| 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 |
$2$ |
$2$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$1.10169$ |
$\textsf{none}$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$19$ |
19Ns.4.1 |
$1$ |
\( 1 \) |
$1$ |
$50.75994773$ |
1.029293857 |
\( 8000 \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -5 a + 15\) , \( -5 a + 21\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a+15\right){x}-5a+21$ |
| 1.1-a2 |
1.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$1.10169$ |
$\textsf{none}$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$19$ |
19Ns.4.1 |
$1$ |
\( 1 \) |
$1$ |
$50.75994773$ |
1.029293857 |
\( 8000 \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 4 a + 15\) , \( 4 a + 21\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4a+15\right){x}+4a+21$ |
| 16.1-a1 |
16.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$2.20338$ |
$(-a-6)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$19$ |
19Ns.2.1 |
$1$ |
\( 1 \) |
$1$ |
$25.37997386$ |
0.514646928 |
\( 8000 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -10 a - 49\) , \( 57 a + 360\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-10a-49\right){x}+57a+360$ |
| 16.1-a2 |
16.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$2.20338$ |
$(-a-6)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$19$ |
19Ns.2.1 |
$1$ |
\( 1 \) |
$1$ |
$25.37997386$ |
0.514646928 |
\( 8000 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 10 a - 49\) , \( -57 a + 360\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(10a-49\right){x}-57a+360$ |
| 19.1-a1 |
19.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
19.1 |
\( 19 \) |
\( 19^{6} \) |
$2.30011$ |
$(3a-19)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2 \) |
$1$ |
$6.315973634$ |
1.024586218 |
\( \frac{10648000}{6859} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 34 a + 219\) , \( 232 a + 1433\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(34a+219\right){x}+232a+1433$ |
| 19.1-b1 |
19.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$2.30011$ |
$(3a-19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$41.68961490$ |
$0.205438503$ |
2.778740071 |
\( -\frac{50357871050752}{19} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -769\) , \( -8470\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-769{x}-8470$ |
| 19.1-b2 |
19.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
19.1 |
\( 19 \) |
\( 19^{6} \) |
$2.30011$ |
$(3a-19)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$13.89653830$ |
$1.848946532$ |
2.778740071 |
\( -\frac{89915392}{6859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -9\) , \( -15\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-9{x}-15$ |
| 19.1-b3 |
19.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$2.30011$ |
$(3a-19)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$4.632179434$ |
$16.64051879$ |
2.778740071 |
\( \frac{32768}{19} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+{x}$ |
| 19.1-c1 |
19.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$2.30011$ |
$(3a-19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.731231101$ |
$12.79541874$ |
3.035619650 |
\( -\frac{2299968}{19} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -17 a - 65\) , \( -149 a - 876\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-17a-65\right){x}-149a-876$ |
| 19.1-d1 |
19.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
19.1 |
\( 19 \) |
\( 19^{6} \) |
$2.30011$ |
$(3a-19)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2 \) |
$1$ |
$6.315973634$ |
1.024586218 |
\( \frac{10648000}{6859} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -35 a + 219\) , \( -232 a + 1433\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-35a+219\right){x}-232a+1433$ |
| 19.1-e1 |
19.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$2.30011$ |
$(3a-19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.595904332$ |
$17.03289160$ |
3.293086381 |
\( -\frac{50357871050752}{19} \) |
\( \bigl[0\) , \( -1\) , \( a + 1\) , \( 341584 a - 2105665\) , \( -269922166 a + 1663911967\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(341584a-2105665\right){x}-269922166a+1663911967$ |
| 19.1-e2 |
19.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
19.1 |
\( 19 \) |
\( 19^{6} \) |
$2.30011$ |
$(3a-19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \cdot 3 \) |
$0.198634777$ |
$17.03289160$ |
3.293086381 |
\( -\frac{89915392}{6859} \) |
\( \bigl[0\) , \( -1\) , \( a + 1\) , \( 4144 a - 25545\) , \( -384936 a + 2372892\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(4144a-25545\right){x}-384936a+2372892$ |
| 19.1-e3 |
19.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$2.30011$ |
$(3a-19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.595904332$ |
$17.03289160$ |
3.293086381 |
\( \frac{32768}{19} \) |
\( \bigl[0\) , \( -1\) , \( a + 1\) , \( 296 a + 1825\) , \( 205 a + 1257\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(296a+1825\right){x}+205a+1257$ |
| 19.1-f1 |
19.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$2.30011$ |
