| 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 |
| 1.1-a1 |
1.1-a |
$8$ |
$28$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.47284$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.309031537 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -15 a - 40\) , \( 67 a + 177\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-15a-40\right){x}+67a+177$ |
| 1.1-a2 |
1.1-a |
$8$ |
$28$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.47284$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.309031537 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 15 a - 40\) , \( -67 a + 177\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(15a-40\right){x}-67a+177$ |
| 1.1-a3 |
1.1-a |
$8$ |
$28$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.47284$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$6.540964764$ |
0.309031537 |
\( -51954490735875 a + 137458661985000 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -270 a - 715\) , \( 3223 a + 8527\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-270a-715\right){x}+3223a+8527$ |
| 1.1-a4 |
1.1-a |
$8$ |
$28$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.47284$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.309031537 |
\( -51954490735875 a + 137458661985000 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -270 a - 718\) , \( -3223 a - 8529\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-270a-718\right){x}-3223a-8529$ |
| 1.1-a5 |
1.1-a |
$8$ |
$28$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.47284$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.309031537 |
\( 16581375 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -255 a - 678\) , \( -3669 a - 9709\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-255a-678\right){x}-3669a-9709$ |
| 1.1-a6 |
1.1-a |
$8$ |
$28$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.47284$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.309031537 |
\( 16581375 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 255 a - 678\) , \( 3669 a - 9709\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(255a-678\right){x}+3669a-9709$ |
| 1.1-a7 |
1.1-a |
$8$ |
$28$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.47284$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$6.540964764$ |
0.309031537 |
\( 51954490735875 a + 137458661985000 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 270 a - 715\) , \( -3223 a + 8527\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(270a-715\right){x}-3223a+8527$ |
| 1.1-a8 |
1.1-a |
$8$ |
$28$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.47284$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.309031537 |
\( 51954490735875 a + 137458661985000 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 270 a - 718\) , \( 3223 a - 8529\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(270a-718\right){x}+3223a-8529$ |
| 9.2-a1 |
9.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{9} \) |
$0.81899$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$17.06155021$ |
1.612164958 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 2 a + 5\) , \( 2 a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+5\right){x}+2a+3$ |
| 9.2-a2 |
9.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{9} \) |
$0.81899$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$17.06155021$ |
1.612164958 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 54 a + 141\) , \( 122 a + 321\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(54a+141\right){x}+122a+321$ |
| 9.3-a1 |
9.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{9} \) |
$0.81899$ |
$(-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$17.06155021$ |
1.612164958 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 3 a + 8\) , \( 3 a + 8\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a+8\right){x}+3a+8$ |
| 9.3-a2 |
9.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{9} \) |
$0.81899$ |
$(-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$17.06155021$ |
1.612164958 |
\( 1728 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -49 a + 144\) , \( 19 a - 38\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-49a+144\right){x}+19a-38$ |
| 14.1-a1 |
14.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{36} \cdot 7^{2} \) |
$0.91464$ |
$(a+3), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.027708105$ |
1.328111995 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -168\) , \( 704\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-168{x}+704$ |
| 14.1-a2 |
14.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$0.91464$ |
$(a+3), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.027708105$ |
1.328111995 |
\( -\frac{15625}{28} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+2{x}$ |
| 14.1-a3 |
14.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \) |
$0.91464$ |
$(a+3), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$7.027708105$ |
1.328111995 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 7\) , \( 11\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+7{x}+11$ |
| 14.1-a4 |
14.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{6} \cdot 7^{12} \) |
$0.91464$ |
$(a+3), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$7.027708105$ |
1.328111995 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -33\) , \( 35\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-33{x}+35$ |
| 14.1-a5 |
14.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{2} \cdot 7^{4} \) |
$0.91464$ |
$(a+3), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.027708105$ |
1.328111995 |
\( \frac{128787625}{98} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -8\) , \( -22\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-8{x}-22$ |
| 14.1-a6 |
14.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{18} \cdot 7^{4} \) |
$0.91464$ |
$(a+3), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.027708105$ |
