| 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 |
| 567.1-a1 |
567.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{23} \cdot 7^{2} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.566767726$ |
$1.735260738$ |
6.733832077 |
\( -\frac{422830592}{45927} a + \frac{1117795136}{45927} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 40 a - 95\) , \( 189 a - 520\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(40a-95\right){x}+189a-520$ |
| 567.1-a2 |
567.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{19} \cdot 7^{4} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.133535453$ |
$1.735260738$ |
6.733832077 |
\( \frac{108334592}{3969} a + \frac{286626496}{3969} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -122 a + 337\) , \( 311067 a - 822994\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-122a+337\right){x}+311067a-822994$ |
| 567.1-b1 |
567.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{15} \cdot 7^{2} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$2.751645710$ |
1.040024320 |
\( -\frac{224768}{7} a + \frac{580672}{7} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -53 a - 143\) , \( -629 a - 1666\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-53a-143\right){x}-629a-1666$ |
| 567.1-b2 |
567.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{9} \cdot 7^{6} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$8.254937131$ |
1.040024320 |
\( -\frac{1204736}{343} a + \frac{3558976}{343} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 148 a - 380\) , \( -1528 a + 4054\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(148a-380\right){x}-1528a+4054$ |
| 567.1-b3 |
567.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{9} \cdot 7^{3} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$16.50987426$ |
1.040024320 |
\( -\frac{3312820736}{49} a + \frac{1252147264}{7} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -8 a - 32\) , \( -7 a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-8a-32\right){x}-7a+1$ |
| 567.1-b4 |
567.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{15} \cdot 7 \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$5.503291420$ |
1.040024320 |
\( \frac{9461248}{7} a + 3577792 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 19 a - 41\) , \( -17 a + 41\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(19a-41\right){x}-17a+41$ |
| 567.1-c1 |
567.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{14} \cdot 7^{16} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$2.638508823$ |
$0.271340145$ |
4.329558047 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -306\) , \( -5859\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-306{x}-5859$ |
| 567.1-c2 |
567.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{32} \cdot 7 \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.638508823$ |
$2.170721162$ |
4.329558047 |
\( -\frac{1153486390269896663}{301327047} a + \frac{435976874792639720}{43046721} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 1035 a - 2871\) , \( -29241 a + 82944\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(1035a-2871\right){x}-29241a+82944$ |
| 567.1-c3 |
567.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{16} \cdot 7^{2} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.319254411$ |
$4.341442324$ |
4.329558047 |
\( \frac{103823}{63} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 9\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+9{x}$ |
| 567.1-c4 |
567.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{20} \cdot 7^{4} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.659627205$ |
$4.341442324$ |
4.329558047 |
\( \frac{7189057}{3969} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -36\) , \( -27\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-36{x}-27$ |
| 567.1-c5 |
567.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{28} \cdot 7^{2} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.319254411$ |
$4.341442324$ |
4.329558047 |
\( \frac{6570725617}{45927} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -351\) , \( 2430\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-351{x}+2430$ |
| 567.1-c6 |
567.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{16} \cdot 7^{8} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1.319254411$ |
$1.085360581$ |
4.329558047 |
\( \frac{13027640977}{21609} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -441\) , \( -3672\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-441{x}-3672$ |
| 567.1-c7 |
567.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{32} \cdot 7 \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.638508823$ |
$2.170721162$ |
4.329558047 |
\( \frac{1153486390269896663}{301327047} a + \frac{435976874792639720}{43046721} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -1035 a - 2871\) , \( 29241 a + 82944\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-1035a-2871\right){x}+29241a+82944$ |
| 567.1-c8 |
567.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{14} \cdot 7^{4} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$2.638508823$ |
$0.271340145$ |
4.329558047 |
\( \frac{53297461115137}{147} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -7056\) , \( -229905\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-7056{x}-229905$ |
| 567.1-d1 |
567.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{15} \cdot 7 \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$5.503291420$ |
1.040024320 |
\( -\frac{9461248}{7} a + 3577792 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -14 a - 44\) , \( -27 a - 76\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-14a-44\right){x}-27a-76$ |
| 567.1-d2 |
567.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{9} \cdot 7^{6} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$8.254937131$ |
1.040024320 |
\( \frac{1204736}{343} a + \frac{3558976}{343} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -143 a - 377\) , \( 1148 a + 3037\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-143a-377\right){x}+1148a+3037$ |
| 567.1-d3 |