$(3a-19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.731231101$ |
$12.79541874$ |
3.035619650 |
\( -\frac{2299968}{19} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 16 a - 65\) , \( 149 a - 876\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(16a-65\right){x}+149a-876$ |
| 22.1-a1 |
22.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{6} \cdot 11^{3} \) |
$2.38598$ |
$(-a-6), (-a+7)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$2.087525364$ |
3.047771981 |
\( \frac{5339530805}{10648} a - \frac{32950208549}{10648} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 601 a - 3690\) , \( 22656 a - 139650\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(601a-3690\right){x}+22656a-139650$ |
| 22.1-b1 |
22.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2 \cdot 11^{5} \) |
$2.38598$ |
$(-a-6), (-a+7)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$9$ |
\( 5 \) |
$1$ |
$1.110557261$ |
4.053513987 |
\( -\frac{689814863492301}{322102} a + \frac{2125836434628648}{161051} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 859 a - 5176\) , \( 33615 a - 206970\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(859a-5176\right){x}+33615a-206970$ |
| 22.1-b2 |
22.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2^{5} \cdot 11 \) |
$2.38598$ |
$(-a-6), (-a+7)$ |
$0$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$9$ |
\( 5 \) |
$1$ |
$27.76393154$ |
4.053513987 |
\( -\frac{21141}{88} a + \frac{33588}{11} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 14 a + 34\) , \( 12 a + 180\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(14a+34\right){x}+12a+180$ |
| 22.1-c1 |
22.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{6} \cdot 11^{3} \) |
$2.38598$ |
$(-a-6), (-a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2 \cdot 3 \) |
$0.093479625$ |
$27.42927522$ |
2.495690633 |
\( \frac{5339530805}{10648} a - \frac{32950208549}{10648} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -3 a - 7\) , \( 15 a + 87\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a-7\right){x}+15a+87$ |
| 22.1-d1 |
22.1-d |
$2$ |
$5$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2 \cdot 11^{5} \) |
$2.38598$ |
$(-a-6), (-a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 5 \) |
$0.175606115$ |
$19.56167963$ |
2.786275040 |
\( -\frac{689814863492301}{322102} a + \frac{2125836434628648}{161051} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -470 a - 2899\) , \( 13901 a + 85693\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-470a-2899\right){x}+13901a+85693$ |
| 22.1-d2 |
22.1-d |
$2$ |
$5$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2^{5} \cdot 11 \) |
$2.38598$ |
$(-a-6), (-a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$0.878030577$ |
$19.56167963$ |
2.786275040 |
\( -\frac{21141}{88} a + \frac{33588}{11} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 5 a + 31\) , \( -6 a - 37\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(5a+31\right){x}-6a-37$ |
| 22.2-a1 |
22.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
22.2 |
\( 2 \cdot 11 \) |
\( 2^{6} \cdot 11^{3} \) |
$2.38598$ |
$(-a-6), (a+7)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$2.087525364$ |
3.047771981 |
\( -\frac{5339530805}{10648} a - \frac{32950208549}{10648} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -601 a - 3690\) , \( -22656 a - 139650\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-601a-3690\right){x}-22656a-139650$ |
| 22.2-b1 |
22.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
22.2 |
\( 2 \cdot 11 \) |
\( - 2^{5} \cdot 11 \) |
$2.38598$ |
$(-a-6), (a+7)$ |
$0$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$9$ |
\( 5 \) |
$1$ |
$27.76393154$ |
4.053513987 |
\( \frac{21141}{88} a + \frac{33588}{11} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 5 a + 15\) , \( 3 a + 9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(5a+15\right){x}+3a+9$ |
| 22.2-b2 |
22.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
22.2 |
\( 2 \cdot 11 \) |
\( - 2 \cdot 11^{5} \) |
$2.38598$ |
$(-a-6), (a+7)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$9$ |
\( 5 \) |
$1$ |
$1.110557261$ |
4.053513987 |
\( \frac{689814863492301}{322102} a + \frac{2125836434628648}{161051} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( -840 a - 5195\) , \( -38810 a - 239251\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-840a-5195\right){x}-38810a-239251$ |
| 22.2-c1 |
22.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
22.2 |
\( 2 \cdot 11 \) |
\( 2^{6} \cdot 11^{3} \) |
$2.38598$ |
$(-a-6), (a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2 \cdot 3 \) |
$0.093479625$ |
$27.42927522$ |
2.495690633 |
\( -\frac{5339530805}{10648} a - \frac{32950208549}{10648} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 2 a - 7\) , \( -15 a + 87\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a-7\right){x}-15a+87$ |
| 22.2-d1 |
22.2-d |
$2$ |
$5$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
22.2 |
\( 2 \cdot 11 \) |
\( - 2^{5} \cdot 11 \) |
$2.38598$ |
