| 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 |
| 49.1-CMa1 |
49.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49.1 |
\( 7^{2} \) |
\( 7^{2} \) |
$0.40949$ |
$(-3a+1)$ |
0 |
$\Z/7\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$7$ |
7Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$10.15449534$ |
0.239293902 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( a\) , \( a\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}$ |
| 49.3-CMa1 |
49.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
49.3 |
\( 7^{2} \) |
\( 7^{2} \) |
$0.40949$ |
$(3a-2)$ |
0 |
$\Z/7\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$7$ |
7Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$10.15449534$ |
0.239293902 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( a\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-a$ |
| 73.1-a1 |
73.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
73.1 |
\( 73 \) |
\( 73^{3} \) |
$0.45241$ |
$(-9a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$3.242334089$ |
0.311993743 |
\( \frac{60988685561}{389017} a - \frac{169775626841}{389017} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 6 a + 10\) , \( -11 a + 20\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a+10\right){x}-11a+20$ |
| 73.1-a2 |
73.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
73.1 |
\( 73 \) |
\( 73^{2} \) |
$0.45241$ |
$(-9a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$4.863501133$ |
0.311993743 |
\( -\frac{927841113}{5329} a - \frac{395933743}{5329} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 5\) , \( -4 a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+5{x}-4a+4$ |
| 73.1-a3 |
73.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
73.1 |
\( 73 \) |
\( 73 \) |
$0.45241$ |
$(-9a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$9.727002267$ |
0.311993743 |
\( \frac{9927}{73} a + \frac{20960}{73} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}$ |
| 73.1-a4 |
73.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
73.1 |
\( 73 \) |
\( 73^{6} \) |
$0.45241$ |
$(-9a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.621167044$ |
0.311993743 |
\( -\frac{55816089234767}{151334226289} a + \frac{107352826006104}{151334226289} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 11 a + 5\) , \( -20 a + 11\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(11a+5\right){x}-20a+11$ |
| 73.2-a1 |
73.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
73.2 |
\( 73 \) |
\( 73^{3} \) |
$0.45241$ |
$(9a-8)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$3.242334089$ |
0.311993743 |
\( -\frac{60988685561}{389017} a - \frac{108786941280}{389017} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -4 a + 14\) , \( 16 a - 6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a+14\right){x}+16a-6$ |
| 73.2-a2 |
73.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
73.2 |
\( 73 \) |
\( 73^{2} \) |
$0.45241$ |
$(9a-8)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$4.863501133$ |
0.311993743 |
\( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -6 a - 1\) , \( 4 a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a-1\right){x}+4a$ |
| 73.2-a3 |
73.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
73.2 |
\( 73 \) |
\( 73 \) |
$0.45241$ |
$(9a-8)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$9.727002267$ |
0.311993743 |
\( -\frac{9927}{73} a + \frac{30887}{73} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-1\right){x}$ |
| 73.2-a4 |
73.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
73.2 |
\( 73 \) |
\( 73^{6} \) |
$0.45241$ |
$(9a-8)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.621167044$ |
0.311993743 |
\( \frac{55816089234767}{151334226289} a + \frac{51536736771337}{151334226289} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -9 a + 14\) , \( 30 a - 24\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9a+14\right){x}+30a-24$ |
| 75.1-a1 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{32} \cdot 5^{2} \) |
$0.45547$ |
$(-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$0.558925428$ |
0.322695746 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-110{x}-880$ |
| 75.1-a2 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$0.45547$ |
$(-2a+1), (5)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.942806850$ |
0.322695746 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$ |
| 75.1-a3 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{16} \) |
$0.45547$ |
$(-2a+1), (5)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.117850856$ |
0.322695746 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$ |
| 75.1-a4 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{8} \) |
$0.45547$ |
$(-2a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.235701712$ |
0.322695746 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$ |
| 75.1-a5 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{4} \) |
$0.45547$ |
$(-2a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$4.471403425$ |
0.322695746 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$ |
| 75.1-a6 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{4} \) |
$0.45547$ |
$(-2a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$1.117850856$ |
0.322695746 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-135{x}-660$ |
| 75.1-a7 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$0.45547$ |
$(-2a+1), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.235701712$ |
0.322695746 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$ |
| 75.1-a8 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{2} \) |
$0.45547$ |
$(-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$0.558925428$ |
0.322695746 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$ |
| 81.1-CMa1 |
81.1-CMa |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{6} \) |
$0.46432$ |
