| 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 |
| 676.2-a2 |
676.2-a |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$0.78920$ |
$(-4a+1), (4a-3), (2)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7 \) |
$1$ |
$3.920899519$ |
0.646780683 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-3{x}+3$ |
| 338.2-b2 |
338.2-b |
$2$ |
$7$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
338.2 |
\( 2 \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$0.76630$ |
$(a+1), (-3a-2), (2a+3)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$3.920899519$ |
1.120257005 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-3{x}+3$ |
| 676.2-b2 |
676.2-b |
$2$ |
$7$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$1.20552$ |
$(a), (-a+1), (13)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1[2] |
$1$ |
\( 7^{2} \) |
$1$ |
$3.920899519$ |
2.963921441 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-3{x}+3$ |
| 338.1-b2 |
338.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$1.08371$ |
$(a), (13)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$0.625224564$ |
$3.920899519$ |
0.990532430 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-3{x}+3$ |
| 676.1-a2 |
676.1-a |
$2$ |
$7$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
676.1 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$1.51120$ |
$(2), (13)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7 \) |
$1.192849768$ |
$3.920899519$ |
0.805818200 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-3{x}+3$ |
| 676.2-c2 |
676.2-c |
$2$ |
$7$ |
\(\Q(\sqrt{-15}) \) |
$2$ |
$[0, 1]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$1.76470$ |
$(2,a), (2,a+1), (13)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7^{2} \) |
$1$ |
$3.920899519$ |
2.024743805 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 676.1-b2 |
676.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-19}) \) |
$2$ |
$[0, 1]$ |
676.1 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$1.98610$ |
$(2), (13)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7 \) |
$6.422386059$ |
$3.920899519$ |
3.301165303 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 338.1-c2 |
338.1-c |
$2$ |
$7$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$1.71349$ |
$(2,a+1), (13)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$1.527173030$ |
$3.920899519$ |
1.530209549 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 676.5-b2 |
676.5-b |
$2$ |
$7$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
676.5 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$2.18519$ |
$(2,a), (2,a+1), (13,a+4), (13,a+8)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7^{2} \) |
$0.862409559$ |
$3.920899519$ |
2.820300263 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 338.1-c2 |
338.1-c |
$2$ |
$7$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$1.87704$ |
$(2,a), (13)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$2.715546088$ |
$3.920899519$ |
2.483872030 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 676.2-b2 |
676.2-b |
$2$ |
$7$ |
\(\Q(\sqrt{-31}) \) |
$2$ |
$[0, 1]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$2.53692$ |
$(2,a), (2,a+1), (13)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$4$ |
\( 7^{2} \) |
$1$ |
$3.920899519$ |
5.633714739 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 676.2-a2 |
676.2-a |
$2$ |
$7$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$2.69562$ |
$(13,a+5), (13,a+7), (2)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7 \) |
$1$ |
$3.920899519$ |
0.189357994 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 52.2-c2 |
52.2-c |
$2$ |
$7$ |
\(\Q(\sqrt{-39}) \) |
$2$ |
$[0, 1]$ |
52.2 |
\( 2^{2} \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$1.49855$ |
$(2,a), (2,a+1), (13,a+6)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \cdot 7^{2} \) |
$0.557712781$ |
$3.920899519$ |
2.801263700 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 338.2-c2 |
338.2-c |
$2$ |
$7$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
338.2 |
\( 2 \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$2.42325$ |
$(2,a), (13,a+4), (13,a+9)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$9$ |
\( 2 \cdot 7 \) |
$1$ |
$3.920899519$ |
3.188307332 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 676.2-b2 |
676.2-b |
$2$ |
$7$ |
\(\Q(\sqrt{-43}) \) |
$2$ |
$[0, 1]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$2.98785$ |
$(a+1), (a-2), (2)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$9$ |
\( 7 \) |
$1$ |
$3.920899519$ |
1.537538325 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 676.2-b2 |
676.2-b |
$2$ |
$7$ |
\(\Q(\sqrt{-47}) \) |
$2$ |
$[0, 1]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$3.12373$ |
$(2,a), (2,a+1), (13)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7^{2} \) |
$1$ |
$3.920899519$ |
1.143843950 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 676.2-a2 |
676.2-a |
$2$ |
$7$ |
\(\Q(\sqrt{-51}) \) |
$2$ |
$[0, 1]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$3.25395$ |
$(a), (a-1), (2)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7 \) |
$1$ |
$3.920899519$ |
0.156867357 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 26.1-d2 |
26.1-d |
