| 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 |
| 256.1-a1 |
256.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{15} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$14.78882033$ |
1.793407891 |
\( -774198 a + 1983150 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a + 1\) , \( -27 a - 42\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}-27a-42$ |
| 256.1-a2 |
256.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{21} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.697205083$ |
1.793407891 |
\( -349618194 a + 895566564 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 16 a + 13\) , \( 32 a + 34\bigr] \) |
${y}^2={x}^{3}+\left(16a+13\right){x}+32a+34$ |
| 256.1-a3 |
256.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{18} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$14.78882033$ |
1.793407891 |
\( -8748 a + 25056 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 7\) , \( 4 a + 6\bigr] \) |
${y}^2={x}^{3}+\left(-4a-7\right){x}+4a+6$ |
| 256.1-a4 |
256.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{18} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$14.78882033$ |
1.793407891 |
\( 8748 a + 16308 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 11\) , \( -4 a + 10\bigr] \) |
${y}^2={x}^{3}+\left(4a-11\right){x}-4a+10$ |
| 256.1-a5 |
256.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{15} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$14.78882033$ |
1.793407891 |
\( 774198 a + 1208952 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a + 2\) , \( 27 a - 69\bigr] \) |
${y}^2={x}^{3}+\left(-a+2\right){x}+27a-69$ |
| 256.1-a6 |
256.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{21} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.697205083$ |
1.793407891 |
\( 349618194 a + 545948370 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -16 a + 29\) , \( -32 a + 66\bigr] \) |
${y}^2={x}^{3}+\left(-16a+29\right){x}-32a+66$ |
| 256.1-b1 |
256.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{51} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.959184588$ |
1.435415367 |
\( -\frac{55573026649}{16777216} a - \frac{85738862931}{16777216} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -144 a + 360\) , \( -6784 a + 17392\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-144a+360\right){x}-6784a+17392$ |
| 256.1-b2 |
256.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{33} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.959184588$ |
1.435415367 |
\( -\frac{110887}{256} a + \frac{66933}{64} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -16 a - 24\) , \( -256 a - 400\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-16a-24\right){x}-256a-400$ |
| 256.1-b3 |
256.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{51} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.959184588$ |
1.435415367 |
\( \frac{55573026649}{16777216} a - \frac{35327972395}{4194304} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 144 a + 216\) , \( 6784 a + 10608\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(144a+216\right){x}+6784a+10608$ |
| 256.1-b4 |
256.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{33} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.959184588$ |
1.435415367 |
\( \frac{110887}{256} a + \frac{156845}{256} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 16 a - 40\) , \( 256 a - 656\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(16a-40\right){x}+256a-656$ |
| 256.1-b5 |
256.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{30} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$5.918369177$ |
1.435415367 |
\( -\frac{915957}{16} a + \frac{2374013}{16} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -15 a - 28\) , \( -16 a - 28\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-15a-28\right){x}-16a-28$ |
| 256.1-b6 |
256.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{33} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.959184588$ |
1.435415367 |
\( -\frac{653762688677050897}{64} a + \frac{418661913522614865}{16} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 15697 a - 40284\) , \( -1536816 a + 3936512\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(15697a-40284\right){x}-1536816a+3936512$ |
| 256.1-b7 |
256.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{42} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$5.918369177$ |
1.435415367 |
\( -\frac{203862548967}{4096} a + \frac{130566616997}{1024} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 977 a - 2524\) , \( -23856 a + 61184\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(977a-2524\right){x}-23856a+61184$ |
| 256.1-b8 |
256.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{30} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$5.918369177$ |
1.435415367 |
\( \frac{915957}{16} a + \frac{182257}{2} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 17 a - 44\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(17a-44\right){x}$ |
| 256.1-b9 |
256.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{27} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.959184588$ |
1.435415367 |
\( -\frac{54503407609}{4} a + \frac{139614751755}{4} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -175 a - 348\) , \( 1936 a + 2788\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-175a-348\right){x}+1936a+2788$ |
| 256.1-b10 |
256.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{42} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$5.918369177$ |
1.435415367 |
\( \frac{203862548967}{4096} a + \frac{318403919021}{4096} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -975 a - 1548\) , \( 22880 a + 35780\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-975a-1548\right){x}+22880a+35780$ |
| 256.1-b11 |
256.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{27} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.959184588$ |
1.435415367 |
\( \frac{54503407609}{4} a + \frac{42555672073}{2} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 177 a - 524\) , \( -2112 a + 5248\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(177a-524\right){x}-2112a+5248$ |
| 256.1-b12 |
256.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{33} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.959184588$ |
1.435415367 |
\( \frac{653762688677050897}{64} a + \frac{1020884965413408563}{64} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -15695 a - 24588\) , \( 1521120 a + 2375108\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-15695a-24588\right){x}+1521120a+2375108$ |
| 256.1-c1 |
256.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{22} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$11.99882659$ |
1.455071453 |
\( -292271882500 a + 748669862250 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -267 a - 420\) , \( 7254 a + 11336\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-267a-420\right){x}+7254a+11336$ |
| 256.1-c2 |
256.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{14} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$11.99882659$ |
