| 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 |
| 128.5-a1 |
128.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{19} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$8.823675287$ |
2.140055600 |
\( -\frac{217}{16} a - \frac{339}{16} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 2 a + 3\) , \( a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+3\right){x}+a+3$ |
| 128.5-a2 |
128.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{7} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$35.29470114$ |
2.140055600 |
\( -\frac{1592342311}{2} a + \frac{4078872403}{2} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 9\) , \( -2 a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-9\right){x}-2a+3$ |
| 128.5-a3 |
128.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{14} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$17.64735057$ |
2.140055600 |
\( \frac{159495}{4} a + \frac{481229}{4} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 47 a - 126\) , \( -221 a + 563\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(47a-126\right){x}-221a+563$ |
| 128.5-a4 |
128.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{16} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$4.411837643$ |
2.140055600 |
\( \frac{23841914775}{2} a + \frac{37230413581}{2} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 97 a - 256\) , \( 459 a - 1181\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(97a-256\right){x}+459a-1181$ |
| 128.5-b1 |
128.5-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{45} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.184918978$ |
1.014991940 |
\( -\frac{55573026649}{16777216} a - \frac{85738862931}{16777216} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -23 a + 42\) , \( -329 a + 864\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-23a+42\right){x}-329a+864$ |
| 128.5-b2 |
128.5-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{27} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.184918978$ |
1.014991940 |
\( -\frac{110887}{256} a + \frac{66933}{64} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -89 a + 228\) , \( -57 a + 146\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-89a+228\right){x}-57a+146$ |
| 128.5-b3 |
128.5-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{45} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.184918978$ |
1.014991940 |
\( \frac{55573026649}{16777216} a - \frac{35327972395}{4194304} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 274 a + 429\) , \( 18518 a + 28917\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(274a+429\right){x}+18518a+28917$ |
| 128.5-b4 |
128.5-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{27} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.184918978$ |
1.014991940 |
\( \frac{110887}{256} a + \frac{156845}{256} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 2 a - 3\) , \( 14 a - 35\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a-3\right){x}+14a-35$ |
| 128.5-b5 |
128.5-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{24} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$8.369837957$ |
1.014991940 |
\( -\frac{915957}{16} a + \frac{2374013}{16} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -33 a - 52\) , \( 13 a + 20\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-33a-52\right){x}+13a+20$ |
| 128.5-b6 |
128.5-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{27} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.184918978$ |
1.014991940 |
\( -\frac{653762688677050897}{64} a + \frac{418661913522614865}{16} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 1996 a - 5262\) , \( -72821 a + 185664\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(1996a-5262\right){x}-72821a+185664$ |
| 128.5-b7 |
128.5-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{36} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$8.369837957$ |
1.014991940 |
\( -\frac{203862548967}{4096} a + \frac{130566616997}{1024} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 116 a - 342\) , \( -1173 a + 3040\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(116a-342\right){x}-1173a+3040$ |
| 128.5-b8 |
128.5-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{24} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$8.369837957$ |
1.014991940 |
\( \frac{915957}{16} a + \frac{182257}{2} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( a - 7\) , \( -7 a - 6\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(a-7\right){x}-7a-6$ |
| 128.5-b9 |
128.5-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{21} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.184918978$ |
1.014991940 |
\( -\frac{54503407609}{4} a + \frac{139614751755}{4} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -373 a - 592\) , \( 5721 a + 8920\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-373a-592\right){x}+5721a+8920$ |
| 128.5-b10 |
128.5-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{36} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$8.369837957$ |
1.014991940 |
\( \frac{203862548967}{4096} a + \frac{318403919021}{4096} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -1898 a - 2967\) , \( 64912 a + 101365\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1898a-2967\right){x}+64912a+101365$ |
| 128.5-b11 |
128.5-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{21} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.184918978$ |
1.014991940 |
\( \frac{54503407609}{4} a + \frac{42555672073}{2} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -9 a - 117\) , \( -339 a - 74\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-9a-117\right){x}-339a-74$ |
| 128.5-b12 |
128.5-b |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{27} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.184918978$ |
1.014991940 |
\( \frac{653762688677050897}{64} a + \frac{1020884965413408563}{64} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 10858 a - 27827\) , \( 698508 a - 1789259\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(10858a-27827\right){x}+698508a-1789259$ |
| 128.5-c1 |
