| 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 |
| 3.1-a1 |
3.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
3.1 |
\( 3 \) |
\( 3^{2} \cdot 11^{12} \) |
$3.55737$ |
$(3,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$7.541802879$ |
$22.75869569$ |
5.674296155 |
\( -\frac{2197}{3} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 2 a - 78\) , \( -15 a - 244\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(2a-78\right){x}-15a-244$ |
| 3.1-a2 |
3.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
3.1 |
\( 3 \) |
\( 3^{4} \cdot 11^{12} \) |
$3.55737$ |
$(3,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$3.770901439$ |
$11.37934784$ |
5.674296155 |
\( \frac{16194277}{9} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 42 a - 103\) , \( -307 a - 7382\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(42a-103\right){x}-307a-7382$ |
| 3.1-b1 |
3.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
3.1 |
\( 3 \) |
\( 3^{2} \cdot 11^{12} \) |
$3.55737$ |
$(3,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$7.541802879$ |
$22.75869569$ |
5.674296155 |
\( -\frac{2197}{3} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -2 a - 76\) , \( 15 a - 259\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-a{x}^2+\left(-2a-76\right){x}+15a-259$ |
| 3.1-b2 |
3.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
3.1 |
\( 3 \) |
\( 3^{4} \cdot 11^{12} \) |
$3.55737$ |
$(3,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$3.770901439$ |
$11.37934784$ |
5.674296155 |
\( \frac{16194277}{9} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -42 a - 61\) , \( 307 a - 7689\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-a{x}^2+\left(-42a-61\right){x}+307a-7689$ |
| 3.1-c1 |
3.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
3.1 |
\( 3 \) |
\( 3^{12} \cdot 11^{12} \) |
$3.55737$ |
$(3,a+1)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3Nn |
|
\( 2 \) |
$1$ |
$5.874637753$ |
7.575174279 |
\( -\frac{620650477}{729} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 142 a - 165\) , \( 1792 a + 15098\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(a-1\right){x}^2+\left(142a-165\right){x}+1792a+15098$ |
| 3.1-d1 |
3.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
3.1 |
\( 3 \) |
\( 3^{12} \cdot 11^{12} \) |
$3.55737$ |
$(3,a+1)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3Nn |
|
\( 2 \) |
$1$ |
$5.874637753$ |
7.575174279 |
\( -\frac{620650477}{729} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -142 a - 23\) , \( -1792 a + 16890\bigr] \) |
${y}^2+{x}{y}={x}^3-a{x}^2+\left(-142a-23\right){x}-1792a+16890$ |
| 3.1-e1 |
3.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
3.1 |
\( 3 \) |
\( 3^{12} \cdot 7^{12} \) |
$3.55737$ |
$(3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$5.874637753$ |
2.330514401 |
\( -\frac{620650477}{729} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 25 a + 1304\) , \( -519 a - 4771\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+{x}^2+\left(25a+1304\right){x}-519a-4771$ |
| 3.1-f1 |
3.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
3.1 |
\( 3 \) |
\( 3^{12} \cdot 7^{12} \) |
$3.55737$ |
$(3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$5.874637753$ |
2.330514401 |
\( -\frac{620650477}{729} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -25 a + 1558\) , \( 543 a - 6619\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-25a+1558\right){x}+543a-6619$ |
| 3.1-g1 |
3.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
3.1 |
\( 3 \) |
\( 3^{2} \cdot 7^{12} \) |
$3.55737$ |
$(3,a+1)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$22.75869569$ |
6.019034171 |
\( -\frac{2197}{3} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -27 a + 1007\) , \( 240 a - 5872\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2+\left(-27a+1007\right){x}+240a-5872$ |
| 3.1-g2 |
3.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
3.1 |
\( 3 \) |
\( 3^{4} \cdot 7^{12} \) |
$3.55737$ |
$(3,a+1)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$11.37934784$ |
6.019034171 |
\( \frac{16194277}{9} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -12 a + 1092\) , \( -36 a - 9837\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2+\left(-12a+1092\right){x}-36a-9837$ |
| 3.1-h1 |
3.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
3.1 |
\( 3 \) |
\( 3^{2} \cdot 7^{12} \) |
$3.55737$ |
$(3,a+1)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$22.75869569$ |
6.019034171 |
\( -\frac{2197}{3} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 28 a + 1208\) , \( -268 a - 6611\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(28a+1208\right){x}-268a-6611$ |
| 3.1-h2 |
3.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
3.1 |
\( 3 \) |
\( 3^{4} \cdot 7^{12} \) |
$3.55737$ |
$(3,a+1)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$11.37934784$ |
6.019034171 |
\( \frac{16194277}{9} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 13 a + 1308\) , \( 23 a - 10952\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(13a+1308\right){x}+23a-10952$ |
| 4.1-a1 |
4.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
4.1 |
\( 2^{2} \) |
\( 2^{12} \cdot 11^{12} \) |
$3.82265$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2 \) |
$2.313276456$ |
$14.00032278$ |
4.282674136 |
\( -\frac{2197}{64} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -a - 75\) , \( 15 a - 248\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(a+1\right){x}^2+\left(-a-75\right){x}+15a-248$ |
| 4.1-b1 |
4.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
4.1 |
\( 2^{2} \) |
\( 2^{12} \cdot 11^{12} \) |
$3.82265$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2 \) |
$2.313276456$ |
$14.00032278$ |
4.282674136 |
\( -\frac{2197}{64} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 3 a - 78\) , \( -17 a - 156\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(3a-78\right){x}-17a-156$ |
| 4.1-c1 |
4.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
4.1 |
\( 2^{2} \) |
\( 2^{12} \cdot 7^{12} \) |
$3.82265$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2 \) |
