| 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 |
| 75.1-a7 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$0.45547$ |
$(-2a+1), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.235701712$ |
0.322695746 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$ |
| 147.2-a8 |
147.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{4} \) |
$0.53893$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.862076929$ |
0.497720347 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \) |
${y}^2+{x}{y}={x}^{3}-784{x}-8515$ |
| 192.1-a1 |
192.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3 \) |
$0.57614$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.635347017$ |
0.524717144 |
\( -\frac{73696}{3} a - \frac{550672}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 11 a - 6\) , \( 11 a - 1\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(11a-6\right){x}+11a-1$ |
| 192.1-a2 |
192.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{16} \cdot 3 \) |
$0.57614$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.635347017$ |
0.524717144 |
\( \frac{73696}{3} a - \frac{624368}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 6 a - 11\) , \( -11 a + 10\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(6a-11\right){x}-11a+10$ |
| 192.1-a7 |
192.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$0.57614$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.817673508$ |
0.524717144 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -64 a + 64\) , \( 220\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-64a+64\right){x}+220$ |
| 241.1-a3 |
241.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
241.1 |
\( 241 \) |
\( 241 \) |
$0.60982$ |
$(-16a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$8.819196109$ |
0.636470655 |
\( \frac{50625}{241} a + \frac{3375}{241} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}$ |
| 241.1-a4 |
241.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
241.1 |
\( 241 \) |
\( 241^{4} \) |
$0.60982$ |
$(-16a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.204799027$ |
0.636470655 |
\( -\frac{2877366290625}{3373402561} a + \frac{4794971198625}{3373402561} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -10 a + 5\) , \( -13 a + 9\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-10a+5\right){x}-13a+9$ |
| 241.2-a3 |
241.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
241.2 |
\( 241 \) |
\( 241 \) |
$0.60982$ |
$(16a-15)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$8.819196109$ |
0.636470655 |
\( -\frac{50625}{241} a + \frac{54000}{241} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -a\) , \( -a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}-a{x}-a$ |
| 241.2-a4 |
241.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
241.2 |
\( 241 \) |
\( 241^{4} \) |
$0.60982$ |
$(16a-15)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.204799027$ |
0.636470655 |
\( \frac{2877366290625}{3373402561} a + \frac{1917604908000}{3373402561} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 9 a - 5\) , \( 12 a - 4\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(9a-5\right){x}+12a-4$ |
| 256.1-CMb2 |
256.1-CMb |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$0.61910$ |
$(2)$ |
0 |
$\Z/4\Z$ |
$\textsf{yes}$ |
$-12$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$4.423757977$ |
0.638514464 |
\( 54000 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4 a\) , \( 8 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-4a{x}+8a-4$ |
| 256.1-CMa2 |
256.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$0.61910$ |
$(2)$ |
0 |
$\Z/4\Z$ |
$\textsf{yes}$ |
$-12$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$4.423757977$ |
0.638514464 |
\( 54000 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6 a - 5\) , \( -3 a - 1\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-5\right){x}-3a-1$ |
| 273.1-a1 |
273.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
273.1 |
\( 3 \cdot 7 \cdot 13 \) |
\( 3 \cdot 7 \cdot 13 \) |
$0.62913$ |
$(-2a+1), (-3a+1), (-4a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$2.149159880$ |
0.620409017 |
\( \frac{1167033434129}{273} a - \frac{1319037947152}{273} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -7 a - 85\) , \( 34 a + 274\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a-85\right){x}+34a+274$ |
| 273.1-a4 |
273.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
273.1 |
\( 3 \cdot 7 \cdot 13 \) |
\( 3 \cdot 7 \cdot 13 \) |
$0.62913$ |
$(-2a+1), (-3a+1), (-4a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$8.596639523$ |
0.620409017 |
\( \frac{222751}{273} a + \frac{183472}{273} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -2 a\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}-2a{x}-a$ |
| 273.4-a1 |
273.4-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
273.4 |
\( 3 \cdot 7 \cdot 13 \) |
\( 3 \cdot 7 \cdot 13 \) |
$0.62913$ |
$(-2a+1), (3a-2), (4a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$2.149159880$ |
0.620409017 |
\( -\frac{1167033434129}{273} a - \frac{152004513023}{273} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 5 a - 90\) , \( -35 a + 309\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(5a-90\right){x}-35a+309$ |