567.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{15} \cdot 7^{2} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$2.751645710$ |
1.040024320 |
\( \frac{224768}{7} a + \frac{580672}{7} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 58 a - 140\) , \( 486 a - 1276\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(58a-140\right){x}+486a-1276$ |
| 567.1-d4 |
567.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{9} \cdot 7^{3} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$16.50987426$ |
1.040024320 |
\( \frac{3312820736}{49} a + \frac{1252147264}{7} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 13 a - 35\) , \( -28 a + 73\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(13a-35\right){x}-28a+73$ |
| 567.1-e1 |
567.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{17} \cdot 7^{2} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.190615875$ |
$7.512474961$ |
2.164975951 |
\( -\frac{17359374619}{63} a + \frac{45928588514}{63} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 349 a + 924\) , \( 100940 a + 267062\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(349a+924\right){x}+100940a+267062$ |
| 567.1-e2 |
567.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{16} \cdot 7 \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.381231750$ |
$15.02494992$ |
2.164975951 |
\( \frac{266548}{21} a - \frac{11591}{3} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 664 a - 1758\) , \( -15679 a + 41481\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(664a-1758\right){x}-15679a+41481$ |
| 567.1-f1 |
567.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{19} \cdot 7^{4} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$5.625830929$ |
4.252728444 |
\( -\frac{108334592}{3969} a + \frac{286626496}{3969} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 127 a + 334\) , \( 311316 a + 823663\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(127a+334\right){x}+311316a+823663$ |
| 567.1-f2 |
567.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{23} \cdot 7^{2} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$5.625830929$ |
4.252728444 |
\( \frac{422830592}{45927} a + \frac{1117795136}{45927} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -35 a - 98\) , \( 114 a + 325\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-35a-98\right){x}+114a+325$ |
| 567.1-g1 |
567.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{16} \cdot 7 \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.736190556$ |
1.034182821 |
\( -\frac{266548}{21} a - \frac{11591}{3} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -665 a - 1758\) , \( -15679 a - 41483\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-665a-1758\right){x}-15679a-41483$ |
| 567.1-g2 |
567.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{17} \cdot 7^{2} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.368095278$ |
1.034182821 |
\( \frac{17359374619}{63} a + \frac{45928588514}{63} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -350 a + 924\) , \( 100940 a - 267064\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-350a+924\right){x}+100940a-267064$ |
| 567.1-h1 |
567.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{19} \cdot 7^{4} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.133535453$ |
$1.735260738$ |
6.733832077 |
\( -\frac{108334592}{3969} a + \frac{286626496}{3969} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 127 a + 334\) , \( -310733 a - 822124\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(127a+334\right){x}-310733a-822124$ |
| 567.1-h2 |
567.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{23} \cdot 7^{2} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.566767726$ |
$1.735260738$ |
6.733832077 |
\( \frac{422830592}{45927} a + \frac{1117795136}{45927} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -35 a - 98\) , \( -287 a - 784\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-35a-98\right){x}-287a-784$ |
| 567.1-i1 |
567.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{16} \cdot 7 \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.381231750$ |
$15.02494992$ |
2.164975951 |
\( -\frac{266548}{21} a - \frac{11591}{3} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -665 a - 1758\) , \( 15679 a + 41481\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-665a-1758\right){x}+15679a+41481$ |
| 567.1-i2 |
567.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{17} \cdot 7^{2} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.190615875$ |
$7.512474961$ |
2.164975951 |
\( \frac{17359374619}{63} a + \frac{45928588514}{63} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -350 a + 924\) , \( -100940 a + 267062\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-350a+924\right){x}-100940a+267062$ |
| 567.1-j1 |
567.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{15} \cdot 7 \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.585879788$ |
$13.23033863$ |
2.929749280 |
\( -\frac{9461248}{7} a + 3577792 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -14 a - 44\) , \( -50 a - 128\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-14a-44\right){x}-50a-128$ |
| 567.1-j2 |
567.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{9} \cdot 7^{6} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.878819682$ |
$4.410112877$ |
2.929749280 |
\( \frac{1204736}{343} a + \frac{3558976}{343} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -143 a - 377\) , \( -1819 a - 4813\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-143a-377\right){x}-1819a-4813$ |
| 567.1-j3 |
567.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{15} \cdot 7^{2} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.292939894$ |
$13.23033863$ |
2.929749280 |
\( \frac{224768}{7} a + \frac{580672}{7} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 58 a - 140\) , \( -518 a + 1381\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(58a-140\right){x}-518a+1381$ |
| 567.1-j4 |
567.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{9} \cdot 7^{3} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1.757639365$ |
