| 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-a1 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{32} \cdot 5^{2} \) |
$0.45547$ |
$(-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$0.558925428$ |
0.322695746 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-110{x}-880$ |
| 1875.1-b1 |
1875.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{32} \cdot 5^{14} \) |
$1.01847$ |
$(-2a+1), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.111785085$ |
1.032626388 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2751\) , \( -104477\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2751{x}-104477$ |
| 11025.1-c1 |
11025.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
11025.1 |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{38} \cdot 5^{2} \cdot 7^{6} \) |
$1.58597$ |
$(-2a+1), (-3a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.121967527$ |
2.253375518 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 1650 a + 990\) , \( -50809 a + 92379\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1650a+990\right){x}-50809a+92379$ |
| 11025.3-c1 |
11025.3-c |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
11025.3 |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{38} \cdot 5^{2} \cdot 7^{6} \) |
$1.58597$ |
$(-2a+1), (3a-2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.121967527$ |
2.253375518 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -988 a - 1651\) , \( 48169 a + 42560\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-988a-1651\right){x}+48169a+42560$ |
| 12675.1-a1 |
12675.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.1 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{32} \cdot 5^{2} \cdot 13^{6} \) |
$1.64224$ |
$(-2a+1), (-4a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.155018022$ |
2.863990301 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -879 a + 1650\) , \( -30133 a - 13197\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-879a+1650\right){x}-30133a-13197$ |
| 12675.3-a1 |
12675.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12675.3 |
\( 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{32} \cdot 5^{2} \cdot 13^{6} \) |
$1.64224$ |
$(-2a+1), (4a-3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.155018022$ |
2.863990301 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -1650 a + 881\) , \( 30903 a - 44980\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1650a+881\right){x}+30903a-44980$ |
| 19200.1-g1 |
19200.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{32} \cdot 5^{2} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1.300312843$ |
$0.139731357$ |
3.356843389 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1760\) , \( 52788\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-1760{x}+52788$ |
| 57600.1-j1 |
57600.1-j |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{38} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$10.65864296$ |
$0.080673936$ |
3.971591054 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -5280 a\) , \( -316728 a + 158364\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-5280a{x}-316728a+158364$ |
| 57600.1-k1 |
57600.1-k |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{38} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$10.65864296$ |
$0.080673936$ |
3.971591054 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 5282 a - 5281\) , \( 322009 a - 163645\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(5282a-5281\right){x}+322009a-163645$ |
| 81225.1-a1 |
81225.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
81225.1 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{38} \cdot 5^{2} \cdot 19^{6} \) |
$2.61289$ |
$(-2a+1), (-5a+3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$8.055414916$ |
$0.074031481$ |
2.754442525 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -1651 a - 5281\) , \( -142860 a - 266580\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-1651a-5281\right){x}-142860a-266580$ |
| 81225.3-a1 |
81225.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
81225.3 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{38} \cdot 5^{2} \cdot 19^{6} \) |
$2.61289$ |
$(-2a+1), (-5a+2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$8.055414916$ |
$0.074031481$ |
2.754442525 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 5281 a + 1650\) , \( 142859 a - 409439\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(5281a+1650\right){x}+142859a-409439$ |
| 102675.1-a1 |
102675.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.1 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{32} \cdot 5^{2} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+4), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$24.14526941$ |
$0.091886774$ |
5.123708641 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 770 a + 3631\) , \( 210053 a - 149676\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(770a+3631\right){x}+210053a-149676$ |
| 102675.3-a1 |
102675.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.3 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{32} \cdot 5^{2} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$24.14526941$ |
$0.091886774$ |
5.123708641 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 4401 a - 3631\) , \( -210053 a + 60377\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(4401a-3631\right){x}-210053a+60377$ |
*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.