| 273.4-a4 |
273.4-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
273.4 |
\( 3 \cdot 7 \cdot 13 \) |
\( 3 \cdot 7 \cdot 13 \) |
$0.62913$ |
$(-2a+1), (3a-2), (4a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$8.596639523$ |
0.620409017 |
\( -\frac{222751}{273} a + \frac{406223}{273} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}$ |
| 289.1-a1 |
289.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
289.1 |
\( 17^{2} \) |
\( 17^{8} \) |
$0.63815$ |
$(17)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.123938699$ |
0.613128289 |
\( -\frac{35937}{83521} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-{x}-14$ |
| 289.1-a2 |
289.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
289.1 |
\( 17^{2} \) |
\( 17^{2} \) |
$0.63815$ |
$(17)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$8.495754796$ |
0.613128289 |
\( \frac{35937}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-{x}$ |
| 343.2-a3 |
343.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
343.2 |
\( 7^{3} \) |
\( 7^{10} \) |
$0.66607$ |
$(-3a+1), (3a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$2.562419546$ |
0.739706807 |
\( -\frac{988929}{343} a + \frac{2130273}{343} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -4 a - 7\) , \( -9 a - 5\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-4a-7\right){x}-9a-5$ |
| 343.2-a4 |
343.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
343.2 |
\( 7^{3} \) |
\( 7^{10} \) |
$0.66607$ |
$(-3a+1), (3a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$2.562419546$ |
0.739706807 |
\( \frac{988929}{343} a + \frac{1141344}{343} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 11 a - 9\) , \( 15 a - 14\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(11a-9\right){x}+15a-14$ |
| 343.3-a3 |
343.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
343.3 |
\( 7^{3} \) |
\( 7^{10} \) |
$0.66607$ |
$(-3a+1), (3a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$2.562419546$ |
0.739706807 |
\( -\frac{988929}{343} a + \frac{2130273}{343} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 8 a - 9\) , \( -14 a + 10\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(8a-9\right){x}-14a+10$ |
| 343.3-a4 |
343.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
343.3 |
\( 7^{3} \) |
\( 7^{10} \) |
$0.66607$ |
$(-3a+1), (3a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$2.562419546$ |
0.739706807 |
\( \frac{988929}{343} a + \frac{1141344}{343} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( 6 a + 4\) , \( 8 a - 14\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(6a+4\right){x}+8a-14$ |
| 363.1-a3 |
363.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( 3^{6} \cdot 11^{2} \) |
$0.67558$ |
$(-2a+1), (11)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.102343908$ |
0.592122339 |
\( \frac{30664297}{297} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -6\) , \( -9\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-6{x}-9$ |
| 363.1-a4 |
363.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( 3^{6} \cdot 11^{8} \) |
$0.67558$ |
$(-2a+1), (11)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.025585977$ |
0.592122339 |
\( \frac{347873904937}{395307} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -146\) , \( 621\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-146{x}+621$ |
| 399.2-a5 |
399.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
399.2 |
\( 3 \cdot 7 \cdot 19 \) |
\( 3^{3} \cdot 7^{2} \cdot 19 \) |
$0.69174$ |
$(-2a+1), (-3a+1), (-5a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.971213806$ |
0.717532907 |
\( -\frac{238255387}{8379} a + \frac{297350960}{8379} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 2 a + 1\) , \( -2\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(2a+1\right){x}-2$ |
| 399.2-a6 |
399.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
399.2 |
\( 3 \cdot 7 \cdot 19 \) |
\( 3^{3} \cdot 7^{8} \cdot 19 \) |
$0.69174$ |
$(-2a+1), (-3a+1), (-5a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.242803451$ |
0.717532907 |
\( \frac{3983977737373759}{985780971} a - \frac{944095350591320}{985780971} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 112 a + 16\) , \( -141 a + 600\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(112a+16\right){x}-141a+600$ |
| 399.3-a5 |
399.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
399.3 |
\( 3 \cdot 7 \cdot 19 \) |
\( 3^{3} \cdot 7^{2} \cdot 19 \) |
$0.69174$ |
$(-2a+1), (3a-2), (-5a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.971213806$ |
0.717532907 |
\( \frac{238255387}{8379} a + \frac{59095573}{8379} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -3 a + 4\) , \( -a - 1\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a+4\right){x}-a-1$ |
| 399.3-a6 |
399.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
399.3 |
\( 3 \cdot 7 \cdot 19 \) |
\( 3^{3} \cdot 7^{8} \cdot 19 \) |
$0.69174$ |
$(-2a+1), (3a-2), (-5a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.242803451$ |
0.717532907 |