$(-a-6), (a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$0.878030577$ |
$19.56167963$ |
2.786275040 |
\( \frac{21141}{88} a + \frac{33588}{11} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -5 a + 31\) , \( 6 a - 37\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-5a+31\right){x}+6a-37$ |
| 22.2-d2 |
22.2-d |
$2$ |
$5$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
22.2 |
\( 2 \cdot 11 \) |
\( - 2 \cdot 11^{5} \) |
$2.38598$ |
$(-a-6), (a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 5 \) |
$0.175606115$ |
$19.56167963$ |
2.786275040 |
\( \frac{689814863492301}{322102} a + \frac{2125836434628648}{161051} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 470 a - 2899\) , \( -13901 a + 85693\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(470a-2899\right){x}-13901a+85693$ |
| 26.1-a1 |
26.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( - 2^{8} \cdot 13 \) |
$2.48773$ |
$(-a-6), (a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.405491309$ |
$10.82199744$ |
5.694913962 |
\( \frac{426533}{208} a - \frac{2186819}{208} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -a + 6\) , \( a + 5\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a+6\right){x}+a+5$ |
| 26.1-b1 |
26.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( - 2^{4} \cdot 13 \) |
$2.48773$ |
$(-a-6), (a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.225757248$ |
$38.42654873$ |
5.629129986 |
\( \frac{37576645441}{52} a + \frac{231628356997}{52} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 106 a - 642\) , \( -1260 a + 7760\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(106a-642\right){x}-1260a+7760$ |
| 26.1-c1 |
26.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( - 2^{4} \cdot 13 \) |
$2.48773$ |
$(-a-6), (a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$3.016839248$ |
$2.728415556$ |
2.670551047 |
\( \frac{37576645441}{52} a + \frac{231628356997}{52} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -106 a - 607\) , \( -1614 a - 9889\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-106a-607\right){x}-1614a-9889$ |
| 26.1-d1 |
26.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( - 2^{8} \cdot 13 \) |
$2.48773$ |
$(-a-6), (a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.249960593$ |
$30.75820572$ |
2.494426677 |
\( \frac{426533}{208} a - \frac{2186819}{208} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 80 a - 504\) , \( -729 a + 4492\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(80a-504\right){x}-729a+4492$ |
| 26.2-a1 |
26.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
26.2 |
\( 2 \cdot 13 \) |
\( - 2^{8} \cdot 13 \) |
$2.48773$ |
$(-a-6), (a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.405491309$ |
$10.82199744$ |
5.694913962 |
\( -\frac{426533}{208} a - \frac{2186819}{208} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 6\) , \( -2 a + 5\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+6{x}-2a+5$ |
| 26.2-b1 |
26.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
26.2 |
\( 2 \cdot 13 \) |
\( - 2^{4} \cdot 13 \) |
$2.48773$ |
$(-a-6), (a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.225757248$ |
$38.42654873$ |
5.629129986 |
\( -\frac{37576645441}{52} a + \frac{231628356997}{52} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -106 a - 642\) , \( 1260 a + 7760\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-106a-642\right){x}+1260a+7760$ |
| 26.2-c1 |
26.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
26.2 |
\( 2 \cdot 13 \) |
\( - 2^{4} \cdot 13 \) |
$2.48773$ |
$(-a-6), (a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$3.016839248$ |
$2.728415556$ |
2.670551047 |
\( -\frac{37576645441}{52} a + \frac{231628356997}{52} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 106 a - 607\) , \( 1614 a - 9889\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(106a-607\right){x}+1614a-9889$ |
| 26.2-d1 |
26.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
26.2 |
\( 2 \cdot 13 \) |
\( - 2^{8} \cdot 13 \) |
$2.48773$ |
$(-a-6), (a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.249960593$ |
$30.75820572$ |
2.494426677 |
\( -\frac{426533}{208} a - \frac{2186819}{208} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -82 a - 504\) , \( 728 a + 4492\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-82a-504\right){x}+728a+4492$ |
| 32.1-a1 |
32.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$2.62028$ |
$(-a-6)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3Nn |
$1$ |
\( 2 \) |
$1$ |
$12.57159272$ |
2.039381637 |
\( -8000 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 11\) , \( -a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+11{x}-a$ |
| 32.1-b1 |
32.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$2.62028$ |
$(-a-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3Nn |
$1$ |
\( 2 \) |
$0.869038602$ |
$12.57159272$ |
3.544602734 |
\( -8000 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -740 a - 4549\) , \( 28481 a + 175560\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-740a-4549\right){x}+28481a+175560$ |
| 32.1-c1 |
