| 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 |
| 4.1-a1 |
4.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{27} \) |
$0.52105$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$2.551261986$ |
0.309385960 |
\( -\frac{55573026649}{16777216} a - \frac{85738862931}{16777216} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -9 a + 22\) , \( 106 a - 272\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-9a+22\right){x}+106a-272$ |
| 4.1-a2 |
4.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{9} \) |
$0.52105$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$22.96135788$ |
0.309385960 |
\( -\frac{110887}{256} a + \frac{66933}{64} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -a - 2\) , \( 4 a + 6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-2\right){x}+4a+6$ |
| 4.1-a3 |
4.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{27} \) |
$0.52105$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$2.551261986$ |
0.309385960 |
\( \frac{55573026649}{16777216} a - \frac{35327972395}{4194304} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 9 a + 13\) , \( -106 a - 166\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(9a+13\right){x}-106a-166$ |
| 4.1-a4 |
4.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{9} \) |
$0.52105$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$22.96135788$ |
0.309385960 |
\( \frac{110887}{256} a + \frac{156845}{256} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( a - 3\) , \( -4 a + 10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-3\right){x}-4a+10$ |
| 4.1-a5 |
4.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$0.52105$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$45.92271576$ |
0.309385960 |
\( -\frac{915957}{16} a + \frac{2374013}{16} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -2 a\) , \( 0\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}-2a{x}$ |
| 4.1-a6 |
4.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{9} \) |
$0.52105$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$2.551261986$ |
0.309385960 |
\( -\frac{653762688677050897}{64} a + \frac{418661913522614865}{16} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 981 a - 2517\) , \( 23628 a - 60528\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(981a-2517\right){x}+23628a-60528$ |
| 4.1-a7 |
4.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{18} \) |
$0.52105$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$5.102523973$ |
0.309385960 |
\( -\frac{203862548967}{4096} a + \frac{130566616997}{1024} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 61 a - 157\) , \( 348 a - 896\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(61a-157\right){x}+348a-896$ |
| 4.1-a8 |
4.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$0.52105$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$45.92271576$ |
0.309385960 |
\( \frac{915957}{16} a + \frac{182257}{2} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( a - 2\) , \( -a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(a-2\right){x}-a$ |
| 4.1-a9 |
4.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{3} \) |
$0.52105$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$22.96135788$ |
0.309385960 |
\( -\frac{54503407609}{4} a + \frac{139614751755}{4} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -12 a - 20\) , \( -28 a - 44\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-12a-20\right){x}-28a-44$ |
| 4.1-a10 |
4.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{18} \) |
$0.52105$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$5.102523973$ |
0.309385960 |
\( \frac{203862548967}{4096} a + \frac{318403919021}{4096} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -62 a - 95\) , \( -349 a - 547\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-62a-95\right){x}-349a-547$ |
| 4.1-a11 |
4.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{3} \) |
$0.52105$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$22.96135788$ |
0.309385960 |
\( \frac{54503407609}{4} a + \frac{42555672073}{2} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 11 a - 32\) , \( 27 a - 72\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(11a-32\right){x}+27a-72$ |
| 4.1-a12 |
4.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{9} \) |
$0.52105$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$2.551261986$ |
0.309385960 |
\( \frac{653762688677050897}{64} a + \frac{1020884965413408563}{64} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -982 a - 1535\) , \( -23629 a - 36899\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-982a-1535\right){x}-23629a-36899$ |
| 8.3-a1 |
8.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{11} \) |
$0.61963$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$12.69057434$ |
0.769479095 |
\( -343 a + 1029 \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 4 a + 7\) , \( -34 a - 53\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(4a+7\right){x}-34a-53$ |
| 8.3-a2 |
8.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
8.3 |
\( 2^{3} \) |
\( - 2^{10} \) |
$0.61963$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6.345287171$ |
0.769479095 |
\( -2701312025 a + 6919553753 \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 80 a + 125\) , \( 1186 a + 1852\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(80a+125\right){x}+1186a+1852$ |
| 8.3-a3 |
8.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{8} \) |
$0.61963$ |
$(-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$25.38114868$ |
0.769479095 |
\( -24225 a + 68453 \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 12 a - 37\) , \( 46 a - 121\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(12a-37\right){x}+46a-121$ |
| 8.3-a4 |
8.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{10} \) |
$0.61963$ |
$(-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$25.38114868$ |
0.769479095 |
\( 1995 a + 5021 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( a + 3\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a+3\right){x}$ |
