Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
1.1-a1 |
1.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.54355$ |
$\textsf{none}$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3, 5$ |
2Cn, 3Ns, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$67.94515897$ |
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 |
$2$ |
$5$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.54355$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3, 5$ |
2Cn, 3Ns, 5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$2.717806358$ |
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 |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$0.94146$ |
$(a-3), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$24.86632948$ |
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 |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{15} \) |
$0.94146$ |
$(a-3), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$12.43316474$ |
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 |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{12} \) |
$0.94146$ |
$(a-3), (a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cs, 3Ns |
$1$ |
\( 2^{2} \) |
$1$ |
$24.86632948$ |
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 |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{15} \) |
$0.94146$ |
$(a-3), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$12.43316474$ |
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 |
$2$ |
$5$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$0.94146$ |
$(a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3, 5$ |
2Cn, 3Ns, 5B.4.1 |
$1$ |
\( 1 \) |
$0.102786295$ |
$30.43428306$ |
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 |
$2$ |
$5$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$0.94146$ |
$(a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3, 5$ |
2Cn, 3Ns, 5B.4.2 |
$1$ |
\( 1 \) |
$0.513931478$ |
$6.086856612$ |
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 |
$2$ |
$5$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{6} \) |
$0.94146$ |
$(a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3, 5$ |
2Cn, 3Ns, 5B.4.1 |
$1$ |
\( 1 \) |
$0.102786295$ |
$30.43428306$ |
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 |
$2$ |
$5$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{6} \) |
$0.94146$ |
$(a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3, 5$ |
2Cn, 3Ns, 5B.4.2 |
$1$ |
\( 1 \) |
$0.513931478$ |
$6.086856612$ |
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 |
$1$ |
$1$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$0.98989$ |
$(a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$10.72865780$ |
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 |
$1$ |
$1$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( 11^{3} \) |
$0.98989$ |
$(a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1$ |
$9.664500298$ |
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 |
$1$ |
$1$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
11.2 |
\( 11 \) |
\( 11 \) |
$0.98989$ |
$(a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$10.72865780$ |
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 |
$1$ |
$1$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
11.2 |
\( 11 \) |
\( 11^{3} \) |
$0.98989$ |
$(a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1$ |
$9.664500298$ |
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 |
$1$ |
$1$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3^{7} \) |
$1.01166$ |
$(a-3), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$9.251314477$ |
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 |
$2$ |
$5$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3 \) |
$1.01166$ |
$(a-3), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$0.310673886$ |
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 |
$2$ |
$5$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{10} \cdot 3^{5} \) |
$1.01166$ |
$(a-3), (2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5^{2} \) |
$1$ |
$7.766847163$ |
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 |
$1$ |
$1$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3^{7} \) |
$1.01166$ |
$(a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$9.251314477$ |
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 |
$2$ |
$5$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3 \) |
$1.01166$ |
$(a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$0.310673886$ |
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 |
$2$ |
$5$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{10} \cdot 3^{5} \) |
$1.01166$ |
$(a+2), (2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5^{2} \) |
$1$ |
$7.766847163$ |
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 |
$2$ |
$3$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$1.08710$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2Cn, 3B |
$1$ |
\( 1 \) |
$1$ |
$10.44146158$ |
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 |
$2$ |
$3$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$1.08710$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2Cn, 3B |
$1$ |
\( 1 \) |
$1$ |
$10.44146158$ |
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 |
$4$ |
$6$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{2} \cdot 7^{3} \) |
$1.16357$ |
$(a+2), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.525790352$ |
$17.24649447$ |
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 |
$4$ |
$6$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{6} \cdot 7 \) |
$1.16357$ |
$(a+2), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.175263450$ |
$17.24649447$ |
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 |
$4$ |
$6$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{12} \cdot 7^{2} \) |
$1.16357$ |
$(a+2), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.087631725$ |
$8.623247237$ |
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 |
$4$ |
$6$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{4} \cdot 7^{6} \) |
$1.16357$ |