1.328111995 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -2728\) , \( 52416\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-2728{x}+52416$ |
| 14.1-b1 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{36} \cdot 7^{2} \) |
$0.91464$ |
$(a+3), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$3.507207167$ |
$0.436190660$ |
0.578214212 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$ |
| 14.1-b2 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$0.91464$ |
$(a+3), (a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$0.389689685$ |
$35.33144352$ |
0.578214212 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}$ |
| 14.1-b3 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \) |
$0.91464$ |
$(a+3), (a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.169069055$ |
$3.925715946$ |
0.578214212 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$ |
| 14.1-b4 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{6} \cdot 7^{12} \) |
$0.91464$ |
$(a+3), (a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.584534527$ |
$3.925715946$ |
0.578214212 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$ |
| 14.1-b5 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{2} \cdot 7^{4} \) |
$0.91464$ |
$(a+3), (a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \) |
$0.194844842$ |
$35.33144352$ |
0.578214212 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$ |
| 14.1-b6 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{18} \cdot 7^{4} \) |
$0.91464$ |
$(a+3), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1.753603583$ |
$0.436190660$ |
0.578214212 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$ |
| 16.1-a1 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$0.94569$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$36.50601953$ |
1.724747304 |
\( -3264 a - 6928 \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 0\) , \( -1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}-1$ |
| 16.1-a2 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$0.94569$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$36.50601953$ |
1.724747304 |
\( 3264 a - 6928 \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 3 a + 4\) , \( 8\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(3a+4\right){x}+8$ |
| 16.1-a3 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$0.94569$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$36.50601953$ |
1.724747304 |
\( -50184204 a + 132776672 \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 18 a - 36\) , \( -66 a + 182\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(18a-36\right){x}-66a+182$ |
| 16.1-a4 |
16.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$0.94569$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$36.50601953$ |
1.724747304 |
\( 50184204 a + 132776672 \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -15 a - 40\) , \( 26 a + 68\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-15a-40\right){x}+26a+68$ |
| 16.1-b1 |
16.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$0.94569$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$11.49111446$ |
0.542904127 |
\( -3264 a - 6928 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -a - 1\) , \( -2 a - 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-1\right){x}-2a-7$ |
| 16.1-b2 |
16.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$0.94569$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$11.49111446$ |
0.542904127 |
\( 3264 a - 6928 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 2 a + 3\) , \( a + 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a+3\right){x}+a+2$ |
| 16.1-b3 |
16.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$0.94569$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$11.49111446$ |
0.542904127 |
\( -50184204 a + 132776672 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 17 a - 37\) , \( 42 a - 107\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(17a-37\right){x}+42a-107$ |
| 16.1-b4 |
16.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$0.94569$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$11.49111446$ |
0.542904127 |
\( 50184204 a + 132776672 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -16 a - 41\) , \( -83 a - 221\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-16a-41\right){x}-83a-221$ |
| 18.1-a1 |
18.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{34} \) |
$0.97395$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.531367511$ |
1.606704330 |
\( -\frac{22026189082216125793}{3706040377703682} a - \frac{54626740869226485845}{3706040377703682} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -6732 a + 17809\) , \( 429164 a - 1135465\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6732a+17809\right){x}+429164a-1135465$ |
| 18.1-a2 |
18.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$0.97395$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$8.501880177$ |
1.606704330 |
\( \frac{4913}{1296} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 16 a + 47\) , \( -1313 a - 3476\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(16a+47\right){x}-1313a-3476$ |
| 18.1-a3 |
18.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{34} \) |
$0.97395$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$2.125470044$ |
1.606704330 |
\( \frac{22026189082216125793}{3706040377703682} a - \frac{54626740869226485845}{3706040377703682} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 6731 a + 17812\) , \( 429164 a + 1135461\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(6731a+17812\right){x}+429164a+1135461$ |
| 18.1-a4 |
18.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{20} \) |
$0.97395$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$8.501880177$ |
1.606704330 |
\( -\frac{15840177853915205}{86093442} a + \frac{20954710660855016}{43046721} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -2274 a - 6013\) , \( 59627 a + 157758\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2274a-6013\right){x}+59627a+157758$ |