$4.410112877$ |
2.929749280 |
\( \frac{3312820736}{49} a + \frac{1252147264}{7} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 13 a - 35\) , \( 14 a - 70\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(13a-35\right){x}+14a-70$ |
| 567.1-k1 |
567.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{17} \cdot 7^{2} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.368095278$ |
1.034182821 |
\( -\frac{17359374619}{63} a + \frac{45928588514}{63} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 349 a + 924\) , \( -100940 a - 267064\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(349a+924\right){x}-100940a-267064$ |
| 567.1-k2 |
567.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{16} \cdot 7 \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.736190556$ |
1.034182821 |
\( \frac{266548}{21} a - \frac{11591}{3} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 664 a - 1758\) , \( 15679 a - 41483\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(664a-1758\right){x}+15679a-41483$ |
| 567.1-l1 |
567.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{14} \cdot 7^{16} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$1.217293980$ |
1.840375511 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -306\) , \( 5859\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-306{x}+5859$ |
| 567.1-l2 |
567.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{32} \cdot 7 \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.304323495$ |
1.840375511 |
\( -\frac{1153486390269896663}{301327047} a + \frac{435976874792639720}{43046721} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 1035 a - 2871\) , \( 29241 a - 82944\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(1035a-2871\right){x}+29241a-82944$ |
| 567.1-l3 |
567.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{16} \cdot 7^{2} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.869175922$ |
1.840375511 |
\( \frac{103823}{63} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 9\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+9{x}$ |
| 567.1-l4 |
567.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{20} \cdot 7^{4} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$4.869175922$ |
1.840375511 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -36\) , \( 27\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-36{x}+27$ |
| 567.1-l5 |
567.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{28} \cdot 7^{2} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$1.217293980$ |
1.840375511 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -351\) , \( -2430\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-351{x}-2430$ |
| 567.1-l6 |
567.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{16} \cdot 7^{8} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$4.869175922$ |
1.840375511 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -441\) , \( 3672\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-441{x}+3672$ |
| 567.1-l7 |
567.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{32} \cdot 7 \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.304323495$ |
1.840375511 |
\( \frac{1153486390269896663}{301327047} a + \frac{435976874792639720}{43046721} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -1035 a - 2871\) , \( -29241 a - 82944\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-1035a-2871\right){x}-29241a-82944$ |
| 567.1-l8 |
567.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{14} \cdot 7^{4} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$4.869175922$ |
1.840375511 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-7056{x}+229905$ |
| 567.1-m1 |
567.1-m |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{15} \cdot 7^{2} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.292939894$ |
$13.23033863$ |
2.929749280 |
\( -\frac{224768}{7} a + \frac{580672}{7} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -53 a - 143\) , \( 375 a + 991\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-53a-143\right){x}+375a+991$ |
| 567.1-m2 |
567.1-m |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{9} \cdot 7^{6} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.878819682$ |
$4.410112877$ |
2.929749280 |
\( -\frac{1204736}{343} a + \frac{3558976}{343} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 148 a - 380\) , \( 1439 a - 3796\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(148a-380\right){x}+1439a-3796$ |
| 567.1-m3 |
567.1-m |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{9} \cdot 7^{3} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1.757639365$ |
$4.410112877$ |
2.929749280 |
\( -\frac{3312820736}{49} a + \frac{1252147264}{7} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -8 a - 32\) , \( -49 a - 142\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-8a-32\right){x}-49a-142$ |
| 567.1-m4 |
567.1-m |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{15} \cdot 7 \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.585879788$ |
$13.23033863$ |
2.929749280 |
\( \frac{9461248}{7} a + 3577792 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 19 a - 41\) , \( 6 a - 11\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(19a-41\right){x}+6a-11$ |
| 567.1-n1 |
567.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{23} \cdot 7^{2} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$5.625830929$ |
4.252728444 |
\( -\frac{422830592}{45927} a + \frac{1117795136}{45927} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 40 a - 95\) , \( -212 a + 589\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(40a-95\right){x}-212a+589$ |
| 567.1-n2 |
567.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{19} \cdot 7^{4} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$5.625830929$ |
4.252728444 |
\( \frac{108334592}{3969} a + \frac{286626496}{3969} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -122 a + 337\) , \( -310982 a + 822793\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-122a+337\right){x}-310982a+822793$ |
*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.