\( -\frac{3983977737373759}{985780971} a + \frac{3039882386782439}{985780971} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -113 a + 129\) , \( 140 a + 460\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-113a+129\right){x}+140a+460$ |
| 475.1-a1 |
475.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
475.1 |
\( 5^{2} \cdot 19 \) |
\( 5^{8} \cdot 19^{2} \) |
$0.72256$ |
$(-5a+3), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.449930551$ |
0.837117794 |
\( \frac{1361807016381}{225625} a - \frac{2510490224016}{225625} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 112 a - 28\) , \( 193 a + 250\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(112a-28\right){x}+193a+250$ |
| 475.1-a2 |
475.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
475.1 |
\( 5^{2} \cdot 19 \) |
\( 5^{2} \cdot 19^{2} \) |
$0.72256$ |
$(-5a+3), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.799722204$ |
0.837117794 |
\( \frac{19435059}{1805} a - \frac{19486224}{1805} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 2 a - 3\) , \( -2 a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(2a-3\right){x}-2a$ |
| 475.2-a1 |
475.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
475.2 |
\( 5^{2} \cdot 19 \) |
\( 5^{8} \cdot 19^{2} \) |
$0.72256$ |
$(-5a+2), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.449930551$ |
0.837117794 |
\( -\frac{1361807016381}{225625} a - \frac{229736641527}{45125} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -113 a + 85\) , \( -194 a + 444\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-113a+85\right){x}-194a+444$ |
| 475.2-a2 |
475.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
475.2 |
\( 5^{2} \cdot 19 \) |
\( 5^{2} \cdot 19^{2} \) |
$0.72256$ |
$(-5a+2), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.799722204$ |
0.837117794 |
\( -\frac{19435059}{1805} a - \frac{10233}{361} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -3 a\) , \( a - 1\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}-3a{x}+a-1$ |
| 507.2-a1 |
507.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
507.2 |
\( 3 \cdot 13^{2} \) |
\( 3^{2} \cdot 13^{2} \) |
$0.73443$ |
$(-2a+1), (-4a+1), (4a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.282583906$ |
$7.561180171$ |
0.616802873 |
\( \frac{12167}{39} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+{x}$ |
| 507.2-a3 |
507.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
507.2 |
\( 3 \cdot 13^{2} \) |
\( 3^{2} \cdot 13^{8} \) |
$0.73443$ |
$(-2a+1), (-4a+1), (4a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.070645976$ |
$1.890295042$ |
0.616802873 |
\( \frac{822656953}{85683} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -19\) , \( 22\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-19{x}+22$ |
| 579.1-b1 |
579.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
579.1 |
\( 3 \cdot 193 \) |
\( 3^{4} \cdot 193^{4} \) |
$0.75922$ |
$(-2a+1), (16a-7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.389035352$ |
0.801959934 |
\( -\frac{407977333075375}{12487392009} a + \frac{36260345789152}{12487392009} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 47 a - 44\) , \( 140 a - 41\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(47a-44\right){x}+140a-41$ |
| 579.1-b3 |
579.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
579.1 |
\( 3 \cdot 193 \) |
\( 3^{4} \cdot 193 \) |
$0.75922$ |
$(-2a+1), (16a-7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.556141409$ |
0.801959934 |
\( \frac{19397959}{1737} a - \frac{982672}{1737} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -3 a + 1\) , \( a - 2\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-3a+1\right){x}+a-2$ |
| 579.2-b1 |
579.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
579.2 |
\( 3 \cdot 193 \) |
\( 3^{4} \cdot 193^{4} \) |
$0.75922$ |
$(-2a+1), (-16a+9)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.389035352$ |
0.801959934 |
\( \frac{407977333075375}{12487392009} a - \frac{41301887476247}{1387488001} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -48 a + 3\) , \( -141 a + 99\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-48a+3\right){x}-141a+99$ |
| 579.2-b3 |
579.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
579.2 |
\( 3 \cdot 193 \) |
\( 3^{4} \cdot 193 \) |
$0.75922$ |
$(-2a+1), (-16a+9)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.556141409$ |
0.801959934 |
\( -\frac{19397959}{1737} a + \frac{2046143}{193} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 2 a - 2\) , \( -2 a - 1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a-2\right){x}-2a-1$ |
| 588.2-a6 |
588.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
588.2 |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{2} \) |
$0.76216$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.685091833$ |
0.791075908 |
\( \frac{268498407453697}{252} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1344\) , \( 18405\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-1344{x}+18405$ |
| 603.1-a2 |
603.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
603.1 |
\( 3^{2} \cdot 67 \) |
\( 3^{11} \cdot 67 \) |
$0.76697$ |
$(-2a+1), (9a-7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.166466092$ |
0.914080025 |