| 18.1-a5 |
18.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{16} \) |
$0.97395$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$8.501880177$ |
1.606704330 |
\( \frac{838561807}{26244} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -944 a - 2493\) , \( -25533 a - 67556\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-944a-2493\right){x}-25533a-67556$ |
| 18.1-a6 |
18.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{10} \) |
$0.97395$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$8.501880177$ |
1.606704330 |
\( -\frac{2350503708439404473473}{13122} a + \frac{6218848268321376696725}{13122} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -32559 a - 86158\) , \( 5180690 a + 13706871\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-32559a-86158\right){x}+5180690a+13706871$ |
| 18.1-a7 |
18.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{20} \) |
$0.97395$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$2.125470044$ |
1.606704330 |
\( \frac{15840177853915205}{86093442} a + \frac{20954710660855016}{43046721} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 2273 a - 6016\) , \( 59627 a - 157762\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2273a-6016\right){x}+59627a-157762$ |
| 18.1-a8 |
18.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{10} \) |
$0.97395$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.531367511$ |
1.606704330 |
\( \frac{2350503708439404473473}{13122} a + \frac{6218848268321376696725}{13122} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 32558 a - 86161\) , \( 5180690 a - 13706875\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(32558a-86161\right){x}+5180690a-13706875$ |
| 18.1-b1 |
18.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{34} \) |
$0.97395$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$2.125470044$ |
1.606704330 |
\( -\frac{22026189082216125793}{3706040377703682} a - \frac{54626740869226485845}{3706040377703682} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -6732 a + 17812\) , \( -429165 a + 1135461\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6732a+17812\right){x}-429165a+1135461$ |
| 18.1-b2 |
18.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$0.97395$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$8.501880177$ |
1.606704330 |
\( \frac{4913}{1296} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 16 a + 44\) , \( 1312 a + 3472\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(16a+44\right){x}+1312a+3472$ |
| 18.1-b3 |
18.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{34} \) |
$0.97395$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.531367511$ |
1.606704330 |
\( \frac{22026189082216125793}{3706040377703682} a - \frac{54626740869226485845}{3706040377703682} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 6731 a + 17809\) , \( -429165 a - 1135465\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(6731a+17809\right){x}-429165a-1135465$ |
| 18.1-b4 |
18.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{20} \) |
$0.97395$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$2.125470044$ |
1.606704330 |
\( -\frac{15840177853915205}{86093442} a + \frac{20954710660855016}{43046721} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -2274 a - 6016\) , \( -59628 a - 157762\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2274a-6016\right){x}-59628a-157762$ |
| 18.1-b5 |
18.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{16} \) |
$0.97395$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$8.501880177$ |
1.606704330 |
\( \frac{838561807}{26244} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -944 a - 2496\) , \( 25532 a + 67552\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-944a-2496\right){x}+25532a+67552$ |
| 18.1-b6 |
18.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{10} \) |
$0.97395$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.531367511$ |
1.606704330 |
\( -\frac{2350503708439404473473}{13122} a + \frac{6218848268321376696725}{13122} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -32559 a - 86161\) , \( -5180691 a - 13706875\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-32559a-86161\right){x}-5180691a-13706875$ |
| 18.1-b7 |
18.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{20} \) |
$0.97395$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$8.501880177$ |
1.606704330 |
\( \frac{15840177853915205}{86093442} a + \frac{20954710660855016}{43046721} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 2273 a - 6013\) , \( -59628 a + 157758\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2273a-6013\right){x}-59628a+157758$ |
| 18.1-b8 |
18.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{10} \) |
$0.97395$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$8.501880177$ |
1.606704330 |
\( \frac{2350503708439404473473}{13122} a + \frac{6218848268321376696725}{13122} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 32558 a - 86158\) , \( -5180691 a + 13706871\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(32558a-86158\right){x}-5180691a+13706871$ |
| 18.2-a1 |
18.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{12} \) |
$0.97395$ |
$(a+3), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.54590844$ |
1.992989364 |
\( -\frac{275587}{1458} a + \frac{289048}{729} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -6 a - 8\) , \( 34 a + 93\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-6a-8\right){x}+34a+93$ |
| 18.2-a2 |
18.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{8} \) |
$0.97395$ |
$(a+3), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$3.515302815$ |
1.992989364 |
\( \frac{1500083}{72} a - \frac{495212}{9} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 74 a - 199\) , \( 691 a - 1830\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(74a-199\right){x}+691a-1830$ |
*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.