$(-2a+1)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$8.108628264$ |
0.346779163 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}$ |
| 81.1-CMa2 |
81.1-CMa |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{10} \) |
$0.46432$ |
$(-2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-27$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$2.702876088$ |
0.346779163 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -30\) , \( 63\bigr] \) |
${y}^2+{y}={x}^{3}-30{x}+63$ |
| 25.1-CMa1 |
25.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25.1 |
\( 5^{2} \) |
\( 5^{3} \) |
$0.39963$ |
$(-a-2)$ |
0 |
$\Z/10\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$5$ |
5Cs.1.1 |
$1$ |
\( 2 \) |
$1$ |
$9.195427721$ |
0.183908554 |
\( 1728 \) |
\( \bigl[i + 1\) , \( i\) , \( 1\) , \( -i - 1\) , \( 0\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-i-1\right){x}$ |
| 25.3-CMa1 |
25.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25.3 |
\( 5^{2} \) |
\( 5^{3} \) |
$0.39963$ |
$(2a+1)$ |
0 |
$\Z/10\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$5$ |
5Cs.1.1 |
$1$ |
\( 2 \) |
$1$ |
$9.195427721$ |
0.183908554 |
\( 1728 \) |
\( \bigl[i + 1\) , \( i\) , \( i\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}$ |
| 64.1-CMa1 |
64.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$0.50549$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$6.875185818$ |
0.429699113 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}$ |
| 64.1-CMa2 |
64.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \) |
$0.50549$ |
$(a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{yes}$ |
$-16$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$6.875185818$ |
0.429699113 |
\( 287496 \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 2\) , \( 3 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+2{x}+3i$ |
| 65.2-a1 |
65.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.2 |
\( 5 \cdot 13 \) |
\( 5^{9} \cdot 13^{2} \) |
$0.50745$ |
$(-a-2), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.850436644$ |
0.425218322 |
\( -\frac{157034896049234432}{330078125} a - \frac{128574568523373376}{330078125} \) |
\( \bigl[i + 1\) , \( 0\) , \( i\) , \( 239 i - 399\) , \( -2869 i + 2627\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+\left(239i-399\right){x}-2869i+2627$ |
| 65.2-a2 |
65.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.2 |
\( 5 \cdot 13 \) |
\( 5^{6} \cdot 13^{3} \) |
$0.50745$ |
$(-a-2), (2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.551309934$ |
0.425218322 |
\( -\frac{2088753403392}{34328125} a - \frac{1627055822656}{34328125} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( 1\) , \( -15 i + 3\) , \( 7 i - 14\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-15i+3\right){x}+7i-14$ |
| 65.2-a3 |
65.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.2 |
\( 5 \cdot 13 \) |
\( 5^{2} \cdot 13 \) |
$0.50745$ |
$(-a-2), (2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$7.653929802$ |
0.425218322 |
\( \frac{732672}{325} a - \frac{3306304}{325} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( 1\) , \( -2\) , \( -i - 1\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+\left(i+1\right){x}^{2}-2{x}-i-1$ |
| 65.2-a4 |
65.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.2 |
\( 5 \cdot 13 \) |
\( 5^{18} \cdot 13 \) |
$0.50745$ |
$(-a-2), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.850436644$ |
0.425218322 |
\( \frac{1110974116587520512}{49591064453125} a - \frac{489671365797093184}{49591064453125} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( 1\) , \( -60 i + 98\) , \( 372 i + 410\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-60i+98\right){x}+372i+410$ |
| 65.2-a5 |
65.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.2 |
\( 5 \cdot 13 \) |
\( 5 \cdot 13^{2} \) |
$0.50745$ |
$(-a-2), (2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$7.653929802$ |
0.425218322 |
\( -\frac{1183232}{845} a - \frac{851776}{845} \) |
\( \bigl[i + 1\) , \( 0\) , \( i\) , \( -i + 1\) , \( 0\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+\left(-i+1\right){x}$ |
| 65.2-a6 |
65.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.2 |
\( 5 \cdot 13 \) |
\( 5^{3} \cdot 13^{6} \) |
$0.50745$ |
$(-a-2), (2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.551309934$ |
0.425218322 |
\( \frac{356394317312}{603351125} a + \frac{580261889216}{603351125} \) |
\( \bigl[i + 1\) , \( 0\) , \( i\) , \( 4 i - 4\) , \( -2 i + 5\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+\left(4i-4\right){x}-2i+5$ |
| 65.3-a1 |
65.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.3 |
\( 5 \cdot 13 \) |
\( 5^{9} \cdot 13^{2} \) |
$0.50745$ |
$(2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.850436644$ |
0.425218322 |
\( \frac{157034896049234432}{330078125} a - \frac{128574568523373376}{330078125} \) |
\( \bigl[i + 1\) , \( -i\) , \( i\) , \( -240 i - 399\) , \( 2869 i + 2627\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(-240i-399\right){x}+2869i+2627$ |
| 65.3-a2 |
65.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.3 |
\( 5 \cdot 13 \) |
\( 5^{6} \cdot 13^{3} \) |
$0.50745$ |
$(2a+1), (-3a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.551309934$ |
0.425218322 |
\( \frac{2088753403392}{34328125} a - \frac{1627055822656}{34328125} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i\) , \( 14 i + 4\) , \( 7 i + 14\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(14i+4\right){x}+7i+14$ |
| 65.3-a3 |
65.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.3 |
\( 5 \cdot 13 \) |
\( 5^{2} \cdot 13 \) |
$0.50745$ |
$(2a+1), (-3a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$7.653929802$ |
0.425218322 |
\( -\frac{732672}{325} a - \frac{3306304}{325} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i\) , \( -i - 1\) , \( -i + 1\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-i-1\right){x}-i+1$ |