\( -\frac{25296887}{1809} a + \frac{8646439}{1809} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -8 a + 1\) , \( -12 a + 9\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-8a+1\right){x}-12a+9$ |
| 603.2-a2 |
603.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
603.2 |
\( 3^{2} \cdot 67 \) |
\( 3^{11} \cdot 67 \) |
$0.76697$ |
$(-2a+1), (9a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.166466092$ |
0.914080025 |
\( \frac{25296887}{1809} a - \frac{16650448}{1809} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 7 a - 6\) , \( 11 a - 2\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(7a-6\right){x}+11a-2$ |
| 651.2-a1 |
651.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
651.2 |
\( 3 \cdot 7 \cdot 31 \) |
\( 3^{8} \cdot 7 \cdot 31 \) |
$0.78180$ |
$(-2a+1), (-3a+1), (6a-5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.803828397$ |
1.041440810 |
\( -\frac{894250329349}{17577} a + \frac{103535650343}{5859} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -69 a + 85\) , \( 92 a + 174\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-69a+85\right){x}+92a+174$ |
| 651.2-a5 |
651.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
651.2 |
\( 3 \cdot 7 \cdot 31 \) |
\( 3^{2} \cdot 7 \cdot 31 \) |
$0.78180$ |
$(-2a+1), (-3a+1), (6a-5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$7.215313588$ |
1.041440810 |
\( -\frac{281749}{651} a - \frac{167497}{217} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( a\) , \( -a + 1\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-a+1$ |
| 651.3-a1 |
651.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
651.3 |
\( 3 \cdot 7 \cdot 31 \) |
\( 3^{8} \cdot 7 \cdot 31 \) |
$0.78180$ |
$(-2a+1), (3a-2), (-6a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.803828397$ |
1.041440810 |
\( \frac{894250329349}{17577} a - \frac{583643378320}{17577} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 70 a + 16\) , \( -23 a + 282\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(70a+16\right){x}-23a+282$ |
| 651.3-a5 |
651.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
651.3 |
\( 3 \cdot 7 \cdot 31 \) |
\( 3^{2} \cdot 7 \cdot 31 \) |
$0.78180$ |
$(-2a+1), (3a-2), (-6a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$7.215313588$ |
1.041440810 |
\( \frac{281749}{651} a - \frac{784240}{651} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 1\) , \( 1\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+{x}+1$ |
| 679.1-a2 |
679.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
679.1 |
\( 7 \cdot 97 \) |
\( 7^{2} \cdot 97^{4} \) |
$0.79007$ |
$(-3a+1), (-11a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.675320661$ |
0.967246834 |
\( -\frac{479451191796243}{4337934769} a + \frac{184136442343272}{4337934769} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 29 a + 15\) , \( -60 a + 103\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(29a+15\right){x}-60a+103$ |
| 679.1-a4 |
679.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
679.1 |
\( 7 \cdot 97 \) |
\( 7^{2} \cdot 97 \) |
$0.79007$ |
$(-3a+1), (-11a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6.701282644$ |
0.967246834 |
\( -\frac{3844017}{4753} a + \frac{11677392}{4753} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -a\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-a{x}$ |
| 679.4-a2 |
679.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
679.4 |
\( 7 \cdot 97 \) |
\( 7^{2} \cdot 97^{4} \) |
$0.79007$ |
$(3a-2), (-11a+8)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.675320661$ |
0.967246834 |
\( \frac{479451191796243}{4337934769} a - \frac{295314749452971}{4337934769} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -29 a + 44\) , \( 60 a + 43\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-29a+44\right){x}+60a+43$ |
| 679.4-a4 |
679.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
679.4 |
\( 7 \cdot 97 \) |
\( 7^{2} \cdot 97 \) |
$0.79007$ |
$(3a-2), (-11a+8)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6.701282644$ |
0.967246834 |
\( \frac{3844017}{4753} a + \frac{7833375}{4753} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( a - 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(a-1\right){x}$ |
| 741.1-a3 |
741.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
741.1 |
\( 3 \cdot 13 \cdot 19 \) |
\( 3 \cdot 13^{8} \cdot 19 \) |
$0.80752$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.494913119$ |
0.863088492 |
\( \frac{662272344834961}{46496651097} a - \frac{1655400483325016}{46496651097} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 9 a + 34\) , \( -103 a + 97\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(9a+34\right){x}-103a+97$ |
| 741.1-a6 |
741.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
741.1 |
\( 3 \cdot 13 \cdot 19 \) |
\( 3 \cdot 13^{2} \cdot 19 \) |
$0.80752$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.979652478$ |
0.863088492 |
\( -\frac{61090897}{9633} a + \frac{54761552}{9633} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -a - 1\) , \( -a - 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-a-1\right){x}-a-1$ |
*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.
