| 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-a4 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{8} \) |
$0.45547$ |
$(-2a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.235701712$ |
0.322695746 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$ |
| 1875.1-b4 |
1875.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{8} \cdot 5^{20} \) |
$1.01847$ |
$(-2a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.447140342$ |
1.032626388 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -251\) , \( -727\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-251{x}-727$ |
| 11025.1-c4 |
11025.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
11025.1 |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{14} \cdot 5^{8} \cdot 7^{6} \) |
$1.58597$ |
$(-2a+1), (-3a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.487870110$ |
2.253375518 |
\( \frac{111284641}{50625} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 150 a + 90\) , \( -409 a + 609\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(150a+90\right){x}-409a+609$ |
| 11025.3-c4 |
11025.3-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
11025.3 |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{14} \cdot 5^{8} \cdot 7^{6} \) |
$1.58597$ |
$(-2a+1), (3a-2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.487870110$ |
2.253375518 |
\( \frac{111284641}{50625} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -88 a - 151\) , \( 169 a + 290\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-88a-151\right){x}+169a+290$ |
| 12675.1-a4 |
12675.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.1 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{8} \cdot 5^{8} \cdot 13^{6} \) |
$1.64224$ |
$(-2a+1), (-4a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.620072089$ |
2.863990301 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -79 a + 150\) , \( -213 a - 7\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-79a+150\right){x}-213a-7$ |
| 12675.3-a4 |
12675.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.3 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{8} \cdot 5^{8} \cdot 13^{6} \) |
$1.64224$ |
$(-2a+1), (4a-3), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.620072089$ |
2.863990301 |
\( \frac{111284641}{50625} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -150 a + 81\) , \( 283 a - 370\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-150a+81\right){x}+283a-370$ |
| 19200.1-g4 |
19200.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{8} \cdot 5^{8} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1.300312843$ |
$0.558925428$ |
3.356843389 |
\( \frac{111284641}{50625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -160\) , \( 308\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-160{x}+308$ |
| 57600.1-j4 |
57600.1-j |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{14} \cdot 5^{8} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.664660740$ |
$0.322695746$ |
3.971591054 |
\( \frac{111284641}{50625} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -480 a\) , \( -1848 a + 924\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-480a{x}-1848a+924$ |
| 57600.1-k4 |
57600.1-k |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{14} \cdot 5^{8} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.664660740$ |
$0.322695746$ |
3.971591054 |
\( \frac{111284641}{50625} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 482 a - 481\) , \( 2329 a - 1405\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(482a-481\right){x}+2329a-1405$ |
| 81225.1-a4 |
81225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
81225.1 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{14} \cdot 5^{8} \cdot 19^{6} \) |
$2.61289$ |
$(-2a+1), (-5a+3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.013853729$ |
$0.296125925$ |
2.754442525 |
\( \frac{111284641}{50625} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -151 a - 481\) , \( -1200 a - 1710\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-151a-481\right){x}-1200a-1710$ |
| 81225.3-a4 |
81225.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
81225.3 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{14} \cdot 5^{8} \cdot 19^{6} \) |
$2.61289$ |
$(-2a+1), (-5a+2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.013853729$ |
$0.296125925$ |
2.754442525 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 481 a + 150\) , \( 1199 a - 2909\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(481a+150\right){x}+1199a-2909$ |
| 102675.1-a4 |
102675.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.1 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{8} \cdot 5^{8} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+4), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$6.036317352$ |
$0.367547097$ |
5.123708641 |
\( \frac{111284641}{50625} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 70 a + 331\) , \( 1413 a - 906\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(70a+331\right){x}+1413a-906$ |
| 102675.3-a4 |
102675.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.3 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{8} \cdot 5^{8} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$6.036317352$ |
$0.367547097$ |
5.123708641 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 401 a - 331\) , \( -1413 a + 507\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(401a-331\right){x}-1413a+507$ |
*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.