| 65.3-a4 |
65.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.3 |
\( 5 \cdot 13 \) |
\( 5^{18} \cdot 13 \) |
$0.50745$ |
$(2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.850436644$ |
0.425218322 |
\( -\frac{1110974116587520512}{49591064453125} a - \frac{489671365797093184}{49591064453125} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i\) , \( 59 i + 99\) , \( 372 i - 410\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(59i+99\right){x}+372i-410$ |
| 65.3-a5 |
65.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.3 |
\( 5 \cdot 13 \) |
\( 5 \cdot 13^{2} \) |
$0.50745$ |
$(2a+1), (-3a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$7.653929802$ |
0.425218322 |
\( \frac{1183232}{845} a - \frac{851776}{845} \) |
\( \bigl[i + 1\) , \( -i\) , \( i\) , \( 1\) , \( 0\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}-i{x}^{2}+{x}$ |
| 65.3-a6 |
65.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65.3 |
\( 5 \cdot 13 \) |
\( 5^{3} \cdot 13^{6} \) |
$0.50745$ |
$(2a+1), (-3a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.551309934$ |
0.425218322 |
\( -\frac{356394317312}{603351125} a + \frac{580261889216}{603351125} \) |
\( \bigl[i + 1\) , \( -i\) , \( i\) , \( -5 i - 4\) , \( 2 i + 5\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(-5i-4\right){x}+2i+5$ |
| 72.1-a1 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{16} \) |
$0.52060$ |
$(a+1), (3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.817673508$ |
0.454418377 |
\( \frac{207646}{6561} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i - 4\) , \( 22 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(-i-4\right){x}+22i$ |
| 72.1-a2 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$0.52060$ |
$(a+1), (3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.270694035$ |
0.454418377 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+{x}$ |
| 72.1-a3 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$0.52060$ |
$(a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$7.270694035$ |
0.454418377 |
\( \frac{35152}{9} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i + 1\) , \( -i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(-i+1\right){x}-i$ |
| 72.1-a4 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$0.52060$ |
$(a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.635347017$ |
0.454418377 |
\( \frac{1556068}{81} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 6\) , \( -5 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+6\right){x}-5i$ |
| 72.1-a5 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$0.52060$ |
$(a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.635347017$ |
0.454418377 |
\( \frac{28756228}{3} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i + 16\) , \( -28 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(-i+16\right){x}-28i$ |
| 72.1-a6 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \) |
$0.52060$ |
$(a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.817673508$ |
0.454418377 |
\( \frac{3065617154}{9} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 96\) , \( -347 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+96\right){x}-347i$ |
| 98.1-a1 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$0.56231$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.875417135$ |
0.437708567 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -170\) , \( 874\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-170{x}+874$ |
| 98.1-a2 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$0.56231$ |
$(a+1), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$7.878754216$ |
0.437708567 |
\( -\frac{15625}{28} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( 0\) , \( 0\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}$ |
| 98.1-a3 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$0.56231$ |
$(a+1), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.626251405$ |
0.437708567 |
\( \frac{9938375}{21952} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( 5\) , \( 6\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+5{x}+6$ |
| 98.1-a4 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$0.56231$ |
$(a+1), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.313125702$ |
0.437708567 |
\( \frac{4956477625}{941192} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -35\) , \( 70\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-35{x}+70$ |
| 98.1-a5 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$0.56231$ |
$(a+1), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$3.939377108$ |
0.437708567 |
\( \frac{128787625}{98} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -10\) , \( -12\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-10{x}-12$ |
| 98.1-a6 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$0.56231$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.437708567$ |
0.437708567 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -2730\) , \( 55146\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-2730{x}+55146$ |
| 100.2-a1 |
100.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{5} \) |
$0.56516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$3.211547828$ |
0.535257971 |
\( -\frac{59648644}{625} a - \frac{119744792}{625} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( 4 i - 11\) , \( 11 i - 12\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(4i-11\right){x}+11i-12$ |
| 100.2-a2 |
100.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{5} \) |
$0.56516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$3.211547828$ |
0.535257971 |
\( \frac{59648644}{625} a - \frac{119744792}{625} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -6 i - 11\) , \( -12 i - 12\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-6i-11\right){x}-12i-12$ |
*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.