$2$ |
$7$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$1.45507$ |
$(2,a+1), (a)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$4$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$3.920899519$ |
2.485627123 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 676.5-d2 |
676.5-d |
$2$ |
$7$ |
\(\Q(\sqrt{-55}) \) |
$2$ |
$[0, 1]$ |
676.5 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$3.37914$ |
$(2,a), (2,a+1), (13,a+3), (13,a+9)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7^{2} \) |
$5.597446900$ |
$3.920899519$ |
11.83734599 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 338.2-c2 |
338.2-c |
$2$ |
$7$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
338.2 |
\( 2 \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$2.86722$ |
$(2,a), (13,a+5), (13,a+8)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$3.920899519$ |
0.299401278 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 676.1-a2 |
676.1-a |
$2$ |
$7$ |
\(\Q(\sqrt{-59}) \) |
$2$ |
$[0, 1]$ |
676.1 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$3.49986$ |
$(2), (13)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7 \) |
$5.660435040$ |
$3.920899519$ |
1.651092745 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 676.1-b2 |
676.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
676.1 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$3.72960$ |
$(2), (13)$ |
$0 \le r \le 1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
|
\( 7 \) |
$1$ |
$3.920899519$ |
6.735217955 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 338.2-e2 |
338.2-e |
$2$ |
$7$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
338.2 |
\( 2 \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$3.15953$ |
$(2,a+1), (13,a+3), (13,a+10)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$3.920899519$ |
0.271702233 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 676.2-b2 |
676.2-b |
$2$ |
$7$ |
\(\Q(\sqrt{-71}) \) |
$2$ |
$[0, 1]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$3.83932$ |
$(2,a), (2,a+1), (13)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7^{2} \) |
$1$ |
$3.920899519$ |
0.930650326 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 676.5-e2 |
676.5-e |
$2$ |
$7$ |
\(\Q(\sqrt{-79}) \) |
$2$ |
$[0, 1]$ |
676.5 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$4.04985$ |
$(2,a), (2,a+1), (13,a+2), (13,a+10)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7^{2} \) |
$6.826236185$ |
$3.920899519$ |
12.04518484 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 676.1-a2 |
676.1-a |
$2$ |
$7$ |
\(\Q(\sqrt{-83}) \) |
$2$ |
$[0, 1]$ |
676.1 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$4.15111$ |
$(2), (13)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7 \) |
$5.434916301$ |
$3.920899519$ |
1.336600066 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 338.1-e2 |
338.1-e |
$2$ |
$7$ |
\(\Q(\sqrt{-21}) \) |
$2$ |
$[0, 1]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$3.51162$ |
$(2,a+1), (13)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$7.030922113$ |
$3.920899519$ |
3.437560131 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 676.5-g2 |
676.5-g |
$2$ |
$7$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
676.5 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$4.24996$ |
$(2,a), (2,a+1), (13,a+5), (13,a+7)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7^{2} \) |
$4.440796669$ |
$3.920899519$ |
7.467014016 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 338.2-d2 |
338.2-d |
$2$ |
$7$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
338.2 |
\( 2 \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$3.59426$ |
$(2,a), (13,a+2), (13,a+11)$ |
$0 \le r \le 2$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$16$ |
\( 2 \cdot 7 \) |
$1$ |
$3.920899519$ |
3.821433537 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 52.1-b2 |
52.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$2.28908$ |
$(13,a+6), (2)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$9$ |
\( 2 \cdot 7 \) |
$1$ |
$3.920899519$ |
2.113827178 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 676.5-c2 |
676.5-c |
$2$ |
$7$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
676.5 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$4.44106$ |
$(2,a), (2,a+1), (13,a+1), (13,a+11)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7^{2} \) |
$2.321642724$ |
$3.920899519$ |
3.735762763 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 676.5-d2 |
676.5-d |
$2$ |
$7$ |
\(\Q(\sqrt{-103}) \) |
$2$ |
$[0, 1]$ |
676.5 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$4.62428$ |
$(2,a), (2,a+1), (13,a), (13,a+12)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7^{2} \) |
$11.44862662$ |
$3.920899519$ |
17.69214473 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 26.1-b2 |
26.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$2.05778$ |
$(2,a), (13,a)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 7$ |
2Cn, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$3.920899519$ |
0.439400948 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 676.2-a2 |
676.2-a |
$2$ |
$7$ |
\(\Q(\sqrt{-107}) \) |
$2$ |
$[0, 1]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$4.71321$ |
