| 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 |
| 67.1-a1 |
67.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
67.1 |
\( 67 \) |
\( 67^{2} \) |
$2.09264$ |
$(-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cn |
$1$ |
\( 2 \) |
$1$ |
$3.859482961$ |
1.886043555 |
\( -\frac{207474688}{67} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -12\) , \( -21\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-12{x}-21$ |
| 121.1-a1 |
121.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.42590$ |
$(11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$0.370308724$ |
0.814327400 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-7820{x}-263580$ |
| 121.1-a2 |
121.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
121.1 |
\( 11^{2} \) |
\( 11^{10} \) |
$2.42590$ |
$(11)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$9$ |
\( 5 \) |
$1$ |
$1.851543623$ |
0.814327400 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-10{x}-20$ |
| 121.1-a3 |
121.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.42590$ |
$(11)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$9$ |
\( 1 \) |
$1$ |
$9.257718117$ |
0.814327400 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^3-{x}^2$ |
| 153.1-a1 |
153.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
153.1 |
\( 3^{2} \cdot 17 \) |
\( 3^{10} \cdot 17^{4} \) |
$2.57246$ |
$(-a), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 5 \) |
$0.178252297$ |
$2.171532488$ |
3.783154287 |
\( \frac{232667875}{6765201} a + \frac{294541375}{20295603} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -3 a - 1\) , \( -5 a + 16\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(-3a-1\right){x}-5a+16$ |
| 153.2-a1 |
153.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
153.2 |
\( 3^{2} \cdot 17 \) |
\( 3^{10} \cdot 17^{4} \) |
$2.57246$ |
$(a-1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 5 \) |
$0.178252297$ |
$2.171532488$ |
3.783154287 |
\( -\frac{232667875}{6765201} a + \frac{58385000}{1193859} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -5 a - 14\) , \( 20\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-5a-14\right){x}+20$ |
| 196.1-a1 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$2.73678$ |
$(2), (7)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
|
\( 2 \cdot 3^{2} \) |
$1$ |
$0.875417135$ |
4.861651226 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-171{x}-874$ |
| 196.1-a2 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$2.73678$ |
$(2), (7)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
|
\( 2 \) |
$1$ |
$7.878754216$ |
4.861651226 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}$ |
| 196.1-a3 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$2.73678$ |
$(2), (7)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
|
\( 2 \cdot 3^{2} \) |
$1$ |
$2.626251405$ |
4.861651226 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+4{x}-6$ |
| 196.1-a4 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$2.73678$ |
$(2), (7)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
|
\( 2 \cdot 3^{2} \) |
$1$ |
$1.313125702$ |
4.861651226 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-36{x}-70$ |
| 196.1-a5 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$2.73678$ |
$(2), (7)$ |
$0 \le r \le 1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
|
\( 2 \) |
$1$ |
$3.939377108$ |
4.861651226 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-11{x}+12$ |
| 196.1-a6 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$2.73678$ |
$(2), (7)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
|
\( 2 \cdot 3^{2} \) |
$1$ |
$0.437708567$ |
4.861651226 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2731{x}-55146$ |
| 225.1-a1 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{32} \cdot 5^{2} \) |
$2.83284$ |
$(3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$3.066020343$ |
$0.558925428$ |
3.349742948 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$ |
| 225.1-a2 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$2.83284$ |
$(3), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$12.26408137$ |
$8.942806850$ |
3.349742948 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2$ |
| 225.1-a3 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{16} \) |
$2.83284$ |
$(3), (5)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$24.52816274$ |
$1.117850856$ |
3.349742948 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+35{x}-28$ |
| 225.1-a4 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{8} \) |
$2.83284$ |
$(3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$12.26408137$ |
