| 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 |
| 4900.2-a1 |
4900.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 5^{6} \cdot 7^{4} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.013481311$ |
$1.454378929$ |
2.134288811 |
\( -\frac{77626969}{8000} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -32\) , \( 64\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-32{x}+64$ |
| 4900.2-a2 |
4900.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{2} \cdot 7^{4} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
$2$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.121331804$ |
$4.363136788$ |
2.134288811 |
\( \frac{34391}{20} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 3\) , \( 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+3{x}+1$ |
| 4900.2-b1 |
4900.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{42} \cdot 5^{2} \cdot 7^{4} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$0.481402474$ |
1.091718195 |
\( -\frac{8990558521}{10485760} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -158\) , \( 1268\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-158{x}+1268$ |
| 4900.2-b2 |
4900.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 5^{6} \cdot 7^{4} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$1.444207423$ |
1.091718195 |
\( \frac{10100279}{16000} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 17\) , \( -27\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+17{x}-27$ |
| 4900.2-c1 |
4900.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{5} \cdot 5^{2} \cdot 7^{8} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.287045288$ |
0.867943370 |
\( -\frac{92065654374401}{280} a - 328860957952 \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 5226 a - 5227\) , \( 178143 a - 32959\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5226a-5227\right){x}+178143a-32959$ |
| 4900.2-c2 |
4900.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 5^{4} \cdot 7^{10} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.574090577$ |
0.867943370 |
\( \frac{44957682561}{78400} a - \frac{22448742401}{39200} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 326 a - 327\) , \( 2723 a - 619\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(326a-327\right){x}+2723a-619$ |
| 4900.2-c3 |
4900.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{7} \cdot 5^{16} \cdot 7^{7} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.287045288$ |
0.867943370 |
\( -\frac{1106567639419}{175000000} a - \frac{2848222090671}{87500000} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 821 a - 582\) , \( 9197 a + 3490\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(821a-582\right){x}+9197a+3490$ |
| 4900.2-c4 |
4900.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 5^{8} \cdot 7^{8} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.574090577$ |
0.867943370 |
\( -\frac{7930761861}{17920000} a + \frac{410560681}{1280000} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 51 a + 48\) , \( 433 a - 458\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(51a+48\right){x}+433a-458$ |
| 4900.2-c5 |
4900.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{11} \cdot 5^{2} \cdot 7^{14} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.574090577$ |
0.867943370 |
\( \frac{1245024751}{3073280} a + \frac{717420015}{614656} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -4 a - 133\) , \( 201 a + 53\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a-133\right){x}+201a+53$ |
| 4900.2-c6 |
4900.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{25} \cdot 5^{4} \cdot 7^{7} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.574090577$ |
0.867943370 |
\( \frac{9917005311763}{2936012800} a + \frac{1614739002967}{1468006400} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 5 a - 187\) , \( -17 a - 805\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a-187\right){x}-17a-805$ |
| 4900.2-d1 |
4900.2-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{5} \cdot 5^{2} \cdot 7^{8} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.287045288$ |
0.867943370 |
\( \frac{92065654374401}{280} a - \frac{184146722600961}{280} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -5227 a - 1\) , \( -178144 a + 145184\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-5227a-1\right){x}-178144a+145184$ |
| 4900.2-d2 |
4900.2-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 5^{4} \cdot 7^{10} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.574090577$ |
0.867943370 |
\( -\frac{44957682561}{78400} a + \frac{60197759}{78400} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -327 a - 1\) , \( -2724 a + 2104\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-327a-1\right){x}-2724a+2104$ |
| 4900.2-d3 |
4900.2-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{7} \cdot 5^{16} \cdot 7^{7} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.287045288$ |
0.867943370 |
\( \frac{1106567639419}{175000000} a - \frac{6803011820761}{175000000} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -822 a + 240\) , \( -9198 a + 12688\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-822a+240\right){x}-9198a+12688$ |
| 4900.2-d4 |
4900.2-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 5^{8} \cdot 7^{8} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.574090577$ |
0.867943370 |
\( \frac{7930761861}{17920000} a - \frac{2182912327}{17920000} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -52 a + 100\) , \( -434 a - 24\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-52a+100\right){x}-434a-24$ |
| 4900.2-d5 |
4900.2-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{11} \cdot 5^{2} \cdot 7^{14} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.574090577$ |
0.867943370 |
\( -\frac{1245024751}{3073280} a + \frac{2416062413}{1536640} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 5 a - 138\) , \( -206 a + 392\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a-138\right){x}-206a+392$ |
| 4900.2-d6 |
