| 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 |
| 338.1-a1 |
338.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{34} \cdot 13^{4} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 17 \) |
$1$ |
$1.465476230$ |
4.708132584 |
\( \frac{20784357060630835715}{22151168} a - \frac{6873779989912045559}{2768896} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 45657 a + 120774\) , \( -6780606 a - 17939743\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(45657a+120774\right){x}-6780606a-17939743$ |
| 338.1-a2 |
338.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{17} \cdot 13^{2} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 17 \) |
$1$ |
$1.465476230$ |
4.708132584 |
\( -\frac{31007892977907785202357308641}{6656} a + \frac{82039173499650034853915343005}{6656} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -237223 a - 628026\) , \( -62218430 a - 164611359\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-237223a-628026\right){x}-62218430a-164611359$ |
| 338.1-b1 |
338.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{18} \cdot 13^{2} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$2.113195961$ |
0.798712997 |
\( -\frac{2673465150439}{6656} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -13880 a - 36719\) , \( 1456495 a + 3853523\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-13880a-36719\right){x}+1456495a+3853523$ |
| 338.1-c1 |
338.1-c |
$2$ |
$7$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{2} \cdot 13^{14} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.3 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$0.385597965$ |
1.020196322 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -213\) , \( -1257\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-213{x}-1257$ |
| 338.1-c2 |
338.1-c |
$2$ |
$7$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$18.89430030$ |
1.020196322 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-3{x}+3$ |
| 338.1-d1 |
338.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{6} \cdot 13^{2} \) |
$2.02743$ |
$(a+3), (13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.154059559$ |
$12.76973976$ |
4.461418149 |
\( -\frac{29791}{104} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -31 a - 83\) , \( 370 a + 978\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-31a-83\right){x}+370a+978$ |
| 338.1-e1 |
338.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{34} \cdot 13^{4} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 17 \) |
$1$ |
$1.465476230$ |
4.708132584 |
\( -\frac{20784357060630835715}{22151168} a - \frac{6873779989912045559}{2768896} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -45658 a + 120774\) , \( 6780606 a - 17939743\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-45658a+120774\right){x}+6780606a-17939743$ |
| 338.1-e2 |
338.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{17} \cdot 13^{2} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 17 \) |
$1$ |
$1.465476230$ |
4.708132584 |
\( \frac{31007892977907785202357308641}{6656} a + \frac{82039173499650034853915343005}{6656} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( 237222 a - 628026\) , \( 62218430 a - 164611359\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(237222a-628026\right){x}+62218430a-164611359$ |
| 338.1-f1 |
338.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{2} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$0.814071910$ |
1.230761042 |
\( \frac{6383618840403271125}{208} a - \frac{1055591744770981638}{13} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 790 a - 2134\) , \( 19805 a - 52274\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(790a-2134\right){x}+19805a-52274$ |
| 338.1-g1 |
338.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{12} \cdot 13^{4} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.968118660$ |
1.127868412 |
\( \frac{68921}{10816} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 40 a + 111\) , \( -3847 a - 10177\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(40a+111\right){x}-3847a-10177$ |
| 338.1-g2 |
338.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{6} \cdot 13^{8} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.968118660$ |
1.127868412 |
\( \frac{6634074439}{228488} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 1879 a - 4969\) , \( -68751 a + 181895\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1879a-4969\right){x}-68751a+181895$ |
| 338.1-h1 |
338.1-h |
$3$ |
$9$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{18} \cdot 13^{2} \) |
$2.02743$ |
$(a+3), (13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$15.19254363$ |
$0.265819283$ |
3.052797172 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -460\) , \( -3830\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-460{x}-3830$ |
| 338.1-h2 |
338.1-h |
$3$ |
$9$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{6} \cdot 13^{6} \) |
$2.02743$ |
$(a+3), (13)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$5.064181210$ |
$2.392373550$ |
3.052797172 |
\( -\frac{10218313}{17576} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -5\) , \( -8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-5{x}-8$ |
| 338.1-h3 |
338.1-h |
$3$ |
$9$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{2} \cdot 13^{2} \) |
$2.02743$ |
$(a+3), (13)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1.688060403$ |
$21.53136195$ |
3.052797172 |
\( \frac{12167}{26} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}$ |
| 338.1-i1 |
338.1-i |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{2} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$3.467896467$ |
5.242966643 |
\( -\frac{6383618840403271125}{208} a - \frac{1055591744770981638}{13} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -791 a - 2134\) , \( 19805 a + 52272\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-791a-2134\right){x}+19805a+52272$ |
| 338.1-j1 |
338.1-j |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{2} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$0.814071910$ |
1.230761042 |
