| 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 |
$2$ |
$3$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{26} \cdot 7^{4} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 11 \) |
$0.123592677$ |
$13.63954876$ |
4.600009703 |
\( -\frac{1071157205}{702464} a - \frac{236252885}{43904} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -2 a + 13\) , \( -77 a + 350\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-2a+13\right){x}-77a+350$ |
| 196.1-a2 |
196.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{46} \cdot 7^{4} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \cdot 11 \) |
$0.370778033$ |
$1.515505418$ |
4.600009703 |
\( \frac{632471691020195}{2946347565056} a + \frac{138967326073715}{184146722816} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 23 a - 67\) , \( 2050 a - 9234\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(23a-67\right){x}+2050a-9234$ |
| 196.1-b1 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{48} \cdot 7^{2} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{4} \) |
$1$ |
$0.436190660$ |
4.382326219 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 309493 a - 1402352\) , \( 189505457 a - 858673648\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(309493a-1402352\right){x}+189505457a-858673648$ |
| 196.1-b2 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{2} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$35.33144352$ |
4.382326219 |
\( -\frac{15625}{28} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 943 a - 4272\) , \( -61883 a + 280400\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(943a-4272\right){x}-61883a+280400$ |
| 196.1-b3 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{6} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$3.925715946$ |
4.382326219 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -8132 a + 36848\) , \( 1323792 a - 5998272\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8132a+36848\right){x}+1323792a-5998272$ |
| 196.1-b4 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{12} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$3.925715946$ |
4.382326219 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 64468 a - 292112\) , \( 14828552 a - 67190080\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(64468a-292112\right){x}+14828552a-67190080$ |
| 196.1-b5 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 7^{4} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$35.33144352$ |
4.382326219 |
\( \frac{128787625}{98} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 19093 a - 86512\) , \( -2833233 a + 12837744\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(19093a-86512\right){x}-2833233a+12837744$ |
| 196.1-b6 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{30} \cdot 7^{4} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{4} \) |
$1$ |
$0.436190660$ |
4.382326219 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 4955893 a - 22455792\) , \( 12070201777 a - 54691639792\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(4955893a-22455792\right){x}+12070201777a-54691639792$ |
| 196.1-c1 |
196.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{20} \cdot 7^{20} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$1$ |
$0.151548824$ |
1.203028369 |
\( -\frac{1478226180460967581603217}{265863444556808} a + \frac{13396066630536158158406673}{531726889113616} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 159108 a - 721128\) , \( 69487828 a - 314864756\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(159108a-721128\right){x}+69487828a-314864756$ |
| 196.1-c2 |
196.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{40} \cdot 7^{4} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.424781197$ |
1.203028369 |
\( -\frac{10188791249212817}{210453397504} a + \frac{46527281763089825}{210453397504} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 240 a + 826\) , \( 28 a + 120\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(240a+826\right){x}+28a+120$ |
| 196.1-c3 |
196.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{44} \cdot 7^{8} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$2.424781197$ |
1.203028369 |
\( \frac{274244925473}{157351936} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 948 a - 4328\) , \( -2300 a + 10380\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(948a-4328\right){x}-2300a+10380$ |
| 196.1-c4 |
196.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{28} \cdot 7^{16} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1$ |
$0.606195299$ |
1.203028369 |
\( \frac{313558873425953}{1475789056} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 9908 a - 45288\) , \( 1088004 a - 4933492\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(9908a-45288\right){x}+1088004a-4933492$ |
| 196.1-c5 |
196.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{40} \cdot 7^{4} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.424781197$ |
1.203028369 |
\( \frac{10188791249212817}{210453397504} a + \frac{2271155657117313}{13153337344} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -241 a + 1067\) , \( -29 a + 149\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-241a+1067\right){x}-29a+149$ |
| 196.1-c6 |
196.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{20} \cdot 7^{20} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$1$ |
$0.151548824$ |
1.203028369 |
\( \frac{1478226180460967581603217}{265863444556808} a + \frac{10439614269614222995200239}{531726889113616} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 4068 a - 24808\) , \( 2165556 a - 10017396\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(4068a-24808\right){x}+2165556a-10017396$ |
| 196.1-d1 |
196.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{46} \cdot 7^{4} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \cdot 11 \) |
$0.370778033$ |
$1.515505418$ |
4.600009703 |
\( -\frac{632471691020195}{2946347565056} a + \frac{2855948908199635}{2946347565056} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -712 a + 3216\) , \( -2220 a + 10048\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-712a+3216\right){x}-2220a+10048$ |