$(13,a+3), (13,a+9), (2)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$4$ |
\( 7 \) |
$1$ |
$3.920899519$ |
0.433197329 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 676.2-c2 |
676.2-c |
$2$ |
$7$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$4.80050$ |
$(2,a), (2,a+1), (13)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7^{2} \) |
$1$ |
$7.841799039$ |
0.744310625 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 676.1-b2 |
676.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-115}) \) |
$2$ |
$[0, 1]$ |
676.1 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$4.88623$ |
$(2), (13)$ |
$0 \le r \le 1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
|
\( 7 \) |
$1$ |
$3.920899519$ |
7.809059467 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 676.2-c2 |
676.2-c |
$2$ |
$7$ |
\(\Q(\sqrt{-119}) \) |
$2$ |
$[0, 1]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$4.97048$ |
$(2,a), (2,a+1), (13)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7^{2} \) |
$1$ |
$7.841799039$ |
0.718856539 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 338.2-e2 |
338.2-e |
$2$ |
$7$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
338.2 |
\( 2 \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$4.19719$ |
$(2,a), (13,a+3), (13,a+10)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$3.920899519$ |
0.204530010 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 52.2-a2 |
52.2-a |
$2$ |
$7$ |
\(\Q(\sqrt{-143}) \) |
$2$ |
$[0, 1]$ |
52.2 |
\( 2^{2} \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$2.86951$ |
$(2,a), (2,a+1), (13,a+6)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \cdot 7^{2} \) |
$1.470512209$ |
$3.920899519$ |
3.857236927 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 676.1-b2 |
676.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
676.1 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$5.81727$ |
$(2), (13)$ |
$0 \le r \le 1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
|
\( 7 \) |
$1$ |
$3.920899519$ |
9.135816748 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 52.1-f2 |
52.1-f |
$2$ |
$7$ |
\(\Q(\sqrt{-195}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$3.35086$ |
$(13,a+6), (2)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$3.920899519$ |
0.160446540 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 52.2-c2 |
52.2-c |
$2$ |
$7$ |
\(\Q(\sqrt{-247}) \) |
$2$ |
$[0, 1]$ |
52.2 |
\( 2^{2} \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$3.77127$ |
$(2,a), (2,a+1), (13,a+6)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \cdot 7^{2} \) |
$6.758727940$ |
$3.920899519$ |
13.48938619 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 26.1-c2 |
26.1-c |
$2$ |
$7$ |
\(\Q(\sqrt{-65}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$3.25363$ |
$(2,a+1), (13,a)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$3.920899519$ |
0.277901560 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 52.1-b2 |
52.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-299}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$4.14930$ |
$(13,a+6), (2)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$4$ |
\( 2 \cdot 7 \) |
$1$ |
$3.920899519$ |
0.518289083 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 26.1-g2 |
26.1-g |
$2$ |
$7$ |
\(\Q(\sqrt{-78}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$3.56418$ |
$(2,a), (13,a)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$9$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$3.920899519$ |
2.283194303 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 52.1-c2 |
52.1-c |
$2$ |
$7$ |
\(\Q(\sqrt{-403}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$4.81717$ |
$(13,a+6), (2)$ |
$0 \le r \le 2$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$16$ |
\( 2 \cdot 7 \) |
$1$ |
$3.920899519$ |
1.785727240 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 52.2-e2 |
52.2-e |
$2$ |
$7$ |
\(\Q(\sqrt{-455}) \) |
$2$ |
$[0, 1]$ |
52.2 |
\( 2^{2} \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$5.11853$ |
$(2,a), (2,a+1), (13,a+6)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \cdot 7^{2} \) |
$3.538330444$ |
$3.920899519$ |
5.203174495 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 26.1-f2 |
26.1-f |
$2$ |
$7$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$4.60133$ |
$(2,a), (13,a)$ |
$0 \le r \le 2$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$16$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$7.841799039$ |
3.144097249 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 52.2-c2 |
52.2-c |
$2$ |
$7$ |
\(\Q(\sqrt{-559}) \) |
$2$ |
$[0, 1]$ |
52.2 |
\( 2^{2} \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$5.67342$ |
$(2,a), (2,a+1), (13,a+6)$ |
$0 \le r \le 1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
|
\( 2 \cdot 7^{2} \) |
$1$ |
$7.841799039$ |
17.76264111 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 52.1-a2 |
52.1-a |
$2$ |
$7$ |
\(\Q(\sqrt{-611}) \) |
$2$ |
$[0, 1]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$5.93144$ |
$(13,a+6), (2)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$7.841799039$ |
0.090641494 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
*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.