$2.235701712$ |
3.349742948 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$ |
| 225.1-a5 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{4} \) |
$2.83284$ |
$(3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$24.52816274$ |
$4.471403425$ |
3.349742948 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$ |
| 225.1-a6 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{4} \) |
$2.83284$ |
$(3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$6.132040686$ |
$1.117850856$ |
3.349742948 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$ |
| 225.1-a7 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$2.83284$ |
$(3), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$49.05632549$ |
$2.235701712$ |
3.349742948 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-80{x}+242$ |
| 225.1-a8 |
225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
225.1 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{2} \) |
$2.83284$ |
$(3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$12.26408137$ |
$0.558925428$ |
3.349742948 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-2160{x}-39540$ |
| 261.1-a1 |
261.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
261.1 |
\( 3^{2} \cdot 29 \) |
\( 3^{2} \cdot 29 \) |
$2.93992$ |
$(a+3), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$8.758249111$ |
2.139980855 |
\( -\frac{863}{87} a + \frac{8884}{29} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -4 a + 6\) , \( 12\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(-4a+6\right){x}+12$ |
| 261.2-a1 |
261.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
261.2 |
\( 3^{2} \cdot 29 \) |
\( 3^{2} \cdot 29 \) |
$2.93992$ |
$(a-4), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$8.758249111$ |
2.139980855 |
\( \frac{863}{87} a + \frac{25789}{87} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -4 a - 6\) , \( -3 a + 17\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-4a-6\right){x}-3a+17$ |
| 284.1-a1 |
284.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
284.1 |
\( 2^{2} \cdot 71 \) |
\( 2^{4} \cdot 71^{3} \) |
$3.00266$ |
$(-2a+3), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$4$ |
\( 2 \) |
$1$ |
$1.614969731$ |
3.156799276 |
\( -\frac{5091264344375}{715822} a - \frac{39429602184747}{1431644} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 18 a + 36\) , \( 8 a - 552\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(a+1\right){x}^2+\left(18a+36\right){x}+8a-552$ |
| 284.1-a2 |
284.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
284.1 |
\( 2^{2} \cdot 71 \) |
\( 2^{12} \cdot 71 \) |
$3.00266$ |
$(-2a+3), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$4.844909195$ |
3.156799276 |
\( -\frac{157087}{2272} a + \frac{3906953}{4544} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -2 a - 4\) , \( 4\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(a+1\right){x}^2+\left(-2a-4\right){x}+4$ |
| 284.2-a1 |
284.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
284.2 |
\( 2^{2} \cdot 71 \) |
\( 2^{4} \cdot 71^{3} \) |
$3.00266$ |
$(2a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$4$ |
\( 2 \) |
$1$ |
$1.614969731$ |
3.156799276 |
\( \frac{5091264344375}{715822} a - \frac{49612130873497}{1431644} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -26 a + 61\) , \( 53 a - 244\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(a-1\right){x}^2+\left(-26a+61\right){x}+53a-244$ |
| 284.2-a2 |
284.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
284.2 |
\( 2^{2} \cdot 71 \) |
\( 2^{12} \cdot 71 \) |
$3.00266$ |
$(2a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$4.844909195$ |
3.156799276 |
\( \frac{157087}{2272} a + \frac{3592779}{4544} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -6 a + 1\) , \( a + 24\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(a-1\right){x}^2+\left(-6a+1\right){x}+a+24$ |
| 289.2-a1 |
289.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
289.2 |
\( 17^{2} \) |
\( 17^{8} \) |
$3.01579$ |
$(-a), (a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.255518444$ |
$2.123938699$ |
2.341051409 |
\( -\frac{35937}{83521} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}-14$ |
| 289.2-a2 |
289.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
289.2 |
\( 17^{2} \) |
\( 17^{2} \) |
$3.01579$ |
$(-a), (a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$9.022073779$ |
$8.495754796$ |
2.341051409 |
\( \frac{35937}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}$ |
| 289.2-a3 |
289.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
289.2 |
\( 17^{2} \) |
\( 17^{4} \) |
$3.01579$ |
$(-a), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$4.511036889$ |
