 27.1-a \(\Q(\sqrt{37}) \) \( 3^{3} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.694071006$ $2.333901855$ 1.299999940 \( -\frac{21580736655842}{531441} a + \frac{8491991437009}{59049} \) \( \bigl[a\) , \( a\) , \( a + 1\) , \( -97 a - 264\) , \( -968 a - 2480\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-97a-264\right){x}-968a-2480$
27.1-a3 27.1-a \(\Q(\sqrt{37}) \) \( 3^{3} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.847035503$ $9.335607421$ 1.299999940 \( \frac{12008989}{729} \) \( \bigl[a\) , \( a\) , \( a + 1\) , \( -32 a - 84\) , \( 101 a + 256\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-32a-84\right){x}+101a+256$
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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.