| 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 |
| 38025.2-a1 |
38025.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
38025.2 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 5^{6} \cdot 13^{2} \) |
$2.16131$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3 \) |
$0.766940191$ |
$1.697962880$ |
2.004923444 |
\( -\frac{303464448}{1625} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 42 a\) , \( 105\bigr] \) |
${y}^2+{y}={x}^{3}+42a{x}+105$ |
| 38025.2-a2 |
38025.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
38025.2 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 5^{2} \cdot 13^{6} \) |
$2.16131$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.255646730$ |
$1.697962880$ |
2.004923444 |
\( \frac{7077888}{10985} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -12 a\) , \( -21\bigr] \) |
${y}^2+{y}={x}^{3}-12a{x}-21$ |
| 38025.2-b1 |
38025.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
38025.2 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 5^{8} \cdot 13^{2} \) |
$2.16131$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.197947061$ |
$1.628388579$ |
2.977600725 |
\( -\frac{57960603}{8125} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -24\) , \( -45\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-24{x}-45$ |
| 38025.2-b2 |
38025.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
38025.2 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 5^{4} \cdot 13^{4} \) |
$2.16131$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.395894122$ |
$0.814194289$ |
2.977600725 |
\( \frac{260549802603}{4225} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -399\) , \( -2970\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-399{x}-2970$ |
| 38025.2-c1 |
38025.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
38025.2 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{9} \cdot 5^{2} \cdot 13^{8} \) |
$2.16131$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.248070663$ |
$0.575108164$ |
3.315263617 |
\( \frac{75342331689491}{217206405} a - \frac{89233997935534}{217206405} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 230 a - 475\) , \( 2458 a - 3904\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(230a-475\right){x}+2458a-3904$ |
| 38025.2-c2 |
38025.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
38025.2 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{12} \cdot 5^{4} \cdot 13^{4} \) |
$2.16131$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.624035331$ |
$1.150216328$ |
3.315263617 |
\( -\frac{540664013}{1482975} a + \frac{48161411}{98865} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 5 a - 25\) , \( 73 a - 79\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5a-25\right){x}+73a-79$ |
| 38025.2-d1 |
38025.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
38025.2 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{9} \cdot 5^{2} \cdot 13^{8} \) |
$2.16131$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.248070663$ |
$0.575108164$ |
3.315263617 |
\( -\frac{75342331689491}{217206405} a - \frac{13891666246043}{217206405} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -228 a - 247\) , \( -2704 a - 972\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-228a-247\right){x}-2704a-972$ |
| 38025.2-d2 |
38025.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
38025.2 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{12} \cdot 5^{4} \cdot 13^{4} \) |
$2.16131$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.624035331$ |
$1.150216328$ |
3.315263617 |
\( \frac{540664013}{1482975} a + \frac{181757152}{1482975} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -3 a - 22\) , \( -94 a + 18\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-3a-22\right){x}-94a+18$ |
| 38025.2-e1 |
38025.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
38025.2 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{10} \cdot 5^{4} \cdot 13^{2} \) |
$2.16131$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.427141385$ |
$1.901954146$ |
3.752330243 |
\( -\frac{19228717}{2925} a - 4432 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 19 a - 17\) , \( -46 a + 18\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(19a-17\right){x}-46a+18$ |
| 38025.2-e2 |
38025.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
38025.2 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{8} \cdot 5^{8} \cdot 13^{4} \) |
$2.16131$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.213570692$ |
$0.950977073$ |
3.752330243 |
\( -\frac{87765443}{316875} a - \frac{243952957}{316875} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 19 a + 28\) , \( -181 a + 171\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(19a+28\right){x}-181a+171$ |
| 38025.2-f1 |
38025.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
38025.2 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{10} \cdot 5^{4} \cdot 13^{2} \) |
$2.16131$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.427141385$ |
$1.901954146$ |
3.752330243 |
\( \frac{19228717}{2925} a - \frac{32192317}{2925} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 3 a + 17\) , \( 45 a - 27\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(3a+17\right){x}+45a-27$ |
| 38025.2-f2 |
38025.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
38025.2 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{8} \cdot 5^{8} \cdot 13^{4} \) |
$2.16131$ |
$(-2a+1), (-4a+1), (4a-3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.213570692$ |
$0.950977073$ |
3.752330243 |
\( \frac{87765443}{316875} a - \frac{340224}{325} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 48 a - 28\) , \( 180 a - 9\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(48a-28\right){x}+180a-9$ |
*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.