| 8.3-a5 |
8.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
8.3 |
\( 2^{3} \) |
\( - 2^{4} \) |
$0.61963$ |
$(-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$25.38114868$ |
0.769479095 |
\( 7659605 a + 11960871 \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -5 a - 8\) , \( 2 a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-5a-8\right){x}+2a+3$ |
| 8.3-a6 |
8.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{11} \) |
$0.61963$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$12.69057434$ |
0.769479095 |
\( 21069823 a + 33751811 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -4 a - 12\) , \( -29 a - 31\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-12\right){x}-29a-31$ |
| 8.4-a1 |
8.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{4} \) |
$0.61963$ |
$(-a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$25.38114868$ |
0.769479095 |
\( -7659605 a + 19620476 \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 3 a - 11\) , \( -3 a + 6\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(3a-11\right){x}-3a+6$ |
| 8.4-a2 |
8.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{11} \) |
$0.61963$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$12.69057434$ |
0.769479095 |
\( 343 a + 686 \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -6 a + 13\) , \( 33 a - 86\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-6a+13\right){x}+33a-86$ |
| 8.4-a3 |
8.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{10} \) |
$0.61963$ |
$(-a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$25.38114868$ |
0.769479095 |
\( -1995 a + 7016 \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 2 a\) , \( a\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+2a{x}+a$ |
| 8.4-a4 |
8.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{8} \) |
$0.61963$ |
$(-a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$25.38114868$ |
0.769479095 |
\( 24225 a + 44228 \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -14 a - 23\) , \( -47 a - 74\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-14a-23\right){x}-47a-74$ |
| 8.4-a5 |
8.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{11} \) |
$0.61963$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$12.69057434$ |
0.769479095 |
\( -21069823 a + 54821634 \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 7 a - 20\) , \( 15 a - 40\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a-20\right){x}+15a-40$ |
| 8.4-a6 |
8.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{10} \) |
$0.61963$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6.345287171$ |
0.769479095 |
\( 2701312025 a + 4218241728 \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -80 a + 205\) , \( -1186 a + 3038\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-80a+205\right){x}-1186a+3038$ |
| 9.1-a1 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$0.63815$ |
$(3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$15.98892188$ |
0.969470791 |
\( -\frac{396321250}{3} a + 338397375 \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 48 a - 123\) , \( 291 a - 749\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(48a-123\right){x}+291a-749$ |
| 9.1-a2 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$0.63815$ |
$(3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$15.98892188$ |
0.969470791 |
\( -\frac{31564213125250}{3} a + \frac{80853398915125}{3} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 32 a - 79\) , \( -131 a + 330\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(32a-79\right){x}-131a+330$ |
| 9.1-a3 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{16} \) |
$0.63815$ |
$(3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$7.994460944$ |
0.969470791 |
\( \frac{5359375}{6561} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 58 a + 92\) , \( 322 a + 503\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(58a+92\right){x}+322a+503$ |
| 9.1-a4 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$0.63815$ |
$(3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$31.97784377$ |
0.969470791 |
\( \frac{274625}{81} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -22 a - 33\) , \( 71 a + 111\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-22a-33\right){x}+71a+111$ |
| 9.1-a5 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$0.63815$ |
$(3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$31.97784377$ |
0.969470791 |
\( -\frac{14326000}{9} a + \frac{36913625}{9} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 2 a - 4\) , \( -2 a + 3\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-4\right){x}-2a+3$ |
| 9.1-a6 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$0.63815$ |
$(3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$31.97784377$ |
0.969470791 |
\( \frac{14326000}{9} a + \frac{22587625}{9} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -a - 2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a-2\right){x}-1$ |
| 9.1-a7 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$0.63815$ |
$(3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$15.98892188$ |
0.969470791 |
\( \frac{396321250}{3} a + \frac{618870875}{3} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -49 a - 74\) , \( -292 a - 457\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-49a-74\right){x}-292a-457$ |
| 9.1-a8 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$0.63815$ |
$(3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$15.98892188$ |
0.969470791 |
\( \frac{31564213125250}{3} a + 16429728596625 \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -31 a - 47\) , \( 99 a + 152\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-31a-47\right){x}+99a+152$ |
| 9.1-b1 |
9.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$0.63815$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.808547756$ |
0.196101635 |
\( -\frac{13549359104}{243} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 795 a - 2035\) , \( 17928 a - 45924\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(795a-2035\right){x}+17928a-45924$ |
