| 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 |
| 44.4-a8 |
44.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44.4 |
\( 2^{2} \cdot 11 \) |
\( 2^{5} \cdot 11^{4} \) |
$0.60891$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.521332337$ |
0.635316032 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( -22 a + 22\) , \( -21 a + 78\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-22a+22\right){x}-21a+78$ |
| 1408.14-b8 |
1408.14-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1408.14 |
\( 2^{7} \cdot 11 \) |
\( 2^{23} \cdot 11^{4} \) |
$1.44823$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.891425596$ |
2.695417647 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -150 a - 66\) , \( -1257 a + 511\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-150a-66\right){x}-1257a+511$ |
| 1408.4-b8 |
1408.4-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1408.4 |
\( 2^{7} \cdot 11 \) |
\( 2^{23} \cdot 11^{4} \) |
$1.44823$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.891425596$ |
1.347708823 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -43 a + 257\) , \( 1131 a - 17\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-43a+257\right){x}+1131a-17$ |
| 2816.10-d8 |
2816.10-d |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2816.10 |
\( 2^{8} \cdot 11 \) |
\( 2^{29} \cdot 11^{4} \) |
$1.72225$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.630333084$ |
1.905948096 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -344 a + 344\) , \( 640 a - 4268\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-344a+344\right){x}+640a-4268$ |
| 3564.4-c8 |
3564.4-c |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3564.4 |
\( 2^{2} \cdot 3^{4} \cdot 11 \) |
\( 2^{5} \cdot 3^{12} \cdot 11^{4} \) |
$1.82672$ |
$(a), (-a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$0.574416847$ |
$0.840444112$ |
2.919489857 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -194 a + 193\) , \( 366 a - 1897\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-194a+193\right){x}+366a-1897$ |
| 3872.15-c8 |
3872.15-c |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.15 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{17} \cdot 11^{10} \) |
$1.86497$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.380105151$ |
2.298659893 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 880 a - 1095\) , \( 14465 a - 6903\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(880a-1095\right){x}+14465a-6903$ |
| 3872.6-c8 |
3872.6-c |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.6 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{17} \cdot 11^{10} \) |
$1.86497$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.380105151$ |
3.447989840 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -732 a + 1289\) , \( 5585 a + 15102\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-732a+1289\right){x}+5585a+15102$ |
| 11264.10-b8 |
11264.10-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
11264.10 |
\( 2^{10} \cdot 11 \) |
\( 2^{35} \cdot 11^{4} \) |
$2.43563$ |
$(a), (-a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$2.536110911$ |
$0.445712798$ |
3.417939054 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 688 a\) , \( -2348 a - 9816\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+688a{x}-2348a-9816$ |
| 11264.14-c8 |
11264.14-c |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
11264.14 |
\( 2^{10} \cdot 11 \) |
\( 2^{35} \cdot 11^{4} \) |
$2.43563$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.445712798$ |
1.347708823 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 344 a - 1032\) , \( 5548 a - 11524\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(344a-1032\right){x}+5548a-11524$ |
| 15488.21-e8 |
15488.21-e |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.21 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{23} \cdot 11^{10} \) |
$2.63746$ |
$(a), (-a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1.045848059$ |
$0.268774930$ |
3.399838683 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -669 a + 2859\) , \( 35834 a + 8222\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-669a+2859\right){x}+35834a+8222$ |
| 15488.6-a8 |
15488.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.6 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{23} \cdot 11^{10} \) |
$2.63746$ |
$(a), (-a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$2.878911906$ |
$0.268774930$ |
2.339688825 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 2020 a - 1115\) , \( 29836 a + 20150\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(2020a-1115\right){x}+29836a+20150$ |
| 17248.10-e8 |
17248.10-e |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
17248.10 |
\( 2^{5} \cdot 7^{2} \cdot 11 \) |
\( 2^{17} \cdot 7^{6} \cdot 11^{4} \) |
$2.70939$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1.083496409$ |
$0.476487024$ |
6.244238937 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -150 a - 753\) , \( 2285 a + 7855\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-150a-753\right){x}+2285a+7855$ |
| 17248.4-a8 |
17248.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
17248.4 |
\( 2^{5} \cdot 7^{2} \cdot 11 \) |
\( 2^{17} \cdot 7^{6} \cdot 11^{4} \) |
$2.70939$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.972502004$ |
$0.476487024$ |
2.802286573 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 300 a + 603\) , \( -5563 a + 9311\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(300a+603\right){x}-5563a+9311$ |
| 23716.6-b8 |
23716.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.6 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{5} \cdot 7^{6} \cdot 11^{10} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1.446902786$ |
$0.287332486$ |
2.514172357 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -1053 a - 1356\) , \( -27440 a - 10664\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1053a-1356\right){x}-27440a-10664$ |
| 27500.4-d8 |
27500.4-d |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27500.4 |
\( 2^{2} \cdot 5^{4} \cdot 11 \) |
\( 2^{5} \cdot 5^{12} \cdot 11^{4} \) |
$3.04453$ |
$(a), (-a+1), (2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.504266467$ |
3.049516954 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -538 a + 537\) , \( -1519 a + 8605\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-538a+537\right){x}-1519a+8605$ |
| 37004.10-a8 |
37004.10-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
37004.10 |
\( 2^{2} \cdot 11 \cdot 29^{2} \) |
\( 2^{5} \cdot 11^{4} \cdot 29^{6} \) |
$3.27906$ |
$(a), (-a+1), (2a+1), (-4a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$2.293268696$ |
$0.468199661$ |
3.246586698 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 667 a - 322\) , \( 5672 a + 4040\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(667a-322\right){x}+5672a+4040$ |
| 37004.12-e8 |
37004.12-e |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
37004.12 |
\( 2^{2} \cdot 11 \cdot 29^{2} \) |
\( 2^{5} \cdot 11^{4} \cdot 29^{6} \) |
$3.27906$ |
$(a), (-a+1), (2a+1), (4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.468199661$ |
8.494216233 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 495 a - 839\) , \( -7247 a + 7289\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(495a-839\right){x}-7247a+7289$ |
| 42592.18-f8 |
42592.18-f |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42592.18 |
\( 2^{5} \cdot 11^{3} \) |
\( 2^{17} \cdot 11^{10} \) |
$3.39641$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.380105151$ |
2.298659893 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -1011 a + 449\) , \( -10902 a + 18942\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-1011a+449\right){x}-10902a+18942$ |
| 42592.6-a8 |
42592.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42592.6 |
\( 2^{5} \cdot 11^{3} \) |
\( 2^{17} \cdot 11^{10} \) |
$3.39641$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1.369337870$ |
$0.380105151$ |
3.147642043 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 989 a - 773\) , \( -12500 a - 2488\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(989a-773\right){x}-12500a-2488$ |
| 45056.14-c8 |
45056.14-c |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
45056.14 |
\( 2^{12} \cdot 11 \) |
\( 2^{41} \cdot 11^{4} \) |
$3.44450$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.315166542$ |
0.952974048 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1376 a + 1375\) , \( -6496 a + 35519\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-1376a+1375\right){x}-6496a+35519$ |
| 45056.14-z8 |
45056.14-z |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
45056.14 |
\( 2^{12} \cdot 11 \) |
\( 2^{41} \cdot 11^{4} \) |
$3.44450$ |
$(a), (-a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$5.944353844$ |
$0.315166542$ |
5.664814948 |
\( \frac{67333244623}{117128} a + \frac{61299754338}{14641} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1376 a + 1375\) , \( 6496 a - 35519\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-1376a+1375\right){x}+6496a-35519$ |
*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.