$2.923017799$ |
$14.00032278$ |
5.411516076 |
\( -\frac{2197}{64} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 28 a + 1055\) , \( -257 a - 6408\bigr] \) |
${y}^2+a{x}{y}={x}^3-a{x}^2+\left(28a+1055\right){x}-257a-6408$ |
| 4.1-d1 |
4.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
4.1 |
\( 2^{2} \) |
\( 2^{12} \cdot 7^{12} \) |
$3.82265$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2 \) |
$2.923017799$ |
$14.00032278$ |
5.411516076 |
\( -\frac{2197}{64} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -28 a + 1083\) , \( 257 a - 6665\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-{x}^2+\left(-28a+1083\right){x}+257a-6665$ |
| 5.1-a1 |
5.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
5.1 |
\( 5 \) |
\( 5^{12} \cdot 7^{12} \) |
$4.04196$ |
$(5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$5.586762818$ |
2.216312179 |
\( \frac{2248091}{15625} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -36 a + 956\) , \( 420 a - 2451\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2+\left(-36a+956\right){x}+420a-2451$ |
| 5.1-a2 |
5.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
5.1 |
\( 5 \) |
\( 5^{6} \cdot 7^{12} \) |
$4.04196$ |
$(5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$11.17352563$ |
2.216312179 |
\( \frac{1295029}{125} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -21 a + 1041\) , \( 144 a - 6416\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2+\left(-21a+1041\right){x}+144a-6416$ |
| 5.1-b1 |
5.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
5.1 |
\( 5 \) |
\( 5^{12} \cdot 7^{12} \) |
$4.04196$ |
$(5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$5.586762818$ |
2.216312179 |
\( \frac{2248091}{15625} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 37 a + 1148\) , \( -457 a - 2950\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(37a+1148\right){x}-457a-2950$ |
| 5.1-b2 |
5.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
5.1 |
\( 5 \) |
\( 5^{6} \cdot 7^{12} \) |
$4.04196$ |
$(5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$11.17352563$ |
2.216312179 |
\( \frac{1295029}{125} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 22 a + 1248\) , \( -166 a - 7291\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(22a+1248\right){x}-166a-7291$ |
| 5.1-c1 |
5.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
5.1 |
\( 5 \) |
\( 5^{12} \cdot 11^{12} \) |
$4.04196$ |
$(5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 2 \) |
$14.88539355$ |
$5.586762818$ |
10.99689301 |
\( \frac{2248091}{15625} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 22 a - 85\) , \( -357 a + 7201\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-a{x}^2+\left(22a-85\right){x}-357a+7201$ |
| 5.1-c2 |
5.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
5.1 |
\( 5 \) |
\( 5^{6} \cdot 11^{12} \) |
$4.04196$ |
$(5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 2 \) |
$7.442696777$ |
$11.17352563$ |
10.99689301 |
\( \frac{1295029}{125} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -18 a - 70\) , \( -65 a - 229\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-a{x}^2+\left(-18a-70\right){x}-65a-229$ |
| 5.1-d1 |
5.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
5.1 |
\( 5 \) |
\( 5^{12} \cdot 11^{12} \) |
$4.04196$ |
$(5,a+2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
|
\( 2 \) |
$1$ |
$5.586762818$ |
10.99689301 |
\( \frac{2248091}{15625} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -22 a - 63\) , \( 357 a + 6844\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-22a-63\right){x}+357a+6844$ |
| 5.1-d2 |
5.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
5.1 |
\( 5 \) |
\( 5^{6} \cdot 11^{12} \) |
$4.04196$ |
$(5,a+2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
|
\( 2 \) |
$1$ |
$11.17352563$ |
10.99689301 |
\( \frac{1295029}{125} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 18 a - 88\) , \( 65 a - 294\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(18a-88\right){x}+65a-294$ |
| 15.1-a1 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{32} \cdot 5^{2} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1$ |
$1.117850856$ |
0.591280150 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$ |
| 15.1-a2 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$17.88561370$ |
0.591280150 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2$ |
| 15.1-a3 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{16} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{5} \) |
$1$ |
$2.235701712$ |
0.591280150 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+35{x}-28$ |
| 15.1-a4 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{4} \) |
$1$ |
$4.471403425$ |
0.591280150 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$ |
| 15.1-a5 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{3} \) |
$1$ |
$8.942806850$ |
0.591280150 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$ |
| 15.1-a6 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{4} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{3} \) |
$1$ |
$2.235701712$ |
0.591280150 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$ |
| 15.1-a7 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1$ |
$4.471403425$ |
0.591280150 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-80{x}+242$ |
| 15.1-a8 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1$ |
$1.117850856$ |
0.591280150 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-2160{x}-39540$ |
| 15.1-b1 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{32} \cdot 5^{2} \cdot 19^{12} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$64$ |
\( 2^{2} \) |
$1$ |
$1.117850856$ |
2.365120600 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 2465 a + 10201\) , \( 99528 a + 4725058\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+a{x}^2+\left(2465a+10201\right){x}+99528a+4725058$ |
| 15.1-b2 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \cdot 19^{12} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
$0 \le r \le 2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1$ |