$4.247877398$ |
2.341051409 |
\( \frac{20346417}{289} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-6{x}-4$ |
| 289.2-a4 |
289.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
289.2 |
\( 17^{2} \) |
\( 17^{2} \) |
$3.01579$ |
$(-a), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$9.022073779$ |
$2.123938699$ |
2.341051409 |
\( \frac{82483294977}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-91{x}-310$ |
| 289.2-b1 |
289.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
289.2 |
\( 17^{2} \) |
\( 17^{3} \) |
$3.01579$ |
$(-a), (a-1)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 2 \) |
$1$ |
$6.344730303$ |
5.440745087 |
\( -\frac{148207}{289} a - \frac{1202001}{289} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -a + 17\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+\left(-a+17\right){x}$ |
| 289.2-b2 |
289.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
289.2 |
\( 17^{2} \) |
\( 17^{6} \) |
$3.01579$ |
$(-a), (a-1)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
|
\( 2^{3} \) |
$1$ |
$3.172365151$ |
5.440745087 |
\( \frac{38622639}{83521} a - \frac{261111040}{83521} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -a + 12\) , \( -a + 14\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+\left(-a+12\right){x}-a+14$ |
| 289.2-b3 |
289.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
289.2 |
\( 17^{2} \) |
\( 17^{9} \) |
$3.01579$ |
$(-a), (a-1)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 2^{3} \) |
$1$ |
$1.586182575$ |
5.440745087 |
\( -\frac{1630752658559}{6975757441} a - \frac{13563750492577}{6975757441} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -6 a + 17\) , \( -a + 31\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+\left(-6a+17\right){x}-a+31$ |
| 289.2-b4 |
289.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
289.2 |
\( 17^{2} \) |
\( 17^{6} \) |
$3.01579$ |
$(-a), (a-1)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 2^{3} \) |
$1$ |
$1.586182575$ |
5.440745087 |
\( -\frac{281039152449}{83521} a + \frac{53838709537}{4913} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 4 a - 73\) , \( -45 a + 473\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+\left(4a-73\right){x}-45a+473$ |
| 289.2-c1 |
289.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
289.2 |
\( 17^{2} \) |
\( 17^{3} \) |
$3.01579$ |
$(-a), (a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$14.03823826$ |
$6.344730303$ |
5.440745087 |
\( \frac{148207}{289} a - 4672 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a + 16\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-a+16\right){x}-a$ |
| 289.2-c2 |
289.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
289.2 |
\( 17^{2} \) |
\( 17^{6} \) |
$3.01579$ |
$(-a), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$7.019119134$ |
$3.172365151$ |
5.440745087 |
\( -\frac{38622639}{83521} a - \frac{13087553}{4913} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a + 11\) , \( 13\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-a+11\right){x}+13$ |
| 289.2-c3 |
289.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
289.2 |
\( 17^{2} \) |
\( 17^{9} \) |
$3.01579$ |
$(-a), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.509559567$ |
$1.586182575$ |
5.440745087 |
\( \frac{1630752658559}{6975757441} a - \frac{893794303008}{410338673} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 4 a + 11\) , \( 30\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(4a+11\right){x}+30$ |
| 289.2-c4 |
289.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
289.2 |
\( 17^{2} \) |
\( 17^{6} \) |
$3.01579$ |
$(-a), (a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$14.03823826$ |
$1.586182575$ |
5.440745087 |
\( \frac{281039152449}{83521} a + \frac{634218909680}{83521} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -6 a - 69\) , \( 44 a + 428\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-6a-69\right){x}+44a+428$ |
| 323.1-a1 |
323.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
323.1 |
\( 17 \cdot 19 \) |
\( 17^{6} \cdot 19^{2} \) |
$3.10082$ |
$(-a), (a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$12.20177321$ |
$1.261704143$ |
5.642405987 |
\( \frac{1748866680606381}{8713662409} a - \frac{9094554943235725}{8713662409} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -16 a + 79\) , \( 27 a + 217\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-16a+79\right){x}+27a+217$ |
| 323.1-a2 |
323.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
323.1 |
\( 17 \cdot 19 \) |
\( 17^{12} \cdot 19 \) |
$3.10082$ |