4900.2-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{25} \cdot 5^{4} \cdot 7^{7} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.574090577$ |
0.867943370 |
\( -\frac{9917005311763}{2936012800} a + \frac{13146483317697}{2936012800} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -4 a - 182\) , \( 12 a - 1004\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a-182\right){x}+12a-1004$ |
| 4900.2-e1 |
4900.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{13} \cdot 5^{4} \cdot 7^{7} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.143055106$ |
$1.211074090$ |
3.143158601 |
\( -\frac{82248083}{179200} a + \frac{347879361}{179200} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 22 a + 2\) , \( -12 a + 28\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(22a+2\right){x}-12a+28$ |
| 4900.2-e2 |
4900.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{11} \cdot 5^{2} \cdot 7^{8} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.286110213$ |
$1.211074090$ |
3.143158601 |
\( \frac{105641161}{2240} a + \frac{136495}{28} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -a + 69\) , \( -191 a + 84\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-a+69\right){x}-191a+84$ |
| 4900.2-f1 |
4900.2-f |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 5^{2} \cdot 7^{2} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.027173378$ |
$2.323832864$ |
3.436861190 |
\( -\frac{2395022293}{1310720} a + \frac{852378511}{655360} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 5 a - 10\) , \( 9 a - 2\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a-10\right){x}+9a-2$ |
| 4900.2-g1 |
4900.2-g |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{13} \cdot 5^{4} \cdot 7^{7} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.143055106$ |
$1.211074090$ |
3.143158601 |
\( \frac{82248083}{179200} a + \frac{132815639}{89600} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -22 a + 24\) , \( 12 a + 16\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-22a+24\right){x}+12a+16$ |
| 4900.2-g2 |
4900.2-g |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{11} \cdot 5^{2} \cdot 7^{8} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.286110213$ |
$1.211074090$ |
3.143158601 |
\( -\frac{105641161}{2240} a + \frac{116560761}{2240} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( a + 68\) , \( 191 a - 107\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a+68\right){x}+191a-107$ |
| 4900.2-h1 |
4900.2-h |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 5^{2} \cdot 7^{2} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.027173378$ |
$2.323832864$ |
3.436861190 |
\( \frac{2395022293}{1310720} a - \frac{690265271}{1310720} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -3 a - 6\) , \( -13 a + 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-3a-6\right){x}-13a+1$ |
| 4900.2-i1 |
4900.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 5^{4} \cdot 7^{6} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \cdot 5^{2} \) |
$0.089990015$ |
$0.899780668$ |
6.120853132 |
\( -\frac{115501303}{25600} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -71\) , \( 265\bigr] \) |
${y}^2+{x}{y}={x}^{3}-71{x}+265$ |
| 4900.2-i2 |
4900.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{25} \cdot 5^{2} \cdot 7^{6} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5^{2} \) |
$0.044995007$ |
$0.899780668$ |
6.120853132 |
\( -\frac{2083468303}{5242880} a - \frac{6453573283}{2621440} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 14 a + 52\) , \( 191 a - 186\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(14a+52\right){x}+191a-186$ |
| 4900.2-i3 |
4900.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{25} \cdot 5^{2} \cdot 7^{6} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5^{2} \) |
$0.044995007$ |
$0.899780668$ |
6.120853132 |
\( \frac{2083468303}{5242880} a - \frac{14990614869}{5242880} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -15 a + 66\) , \( -192 a + 5\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-15a+66\right){x}-192a+5$ |
| 4900.2-i4 |
4900.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 5^{8} \cdot 7^{6} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5^{2} \) |
$0.179980030$ |
$0.449890334$ |
6.120853132 |
\( \frac{544737993463}{20000} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1191\) , \( 15721\bigr] \) |
${y}^2+{x}{y}={x}^{3}-1191{x}+15721$ |
| 4900.2-j1 |
4900.2-j |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 5^{6} \cdot 7^{8} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{2} \) |
$1$ |
$0.691579459$ |
4.705064387 |
\( -\frac{5452947409}{250} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -491\) , \( -4229\bigr] \) |
${y}^2+{x}{y}={x}^{3}-491{x}-4229$ |
| 4900.2-j2 |
4900.2-j |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 5^{2} \cdot 7^{8} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{3} \) |
$1$ |
$2.074738378$ |
4.705064387 |
\( -\frac{49}{40} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1\) , \( -15\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}-15$ |
| 4900.2-k1 |
4900.2-k |
$2$ |
$7$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{2} \cdot 7^{4} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$7$ |
7B.1.2[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.530583180$ |
4.628048522 |
\( -\frac{5154200289}{20} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -132\) , \( -549\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-132{x}-549$ |
| 4900.2-k2 |
4900.2-k |
$2$ |
$7$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4900.2 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{28} \cdot 5^{14} \cdot 7^{4} \) |
$1.97805$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$7$ |
7B.1.1[2] |
$1$ |
\( 2^{2} \cdot 7^{3} \) |
$1$ |
$0.218654740$ |
4.628048522 |
\( \frac{1747829720511}{1280000000} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 918\) , \( 5289\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+918{x}+5289$ |
*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.
