| 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 |
| 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 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 4401 a - 3631\) , \( -210053 a + 60377\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(4401a-3631\right){x}-210053a+60377$ |
| 102675.3-a2 |
102675.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.3 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{2} \cdot 5^{2} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.509079338$ |
$1.470188389$ |
5.123708641 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( a - 1\) , \( 47 a - 13\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(a-1\right){x}+47a-13$ |
| 102675.3-a3 |
102675.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.3 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{4} \cdot 5^{16} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$3.018158676$ |
$0.183773548$ |
5.123708641 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -1399 a + 1154\) , \( -10719 a + 2640\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-1399a+1154\right){x}-10719a+2640$ |
| 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 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 401 a - 331\) , \( -1413 a + 507\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(401a-331\right){x}-1413a+507$ |
| 102675.3-a5 |
102675.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.3 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{4} \cdot 5^{4} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$3.018158676$ |
$0.735094194$ |
5.123708641 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 201 a - 166\) , \( 1081 a - 250\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(201a-166\right){x}+1081a-250$ |
| 102675.3-a6 |
102675.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.3 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{16} \cdot 5^{4} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$12.07263470$ |
$0.183773548$ |
5.123708641 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 5401 a - 4456\) , \( -151963 a + 44282\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(5401a-4456\right){x}-151963a+44282$ |
| 102675.3-a7 |
102675.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.3 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{2} \cdot 5^{2} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$6.036317352$ |
$0.367547097$ |
5.123708641 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 3201 a - 2641\) , \( 69511 a - 18715\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(3201a-2641\right){x}+69511a-18715$ |
| 102675.3-a8 |
102675.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.3 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{8} \cdot 5^{2} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$24.14526941$ |
$0.091886774$ |
5.123708641 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 86401 a - 71281\) , \( -9735073 a + 2766287\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(86401a-71281\right){x}-9735073a+2766287$ |
| 102675.3-b1 |
102675.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.3 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{17} \cdot 5^{4} \cdot 37^{2} \) |
$2.77055$ |
$(-2a+1), (-7a+3), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 17 \) |
$0.036037605$ |
$0.849817062$ |
2.404693104 |
\( -\frac{4729205494}{492075} a + \frac{3669576407}{492075} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -33 a + 106\) , \( 345 a + 54\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-33a+106\right){x}+345a+54$ |
| 102675.3-c1 |
102675.3-c |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.3 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{17} \cdot 5^{4} \cdot 37^{8} \) |
$2.77055$ |
$(-2a+1), (-7a+3), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 17 \) |
$1$ |
$0.139709064$ |
5.484952487 |
\( -\frac{4729205494}{492075} a + \frac{3669576407}{492075} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -4009 a + 2205\) , \( 64146 a - 84312\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4009a+2205\right){x}+64146a-84312$ |
*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.