32.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$2.62028$ |
$(-a-6)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$7.228619307$ |
$27.50074327$ |
4.031048281 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}$ |
| 32.1-c2 |
32.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$2.62028$ |
$(-a-6)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$14.45723861$ |
$13.75037163$ |
4.031048281 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 444 a + 2737\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(444a+2737\right){x}$ |
| 32.1-c3 |
32.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$2.62028$ |
$(-a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$3.614309653$ |
$13.75037163$ |
4.031048281 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -1221 a - 7509\) , \( -61761 a - 380687\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-1221a-7509\right){x}-61761a-380687$ |
| 32.1-c4 |
32.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$2.62028$ |
$(-a-6)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$3.614309653$ |
$55.00148654$ |
4.031048281 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -1221 a - 7490\) , \( 53214 a + 328076\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-1221a-7490\right){x}+53214a+328076$ |
| 32.1-d1 |
32.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$2.62028$ |
$(-a-6)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$13.75037163$ |
0.557651206 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}$ |
| 32.1-d2 |
32.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$2.62028$ |
$(-a-6)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$27.50074327$ |
0.557651206 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -444 a - 2737\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-444a-2737\right){x}$ |
| 32.1-d3 |
32.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$2.62028$ |
$(-a-6)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$13.75037163$ |
0.557651206 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 15\) , \( 22\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+15{x}+22$ |
| 32.1-d4 |
32.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$2.62028$ |
$(-a-6)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$55.00148654$ |
0.557651206 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 34\) , \( 35\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+34{x}+35$ |
| 32.1-e1 |
32.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$2.62028$ |
$(-a-6)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3Nn |
$1$ |
\( 2 \) |
$1$ |
$12.57159272$ |
2.039381637 |
\( -8000 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 11\) , \( a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+11{x}+a$ |
| 32.1-f1 |
32.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$2.62028$ |
$(-a-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3Nn |
$1$ |
\( 2 \) |
$0.869038602$ |
$12.57159272$ |
3.544602734 |
\( -8000 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 740 a - 4549\) , \( -28481 a + 175560\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(740a-4549\right){x}-28481a+175560$ |
| 34.1-a1 |
34.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
34.1 |
\( 2 \cdot 17 \) |
\( 2^{4} \cdot 17 \) |
$2.66030$ |
$(-a-6), (2a-13)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$43.84367238$ |
1.778095710 |
\( -\frac{30286}{17} a + \frac{933185}{68} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 299 a - 1832\) , \( -6106 a + 37632\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(299a-1832\right){x}-6106a+37632$ |
| 34.1-a2 |
34.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
34.1 |
\( 2 \cdot 17 \) |
\( 2^{2} \cdot 17^{2} \) |
$2.66030$ |
$(-a-6), (2a-13)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$21.92183619$ |
1.778095710 |
\( -\frac{13448510910}{289} a + \frac{165825143353}{578} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 4739 a - 29202\) , \( -430790 a + 2655560\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(4739a-29202\right){x}-430790a+2655560$ |
| 34.1-b1 |
34.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
34.1 |
\( 2 \cdot 17 \) |
\( 2^{4} \cdot 17 \) |
$2.66030$ |
$(-a-6), (2a-13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.703437555$ |
$22.75725313$ |
6.288604174 |
\( -\frac{30286}{17} a + \frac{933185}{68} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -4 a + 8\) , \( -5 a + 21\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a+8\right){x}-5a+21$ |
| 34.1-b2 |
34.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{38}) \) |
$2$ |
$[2, 0]$ |
34.1 |
\( 2 \cdot 17 \) |
\( 2^{2} \cdot 17^{2} \) |
$2.66030$ |
$(-a-6), (2a-13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.406875110$ |
$11.37862656$ |
6.288604174 |
\( -\frac{13448510910}{289} a + \frac{165825143353}{578} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -4 a - 2\) , \( -a - 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a-2\right){x}-a-7$ |
*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.