128.5-c |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{45} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$1.373831790$ |
1.999218911 |
\( -\frac{55573026649}{16777216} a - \frac{85738862931}{16777216} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -285 a - 443\) , \( -4041 a - 6307\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-285a-443\right){x}-4041a-6307$ |
| 128.5-c2 |
128.5-c |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{27} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.242990742$ |
1.999218911 |
\( -\frac{110887}{256} a + \frac{66933}{64} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -a + 4\) , \( a + 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+4\right){x}+a+2$ |
| 128.5-c3 |
128.5-c |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{45} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.747663580$ |
1.999218911 |
\( \frac{55573026649}{16777216} a - \frac{35327972395}{4194304} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 24 a - 41\) , \( -98 a + 129\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(24a-41\right){x}-98a+129$ |
| 128.5-c4 |
128.5-c |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{27} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$4.121495371$ |
1.999218911 |
\( \frac{110887}{256} a + \frac{156845}{256} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 20 a + 32\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(20a+32\right){x}$ |
| 128.5-c5 |
128.5-c |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{24} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$8.242990742$ |
1.999218911 |
\( -\frac{915957}{16} a + \frac{2374013}{16} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 9 a - 24\) , \( 15 a - 41\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(9a-24\right){x}+15a-41$ |
| 128.5-c6 |
128.5-c |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{27} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$5.495327161$ |
1.999218911 |
\( -\frac{653762688677050897}{64} a + \frac{418661913522614865}{16} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -2431 a - 3923\) , \( 73584 a + 115495\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-2431a-3923\right){x}+73584a+115495$ |
| 128.5-c7 |
128.5-c |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{36} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$5.495327161$ |
1.999218911 |
\( -\frac{203862548967}{4096} a + \frac{130566616997}{1024} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -791 a - 1243\) , \( -16960 a - 26473\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-791a-1243\right){x}-16960a-26473$ |
| 128.5-c8 |
128.5-c |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{24} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$16.48598148$ |
1.999218911 |
\( \frac{915957}{16} a + \frac{182257}{2} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 146 a - 374\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(146a-374\right){x}$ |
| 128.5-c9 |
128.5-c |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{21} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$2.060747685$ |
1.999218911 |
\( -\frac{54503407609}{4} a + \frac{139614751755}{4} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 149 a - 404\) , \( 1359 a - 3561\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(149a-404\right){x}+1359a-3561$ |
| 128.5-c10 |
128.5-c |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{36} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$2.747663580$ |
1.999218911 |
\( \frac{203862548967}{4096} a + \frac{318403919021}{4096} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 24 a - 179\) , \( -493 a + 579\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(24a-179\right){x}-493a+579$ |
| 128.5-c11 |
128.5-c |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{21} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$16.48598148$ |
1.999218911 |
\( \frac{54503407609}{4} a + \frac{42555672073}{2} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 1656 a - 4244\) , \( -51666 a + 132346\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(1656a-4244\right){x}-51666a+132346$ |
| 128.5-c12 |
128.5-c |
$12$ |
$24$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{27} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.686915895$ |
1.999218911 |
\( \frac{653762688677050897}{64} a + \frac{1020884965413408563}{64} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -296 a - 1139\) , \( -7277 a - 16189\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-296a-1139\right){x}-7277a-16189$ |
| 128.5-d1 |
128.5-d |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{19} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.081969010$ |
$17.28603663$ |
1.374613658 |
\( -\frac{217}{16} a - \frac{339}{16} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( a - 1\) , \( -197 a + 505\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(a-1\right){x}-197a+505$ |
| 128.5-d2 |
128.5-d |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{7} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.327876043$ |
$34.57207326$ |
1.374613658 |
\( -\frac{1592342311}{2} a + \frac{4078872403}{2} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -85 a - 133\) , \( -137 a - 214\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-85a-133\right){x}-137a-214$ |
| 128.5-d3 |
128.5-d |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{14} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.163938021$ |
$34.57207326$ |
1.374613658 |
\( \frac{159495}{4} a + \frac{481229}{4} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -3 a - 7\) , \( a + 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-3a-7\right){x}+a+2$ |
| 128.5-d4 |
128.5-d |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
128.5 |
\( 2^{7} \) |
\( 2^{16} \) |
$1.23927$ |
$(-a+2), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.327876043$ |
$17.28603663$ |
1.374613658 |
\( \frac{23841914775}{2} a + \frac{37230413581}{2} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -33 a - 57\) , \( 141 a + 214\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-33a-57\right){x}+141a+214$ |
*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.
