| 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 |
| 102675.1-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 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 770 a + 3631\) , \( 210053 a - 149676\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(770a+3631\right){x}+210053a-149676$ |
| 102675.1-a2 |
102675.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.1 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{2} \cdot 5^{2} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+4), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.509079338$ |
$1.470188389$ |
5.123708641 |
\( -\frac{1}{15} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 1\) , \( -47 a + 34\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+{x}-47a+34$ |
| 102675.1-a3 |
102675.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.1 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{4} \cdot 5^{16} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+4), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$3.018158676$ |
$0.183773548$ |
5.123708641 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -245 a - 1154\) , \( 10719 a - 8079\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-245a-1154\right){x}+10719a-8079$ |
| 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 |
\( \frac{111284641}{50625} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 70 a + 331\) , \( 1413 a - 906\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(70a+331\right){x}+1413a-906$ |
| 102675.1-a5 |
102675.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.1 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{4} \cdot 5^{4} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+4), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$3.018158676$ |
$0.735094194$ |
5.123708641 |
\( \frac{13997521}{225} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 35 a + 166\) , \( -1081 a + 831\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(35a+166\right){x}-1081a+831$ |
| 102675.1-a6 |
102675.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.1 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{16} \cdot 5^{4} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+4), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$12.07263470$ |
$0.183773548$ |
5.123708641 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 945 a + 4456\) , \( 151963 a - 107681\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(945a+4456\right){x}+151963a-107681$ |
| 102675.1-a7 |
102675.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.1 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{2} \cdot 5^{2} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+4), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$6.036317352$ |
$0.367547097$ |
5.123708641 |
\( \frac{56667352321}{15} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 560 a + 2641\) , \( -69511 a + 50796\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(560a+2641\right){x}-69511a+50796$ |
| 102675.1-a8 |
102675.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.1 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{8} \cdot 5^{2} \cdot 37^{6} \) |
$2.77055$ |
$(-2a+1), (-7a+4), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$24.14526941$ |
$0.091886774$ |
5.123708641 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 15120 a + 71281\) , \( 9735073 a - 6968786\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(15120a+71281\right){x}+9735073a-6968786$ |
| 102675.1-b1 |
102675.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.1 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{17} \cdot 5^{4} \cdot 37^{2} \) |
$2.77055$ |
$(-2a+1), (-7a+4), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 17 \) |
$0.036037605$ |
$0.849817062$ |
2.404693104 |
\( \frac{4729205494}{492075} a - \frac{1059629087}{492075} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -107 a + 32\) , \( -346 a + 400\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-107a+32\right){x}-346a+400$ |
| 102675.1-c1 |
102675.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102675.1 |
\( 3 \cdot 5^{2} \cdot 37^{2} \) |
\( 3^{17} \cdot 5^{4} \cdot 37^{8} \) |
$2.77055$ |
$(-2a+1), (-7a+4), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 17 \) |
$1$ |
$0.139709064$ |
5.484952487 |
\( \frac{4729205494}{492075} a - \frac{1059629087}{492075} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -1802 a - 2206\) , \( -65949 a - 22372\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1802a-2206\right){x}-65949a-22372$ |
*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.