$(-a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$6.100886608$ |
$0.630852071$ |
5.642405987 |
\( -\frac{2419318767383236671}{11069822507365459} a + \frac{4286199549368669726}{11069822507365459} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -11 a + 84\) , \( -5 a + 394\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-11a+84\right){x}-5a+394$ |
| 323.1-a3 |
323.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
323.1 |
\( 17 \cdot 19 \) |
\( 17^{3} \cdot 19^{4} \) |
$3.10082$ |
$(-a), (a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$6.100886608$ |
$2.523408287$ |
5.642405987 |
\( \frac{136407521111}{640267073} a + \frac{689979389248}{640267073} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -a - 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-a-1\right){x}$ |
| 323.1-a4 |
323.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
323.1 |
\( 17 \cdot 19 \) |
\( 17^{3} \cdot 19 \) |
$3.10082$ |
$(-a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$24.40354643$ |
$0.630852071$ |
5.642405987 |
\( -\frac{35375796455931953}{93347} a + \frac{37907536261605426}{93347} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -261 a + 1354\) , \( 2647 a + 18968\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-261a+1354\right){x}+2647a+18968$ |
| 323.4-a1 |
323.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
323.4 |
\( 17 \cdot 19 \) |
\( 17^{6} \cdot 19^{2} \) |
$3.10082$ |
$(a-1), (a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$12.20177321$ |
$1.261704143$ |
5.642405987 |
\( -\frac{1748866680606381}{8713662409} a - \frac{432099309566432}{512568377} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 17 a + 63\) , \( -12 a + 308\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(17a+63\right){x}-12a+308$ |
| 323.4-a2 |
323.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
323.4 |
\( 17 \cdot 19 \) |
\( 17^{12} \cdot 19 \) |
$3.10082$ |
$(a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$6.100886608$ |
$0.630852071$ |
5.642405987 |
\( \frac{2419318767383236671}{11069822507365459} a + \frac{109816516587378415}{651166029845027} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 12 a + 73\) , \( 15 a + 463\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(12a+73\right){x}+15a+463$ |
| 323.4-a3 |
323.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
323.4 |
\( 17 \cdot 19 \) |
\( 17^{3} \cdot 19^{4} \) |
$3.10082$ |
$(a-1), (a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$6.100886608$ |
$2.523408287$ |
5.642405987 |
\( -\frac{136407521111}{640267073} a + \frac{48610994727}{37662769} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 2 a - 2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(2a-2\right){x}-1$ |
| 323.4-a4 |
323.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
323.4 |
\( 17 \cdot 19 \) |
\( 17^{3} \cdot 19 \) |
$3.10082$ |
$(a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$24.40354643$ |
$0.630852071$ |
5.642405987 |
\( \frac{35375796455931953}{93347} a + \frac{148925870921969}{5491} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 262 a + 1093\) , \( -2387 a + 22709\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(262a+1093\right){x}-2387a+22709$ |
| 361.2-a1 |
361.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
361.2 |
\( 19^{2} \) |
\( 19^{2} \) |
$3.18825$ |
$(a+1), (a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$5.618953292$ |
$0.935309008$ |
2.568225355 |
\( -\frac{50357871050752}{19} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -769\) , \( -8470\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-769{x}-8470$ |
| 361.2-a2 |
361.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
361.2 |
\( 19^{2} \) |
\( 19^{6} \) |
$3.18825$ |
$(a+1), (a-2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{2} \) |
$1.872984430$ |
$2.805927025$ |
2.568225355 |
\( -\frac{89915392}{6859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -9\) , \( -15\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-9{x}-15$ |
| 361.2-a3 |
361.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
361.2 |
\( 19^{2} \) |
\( 19^{2} \) |
$3.18825$ |
$(a+1), (a-2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$5.618953292$ |
$8.417781075$ |
2.568225355 |
\( \frac{32768}{19} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^3+{x}^2+{x}$ |
| 400.1-a1 |
400.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{12} \) |
$3.27108$ |
$(2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$1.070515942$ |
1.177059041 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -36\) , \( -140\bigr] \) |
${y}^2={x}^3+{x}^2-36{x}-140$ |
*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.