$(a+2), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.262895176$ |
$8.623247237$ |
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 |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{14} \cdot 7 \) |
$1.16357$ |
$(a+2), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.09657311$ |
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 |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{7} \cdot 7^{2} \) |
$1.16357$ |
$(a+2), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.09657311$ |
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 |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{2} \cdot 7 \) |
$1.16357$ |
$(a+2), (a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$21.12141524$ |
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 |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{4} \cdot 7^{2} \) |
$1.16357$ |
$(a+2), (a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$10.56070762$ |
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 |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{2} \cdot 7 \) |
$1.16357$ |
$(a+2), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.280353810$ |
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 |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{8} \cdot 7^{4} \) |
$1.16357$ |
$(a+2), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.640176905$ |
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 |
$4$ |
$6$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
21.4 |
\( 3 \cdot 7 \) |
\( - 3^{4} \cdot 7^{6} \) |
$1.16357$ |
$(a-3), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.262895176$ |
$8.623247237$ |
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 |
$4$ |
$6$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
21.4 |
\( 3 \cdot 7 \) |
\( - 3^{12} \cdot 7^{2} \) |
$1.16357$ |
$(a-3), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.087631725$ |
$8.623247237$ |
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 |
$4$ |
$6$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
21.4 |
\( 3 \cdot 7 \) |
\( - 3^{6} \cdot 7 \) |
$1.16357$ |
$(a-3), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.175263450$ |
$17.24649447$ |
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 |
$4$ |
$6$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
21.4 |
\( 3 \cdot 7 \) |
\( - 3^{2} \cdot 7^{3} \) |
$1.16357$ |
$(a-3), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.525790352$ |
$17.24649447$ |
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 |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
21.4 |
\( 3 \cdot 7 \) |
\( - 3^{14} \cdot 7 \) |
$1.16357$ |
$(a-3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.09657311$ |
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 |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
21.4 |
\( 3 \cdot 7 \) |
\( 3^{7} \cdot 7^{2} \) |
$1.16357$ |
$(a-3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.09657311$ |
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 |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
21.4 |
\( 3 \cdot 7 \) |
\( - 3^{8} \cdot 7^{4} \) |
$1.16357$ |
$(a-3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.640176905$ |
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 |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
21.4 |
\( 3 \cdot 7 \) |
\( - 3^{2} \cdot 7 \) |
$1.16357$ |
$(a-3), (-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$21.12141524$ |
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 |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
21.4 |
\( 3 \cdot 7 \) |
\( 3^{4} \cdot 7^{2} \) |
$1.16357$ |
$(a-3), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$10.56070762$ |
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 |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
21.4 |
\( 3 \cdot 7 \) |
\( 3^{2} \cdot 7 \) |
$1.16357$ |
$(a-3), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.280353810$ |
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 |
$1$ |
$1$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$1.21541$ |
$(5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cn |
$1$ |
\( 2 \) |
$0.076542676$ |
$26.47599750$ |
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 |
$3$ |
$9$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{12} \) |
$1.21541$ |
$(5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cn, 3Cs |
$1$ |
\( 2 \) |
$1$ |
$7.639049474$ |
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 |
$3$ |
$9$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$1.21541$ |
$(5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cn, 3B |
$1$ |
\( 2 \) |
$1$ |
$7.639049474$ |
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 |
$3$ |
$9$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$1.21541$ |
$(5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cn, 3B |
$1$ |
\( 2 \) |
$1$ |
$7.639049474$ |
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 |
$1$ |
$1$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$1.21541$ |
$(5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cn |
$1$ |
\( 2 \) |
$0.076542676$ |
$26.47599750$ |
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 |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{12} \) |
$1.23903$ |
$(a-3), (a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \) |
$1.694071006$ |
$9.335607421$ |
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 |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{21} \) |
$1.23903$ |
$(a-3), (a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \) |
$1.694071006$ |
$2.333901855$ |
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 |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{18} \) |
$1.23903$ |
$(a-3), (a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3Ns |
$1$ |
\( 2^{3} \) |
$0.847035503$ |
$9.335607421$ |
1.299999940 |
\( \frac{12008989}{729} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -32 a - 84\) , \( 101 a + 256\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-32a-84\right){x}+101a+256$ |
*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.