| 9.1-b2 |
9.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$0.63815$ |
$(3)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$20.21369391$ |
0.196101635 |
\( \frac{4096}{3} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -5 a + 15\) , \( 2 a - 6\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-5a+15\right){x}+2a-6$ |
| 16.1-a1 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{12} \) |
$0.73687$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$1.518320950$ |
0.828555571 |
\( -50671167248 a + 129796414656 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -38 a - 77\) , \( -268 a - 444\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-38a-77\right){x}-268a-444$ |
| 16.1-a2 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{12} \) |
$0.73687$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$13.66488855$ |
0.828555571 |
\( -1552 a + 4288 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a + 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+3\right){x}$ |
| 16.1-a3 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{12} \) |
$0.73687$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$13.66488855$ |
0.828555571 |
\( 1552 a + 2736 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4\) , \( a - 4\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+4{x}+a-4$ |
| 16.1-a4 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{12} \) |
$0.73687$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$1.518320950$ |
0.828555571 |
\( 50671167248 a + 79125247408 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 40 a - 116\) , \( 229 a - 596\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(40a-116\right){x}+229a-596$ |
| 16.4-a1 |
16.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.4 |
\( 2^{4} \) |
\( - 2^{4} \) |
$0.73687$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$9.235230655$ |
0.559968109 |
\( -7659605 a + 19620476 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -a - 3\) , \( -6 a - 10\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-a-3\right){x}-6a-10$ |
| 16.4-a2 |
16.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{11} \) |
$0.73687$ |
$(-a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.47046131$ |
0.559968109 |
\( 343 a + 686 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}$ |
| 16.4-a3 |
16.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{10} \) |
$0.73687$ |
$(-a+2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$36.94092262$ |
0.559968109 |
\( -1995 a + 7016 \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -9 a - 15\) , \( -6 a - 10\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-9a-15\right){x}-6a-10$ |
| 16.4-a4 |
16.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{8} \) |
$0.73687$ |
$(-a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$18.47046131$ |
0.559968109 |
\( 24225 a + 44228 \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( a\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+a{x}$ |
| 16.4-a5 |
16.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{11} \) |
$0.73687$ |
$(-a+2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$36.94092262$ |
0.559968109 |
\( -21069823 a + 54821634 \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -124 a - 195\) , \( 916 a + 1430\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-124a-195\right){x}+916a+1430$ |
| 16.4-a6 |
16.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.4 |
\( 2^{4} \) |
\( - 2^{10} \) |
$0.73687$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.617615327$ |
0.559968109 |
\( 2701312025 a + 4218241728 \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -4 a\) , \( -5 a - 20\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}-4a{x}-5a-20$ |
| 16.5-a1 |
16.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.5 |
\( 2^{4} \) |
\( 2^{11} \) |
$0.73687$ |
$(-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.47046131$ |
0.559968109 |
\( -343 a + 1029 \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -2 a\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}-2a{x}-a$ |
| 16.5-a2 |
16.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.5 |
\( 2^{4} \) |
\( - 2^{10} \) |
$0.73687$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.617615327$ |
0.559968109 |
\( -2701312025 a + 6919553753 \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 7 a - 2\) , \( 5 a - 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(7a-2\right){x}+5a-5$ |
| 16.5-a3 |
16.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.5 |
\( 2^{4} \) |
\( 2^{8} \) |
$0.73687$ |
$(-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$18.47046131$ |
0.559968109 |
\( -24225 a + 68453 \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 2 a + 3\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(2a+3\right){x}$ |
| 16.5-a4 |
16.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.5 |
\( 2^{4} \) |
\( 2^{10} \) |
$0.73687$ |
$(-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$36.94092262$ |
0.559968109 |
\( 1995 a + 5021 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 12 a - 22\) , \( -7 a + 26\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(12a-22\right){x}-7a+26$ |
| 16.5-a5 |
16.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.5 |
\( 2^{4} \) |
\( - 2^{4} \) |
$0.73687$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$9.235230655$ |
0.559968109 |
\( 7659605 a + 11960871 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 4\) , \( 5 a - 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-4\right){x}+5a-16$ |
| 16.5-a6 |
16.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
16.5 |
\( 2^{4} \) |
\( 2^{11} \) |
$0.73687$ |
$(-a-1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$36.94092262$ |
0.559968109 |
\( 21069823 a + 33751811 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 127 a - 317\) , \( -1109 a + 2848\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(127a-317\right){x}-1109a+2848$ |
*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.