1.455071453 |
\( -20500 a + 54000 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2 a - 2\) , \( a - 1\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(2a-2\right){x}+a-1$ |
| 256.1-c3 |
256.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$23.99765318$ |
1.455071453 |
\( 2000 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -27 a - 40\) , \( 26 a + 40\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-27a-40\right){x}+26a+40$ |
| 256.1-c4 |
256.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{14} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$11.99882659$ |
1.455071453 |
\( 20500 a + 33500 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a\) , \( -a\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-2a{x}-a$ |
| 256.1-c5 |
256.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{20} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$23.99765318$ |
1.455071453 |
\( 1098500 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 347 a - 887\) , \( -4862 a + 12454\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(347a-887\right){x}-4862a+12454$ |
| 256.1-c6 |
256.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{22} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$11.99882659$ |
1.455071453 |
\( 292271882500 a + 456397979750 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 267 a - 687\) , \( -7254 a + 18590\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(267a-687\right){x}-7254a+18590$ |
| 256.1-d1 |
256.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{12} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$26.12924634$ |
1.584318273 |
\( -50671167248 a + 129796414656 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -38 a - 77\) , \( 268 a + 444\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-38a-77\right){x}+268a+444$ |
| 256.1-d2 |
256.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{12} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$26.12924634$ |
1.584318273 |
\( -1552 a + 4288 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a + 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a+3\right){x}$ |
| 256.1-d3 |
256.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{12} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$26.12924634$ |
1.584318273 |
\( 1552 a + 2736 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4\) , \( -a + 4\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+4{x}-a+4$ |
| 256.1-d4 |
256.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{12} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$26.12924634$ |
1.584318273 |
\( 50671167248 a + 79125247408 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 40 a - 116\) , \( -229 a + 596\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(40a-116\right){x}-229a+596$ |
| 256.1-e1 |
256.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{23} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.134949823$ |
$8.500633610$ |
2.225815404 |
\( -343 a + 1029 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+4\right){x}$ |
| 256.1-e2 |
256.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{22} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.079598584$ |
$8.500633610$ |
2.225815404 |
\( -2701312025 a + 6919553753 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 16 a - 8\) , \( -48 a - 12\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(16a-8\right){x}-48a-12$ |
| 256.1-e3 |
256.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{20} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.539799292$ |
$17.00126722$ |
2.225815404 |
\( -24225 a + 68453 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -4 a - 8\) , \( -8 a - 12\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-4a-8\right){x}-8a-12$ |
| 256.1-e4 |
256.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{22} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.269899646$ |
$17.00126722$ |
2.225815404 |
\( 1995 a + 5021 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 25 a - 60\) , \( 24 a - 60\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(25a-60\right){x}+24a-60$ |
| 256.1-e5 |
256.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{16} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.079598584$ |
$8.500633610$ |
2.225815404 |
\( 7659605 a + 11960871 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( a - 4\) , \( -22 a + 56\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(a-4\right){x}-22a+56$ |
| 256.1-e6 |
256.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{23} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.539799292$ |
$8.500633610$ |
2.225815404 |
\( 21069823 a + 33751811 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 305 a - 780\) , \( 4096 a - 10492\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(305a-780\right){x}+4096a-10492$ |
| 256.1-f1 |
256.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{16} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.079598584$ |
$8.500633610$ |
2.225815404 |
\( -7659605 a + 19620476 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -a - 3\) , \( 22 a + 34\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-a-3\right){x}+22a+34$ |
| 256.1-f2 |
256.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{23} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.134949823$ |
$8.500633610$ |
2.225815404 |
\( 343 a + 686 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 4\) , \( 4\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+4\right){x}+4$ |
| 256.1-f3 |
256.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{22} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.269899646$ |
$17.00126722$ |
2.225815404 |
\( -1995 a + 7016 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -23 a - 36\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-23a-36\right){x}$ |
| 256.1-f4 |
256.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{20} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.539799292$ |
$17.00126722$ |
2.225815404 |
\( 24225 a + 44228 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4 a - 12\) , \( 8 a - 20\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(4a-12\right){x}+8a-20$ |
| 256.1-f5 |
256.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{23} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.539799292$ |
$8.500633610$ |
2.225815404 |
\( -21069823 a + 54821634 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -303 a - 476\) , \( -3792 a - 5920\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-303a-476\right){x}-3792a-5920$ |
| 256.1-f6 |
256.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{22} \) |
$1.47375$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.079598584$ |
$8.500633610$ |
2.225815404 |
\( 2701312025 a + 4218241728 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -16 a + 8\) , \( 48 a - 60\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-16a+8\right){x}+48a-60$ |
*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.