| 196.1-d2 |
196.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{26} \cdot 7^{4} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 11 \) |
$0.123592677$ |
$13.63954876$ |
4.600009703 |
\( \frac{1071157205}{702464} a - \frac{4851203365}{702464} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 118 a - 544\) , \( -1244 a + 5632\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(118a-544\right){x}-1244a+5632$ |
| 196.1-e1 |
196.1-e |
$2$ |
$3$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{34} \cdot 7^{4} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$4.417334046$ |
$1.515505418$ |
4.982098484 |
\( -\frac{632471691020195}{2946347565056} a + \frac{2855948908199635}{2946347565056} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -86 a - 302\) , \( -19642 a - 69360\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-86a-302\right){x}-19642a-69360$ |
| 196.1-e2 |
196.1-e |
$2$ |
$3$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 7^{4} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1.472444682$ |
$13.63954876$ |
4.982098484 |
\( \frac{1071157205}{702464} a - \frac{4851203365}{702464} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 9 a + 33\) , \( 726 a + 2562\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(9a+33\right){x}+726a+2562$ |
| 196.1-f1 |
196.1-f |
$6$ |
$18$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$0.436190660$ |
0.486925135 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$ |
| 196.1-f2 |
196.1-f |
$6$ |
$18$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$35.33144352$ |
0.486925135 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}$ |
| 196.1-f3 |
196.1-f |
$6$ |
$18$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$3.925715946$ |
0.486925135 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$ |
| 196.1-f4 |
196.1-f |
$6$ |
$18$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$3.925715946$ |
0.486925135 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$ |
| 196.1-f5 |
196.1-f |
$6$ |
$18$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$35.33144352$ |
0.486925135 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$ |
| 196.1-f6 |
196.1-f |
$6$ |
$18$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$0.436190660$ |
0.486925135 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$ |
| 196.1-g1 |
196.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{8} \cdot 7^{20} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{6} \) |
$1$ |
$0.151548824$ |
4.812113476 |
\( -\frac{1478226180460967581603217}{265863444556808} a + \frac{13396066630536158158406673}{531726889113616} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -22091 a - 78090\) , \( -21183610 a - 74802455\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-22091a-78090\right){x}-21183610a-74802455$ |
| 196.1-g2 |
196.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{52} \cdot 7^{4} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{10} \) |
$1$ |
$2.424781197$ |
4.812113476 |
\( -\frac{10188791249212817}{210453397504} a + \frac{46527281763089825}{210453397504} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 17247 a + 60896\) , \( 279549 a + 987132\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(17247a+60896\right){x}+279549a+987132$ |
| 196.1-g3 |
196.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{32} \cdot 7^{8} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{10} \) |
$1$ |
$2.424781197$ |
4.812113476 |
\( \frac{274244925473}{157351936} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -4331 a - 15290\) , \( 36406 a + 128553\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4331a-15290\right){x}+36406a+128553$ |
| 196.1-g4 |
196.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{16} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{8} \) |
$1$ |
$0.606195299$ |
4.812113476 |
\( \frac{313558873425953}{1475789056} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -45291 a - 159930\) , \( -10411722 a - 36765143\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-45291a-159930\right){x}-10411722a-36765143$ |
| 196.1-g5 |
196.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{52} \cdot 7^{4} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{10} \) |
$1$ |
$2.424781197$ |
4.812113476 |
\( \frac{10188791249212817}{210453397504} a + \frac{2271155657117313}{13153337344} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -297 a - 635\) , \( 3439 a + 12390\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-297a-635\right){x}+3439a+12390$ |
| 196.1-g6 |
196.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{8} \cdot 7^{20} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{6} \) |
$1$ |
$0.151548824$ |
4.812113476 |
\( \frac{1478226180460967581603217}{265863444556808} a + \frac{10439614269614222995200239}{531726889113616} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -723851 a - 2556010\) , \( -671781146 a - 2372145815\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-723851a-2556010\right){x}-671781146a-2372145815$ |
| 196.1-h1 |
196.1-h |
$2$ |
$3$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 7^{4} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1.472444682$ |
$13.63954876$ |
4.982098484 |
\( -\frac{1071157205}{702464} a - \frac{236252885}{43904} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -550 a - 1935\) , \( 15635 a + 55213\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-550a-1935\right){x}+15635a+55213$ |
| 196.1-h2 |
196.1-h |
$2$ |
$3$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{34} \cdot 7^{4} \) |
$2.69562$ |
$(2,a), (2,a+1), (7,a+1), (7,a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$4.417334046$ |
$1.515505418$ |
4.982098484 |
\( \frac{632471691020195}{2946347565056} a + \frac{138967326073715}{184146722816} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 3225 a + 11395\) , \( 441 a + 1561\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(3225a+11395\right){x}+441a+1561$ |
*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.