\( -\frac{6383618840403271125}{208} a - \frac{1055591744770981638}{13} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -791 a - 2134\) , \( -19805 a - 52274\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-791a-2134\right){x}-19805a-52274$ |
| 338.1-k1 |
338.1-k |
$3$ |
$9$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{18} \cdot 13^{2} \) |
$2.02743$ |
$(a+3), (13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.166288191$ |
$12.10583107$ |
1.521727872 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -457\) , \( 3371\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-457{x}+3371$ |
| 338.1-k2 |
338.1-k |
$3$ |
$9$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{6} \cdot 13^{6} \) |
$2.02743$ |
$(a+3), (13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \cdot 3 \) |
$0.055429397$ |
$12.10583107$ |
1.521727872 |
\( -\frac{10218313}{17576} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -2\) , \( 4\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-2{x}+4$ |
| 338.1-k3 |
338.1-k |
$3$ |
$9$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{2} \cdot 13^{2} \) |
$2.02743$ |
$(a+3), (13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.166288191$ |
$12.10583107$ |
1.521727872 |
\( \frac{12167}{26} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 3\) , \( 1\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+3{x}+1$ |
| 338.1-l1 |
338.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{12} \cdot 13^{4} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.968118660$ |
1.127868412 |
\( \frac{68921}{10816} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -41 a + 111\) , \( 3847 a - 10177\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-41a+111\right){x}+3847a-10177$ |
| 338.1-l2 |
338.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{6} \cdot 13^{8} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.968118660$ |
1.127868412 |
\( \frac{6634074439}{228488} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -1880 a - 4969\) , \( 68751 a + 181895\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1880a-4969\right){x}+68751a+181895$ |
| 338.1-m1 |
338.1-m |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{2} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$3.467896467$ |
5.242966643 |
\( \frac{6383618840403271125}{208} a - \frac{1055591744770981638}{13} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 790 a - 2134\) , \( -19805 a + 52272\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(790a-2134\right){x}-19805a+52272$ |
| 338.1-n1 |
338.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{34} \cdot 13^{4} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 17 \) |
$1$ |
$0.188797282$ |
0.606548655 |
\( -\frac{20784357060630835715}{22151168} a - \frac{6873779989912045559}{2768896} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -45656 a + 120773\) , \( -6826263 a + 18060514\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-45656a+120773\right){x}-6826263a+18060514$ |
| 338.1-n2 |
338.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{17} \cdot 13^{2} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 17 \) |
$1$ |
$0.188797282$ |
0.606548655 |
\( \frac{31007892977907785202357308641}{6656} a + \frac{82039173499650034853915343005}{6656} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 237224 a - 628027\) , \( -61981207 a + 163983330\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(237224a-628027\right){x}-61981207a+163983330$ |
| 338.1-o1 |
338.1-o |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{6} \cdot 13^{2} \) |
$2.02743$ |
$(a+3), (13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.154059559$ |
$12.76973976$ |
4.461418149 |
\( -\frac{29791}{104} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 30 a - 83\) , \( -371 a + 978\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(30a-83\right){x}-371a+978$ |
| 338.1-p1 |
338.1-p |
$2$ |
$7$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{2} \cdot 13^{14} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.4 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$3.254622356$ |
8.610921368 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -216\) , \( 1255\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-216{x}+1255$ |
| 338.1-p2 |
338.1-p |
$2$ |
$7$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.6 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$3.254622356$ |
8.610921368 |
\( -\frac{2146689}{1664} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -6\) , \( -5\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-6{x}-5$ |
| 338.1-q1 |
338.1-q |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{18} \cdot 13^{2} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$2.113195961$ |
0.798712997 |
\( -\frac{2673465150439}{6656} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 13879 a - 36719\) , \( -1456495 a + 3853523\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(13879a-36719\right){x}-1456495a+3853523$ |
| 338.1-r1 |
338.1-r |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{34} \cdot 13^{4} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 17 \) |
$1$ |
$0.188797282$ |
0.606548655 |
\( \frac{20784357060630835715}{22151168} a - \frac{6873779989912045559}{2768896} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 45655 a + 120773\) , \( 6826262 a + 18060514\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(45655a+120773\right){x}+6826262a+18060514$ |
| 338.1-r2 |
338.1-r |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
338.1 |
\( 2 \cdot 13^{2} \) |
\( 2^{17} \cdot 13^{2} \) |
$2.02743$ |
$(a+3), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 17 \) |
$1$ |
$0.188797282$ |
0.606548655 |
\( -\frac{31007892977907785202357308641}{6656} a + \frac{82039173499650034853915343005}{6656} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -237225 a - 628027\) , \( 61981206 a + 163983330\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-237225a-628027\right){x}+61981206a+163983330$ |
*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.
