| 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 |
| 196.1-a1 |
196.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{6} \) |
$1.80054$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.544202604$ |
0.843837239 |
\( -\frac{1476235590834}{2401} a + \frac{37704153305557}{19208} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 213 a - 685\) , \( 2873 a - 9175\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(213a-685\right){x}+2873a-9175$ |
| 196.1-a2 |
196.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{3} \) |
$1.80054$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.544202604$ |
0.843837239 |
\( \frac{1217675}{98} a - \frac{92692567}{3136} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 13 a - 45\) , \( 49 a - 159\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(13a-45\right){x}+49a-159$ |
| 196.1-b1 |
196.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{4} \) |
$1.80054$ |
$(-a), (a-1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.039122600$ |
$19.67788774$ |
2.287321324 |
\( \frac{30676469}{196} a - \frac{24404566}{49} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( a - 1\) , \( -a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}-a$ |
| 196.1-c1 |
196.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{20} \cdot 7^{5} \) |
$1.80054$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.511182680$ |
$6.100755250$ |
2.316438238 |
\( -\frac{6717146489}{2458624} a + \frac{452450953}{43904} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 54 a - 170\) , \( -276 a + 880\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(54a-170\right){x}-276a+880$ |
| 196.1-c2 |
196.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{10} \) |
$1.80054$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.255591340$ |
$6.100755250$ |
2.316438238 |
\( -\frac{8271409004059059}{184473632} a + \frac{3772500342785869}{26353376} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -648 a - 1422\) , \( -4308 a - 9446\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-648a-1422\right){x}-4308a-9446$ |
| 196.1-d1 |
196.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$1.80054$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$4.267658818$ |
$0.436190660$ |
3.111068440 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$ |
| 196.1-d2 |
196.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$1.80054$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$4.267658818$ |
$35.33144352$ |
3.111068440 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}$ |
| 196.1-d3 |
196.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$1.80054$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$1.422552939$ |
$3.925715946$ |
3.111068440 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$ |
| 196.1-d4 |
196.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$1.80054$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$0.711276469$ |
$3.925715946$ |
3.111068440 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$ |
| 196.1-d5 |
196.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$1.80054$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$2.133829409$ |
$35.33144352$ |
3.111068440 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$ |
| 196.1-d6 |
196.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$1.80054$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$2.133829409$ |
$0.436190660$ |
3.111068440 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$ |
| 196.1-e1 |
196.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{20} \cdot 7^{5} \) |
$1.80054$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.511182680$ |
$6.100755250$ |
2.316438238 |
\( \frac{6717146489}{2458624} a + \frac{18620106879}{2458624} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -54 a - 116\) , \( 276 a + 604\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-54a-116\right){x}+276a+604$ |
| 196.1-e2 |
196.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{10} \) |
$1.80054$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.255591340$ |
$6.100755250$ |
2.316438238 |
\( \frac{8271409004059059}{184473632} a + \frac{2267011674430253}{23059204} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 646 a - 2069\) , \( 4307 a - 13753\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(646a-2069\right){x}+4307a-13753$ |
| 196.1-f1 |
196.1-f |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{4} \) |
$1.80054$ |
$(-a), (a-1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.1.2 |
$100$ |
\( 2^{3} \) |
$1$ |
$0.014459755$ |
2.148087278 |
\( -\frac{414183515883649725221}{50176} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 776475 a - 2484709\) , \( 612108065 a - 1954384693\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(776475a-2484709\right){x}+612108065a-1954384693$ |
| 196.1-f2 |
196.1-f |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{20} \) |
$1.80054$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.1.1 |
$4$ |
\( 2^{3} \cdot 5^{2} \) |
$1$ |
$0.361493875$ |
2.148087278 |
\( -\frac{1018411856981}{1129900996} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 1050 a - 3349\) , \( 51515 a - 164488\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(1050a-3349\right){x}+51515a-164488$ |
| 196.1-g1 |
196.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{4} \) |
$1.80054$ |
$(-a), (a-1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.039122600$ |
$19.67788774$ |
2.287321324 |
\( -\frac{30676469}{196} a - \frac{66941795}{196} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -2 a + 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-2a+1\right){x}$ |
| 196.1-h1 |
196.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{3} \) |
$1.80054$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.544202604$ |
0.843837239 |
\( -\frac{1217675}{98} a - \frac{7675281}{448} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -15 a - 32\) , \( -50 a - 110\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-15a-32\right){x}-50a-110$ |
| 196.1-h2 |
196.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{6} \) |
$1.80054$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.544202604$ |
0.843837239 |
\( \frac{1476235590834}{2401} a + \frac{3699181225555}{2744} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -215 a - 472\) , \( -2874 a - 6302\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-215a-472\right){x}-2874a-6302$ |
*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.