$17.88561370$ |
2.365120600 |
\( -\frac{1}{15} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -65 a + 851\) , \( 528 a - 3732\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+a{x}^2+\left(-65a+851\right){x}+528a-3732$ |
| 15.1-b3 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{16} \cdot 19^{12} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$2.235701712$ |
2.365120600 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -870 a - 2124\) , \( 20772 a + 428049\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+a{x}^2+\left(-870a-2124\right){x}+20772a+428049$ |
| 15.1-b4 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \cdot 19^{12} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{4} \) |
$1$ |
$4.471403425$ |
2.365120600 |
\( \frac{111284641}{50625} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 165 a + 1701\) , \( -2232 a - 13932\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+a{x}^2+\left(165a+1701\right){x}-2232a-13932$ |
| 15.1-b5 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \cdot 19^{12} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{3} \) |
$1$ |
$8.942806850$ |
2.365120600 |
\( \frac{13997521}{225} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 50 a + 1276\) , \( -2028 a - 52841\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+a{x}^2+\left(50a+1276\right){x}-2028a-52841$ |
| 15.1-b6 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{4} \cdot 19^{12} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$64$ |
\( 2^{3} \) |
$1$ |
$2.235701712$ |
2.365120600 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 3040 a + 12326\) , \( 51468 a + 3159243\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+a{x}^2+\left(3040a+12326\right){x}+51468a+3159243$ |
| 15.1-b7 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \cdot 19^{12} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1$ |
$4.471403425$ |
2.365120600 |
\( \frac{56667352321}{15} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 1775 a + 7651\) , \( -75648 a - 2109746\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+a{x}^2+\left(1775a+7651\right){x}-75648a-2109746$ |
| 15.1-b8 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \cdot 19^{12} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$64$ |
\( 2^{2} \) |
$1$ |
$1.117850856$ |
2.365120600 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 49615 a + 184451\) , \( 5684208 a + 232801128\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+a{x}^2+\left(49615a+184451\right){x}+5684208a+232801128$ |
| 15.1-c1 |
15.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{18} \cdot 5^{6} \cdot 11^{12} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cn, 3Nn |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.414514081$ |
2.244594867 |
\( -\frac{4359504941056}{2460375} \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -2723 a + 945\) , \( 151974 a - 2530791\bigr] \) |
${y}^2+{y}={x}^3+\left(-a+1\right){x}^2+\left(-2723a+945\right){x}+151974a-2530791$ |
| 15.1-d1 |
15.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{18} \cdot 5^{6} \cdot 11^{12} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cn, 3Nn |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.414514081$ |
2.244594867 |
\( -\frac{4359504941056}{2460375} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( 2723 a - 1778\) , \( -151974 a - 2378817\bigr] \) |
${y}^2+{y}={x}^3+a{x}^2+\left(2723a-1778\right){x}-151974a-2378817$ |
| 15.1-e1 |
15.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{32} \cdot 5^{14} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$16.01324138$ |
$1.117850856$ |
9.468311766 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2751\) , \( -104477\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2751{x}-104477$ |
| 15.1-e2 |
15.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{14} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$4.003310345$ |
$17.88561370$ |
9.468311766 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 23\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}+23$ |
| 15.1-e3 |
15.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{28} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$16.01324138$ |
$2.235701712$ |
9.468311766 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 874\) , \( -5227\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+874{x}-5227$ |
| 15.1-e4 |
15.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{20} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$16.01324138$ |
$4.471403425$ |
9.468311766 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -251\) , \( -727\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-251{x}-727$ |
| 15.1-e5 |
15.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{16} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$16.01324138$ |
$8.942806850$ |
9.468311766 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( 523\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-126{x}+523$ |
| 15.1-e6 |
15.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{16} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$16.01324138$ |
$2.235701712$ |
9.468311766 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -3376\) , \( -75727\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-3376{x}-75727$ |
| 15.1-e7 |
15.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{14} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$16.01324138$ |
$4.471403425$ |
9.468311766 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2001\) , \( 34273\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2001{x}+34273$ |
| 15.1-e8 |
15.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{-915}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{14} \) |
$5.31951$ |
$(3,a+1), (5,a+2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$16.01324138$ |
$1.117850856$ |
9.468311766 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -54001\) , \( -4834477\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-54001{x}-4834477$ |
*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.
