| 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 |
| 275.1-a1 |
275.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
275.1 |
\( 5^{2} \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$2.09040$ |
$(-4a-9), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.506787596$ |
$16.93058676$ |
4.440859943 |
\( \frac{59319}{55} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+{x}$ |
| 275.1-a2 |
275.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
275.1 |
\( 5^{2} \cdot 11 \) |
\( 5^{4} \cdot 11^{4} \) |
$2.09040$ |
$(-4a-9), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$3.013575193$ |
$16.93058676$ |
4.440859943 |
\( \frac{8120601}{3025} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -4\) , \( 3\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-4{x}+3$ |
| 275.1-a3 |
275.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
275.1 |
\( 5^{2} \cdot 11 \) |
\( 5^{2} \cdot 11^{8} \) |
$2.09040$ |
$(-4a-9), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$6.027150387$ |
$4.232646692$ |
4.440859943 |
\( \frac{2749884201}{73205} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -29\) , \( -52\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-29{x}-52$ |
| 275.1-a4 |
275.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
275.1 |
\( 5^{2} \cdot 11 \) |
\( 5^{8} \cdot 11^{2} \) |
$2.09040$ |
$(-4a-9), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.506787596$ |
$16.93058676$ |
4.440859943 |
\( \frac{22930509321}{6875} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -59\) , \( 190\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-59{x}+190$ |
| 275.1-b1 |
275.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
275.1 |
\( 5^{2} \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$2.09040$ |
$(-4a-9), (5)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.858870826$ |
$11.85112914$ |
1.917440855 |
\( \frac{59319}{55} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 299 a + 709\) , \( -3776 a - 8958\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(299a+709\right){x}-3776a-8958$ |
| 275.1-b2 |
275.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
275.1 |
\( 5^{2} \cdot 11 \) |
\( 5^{4} \cdot 11^{4} \) |
$2.09040$ |
$(-4a-9), (5)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.464717706$ |
$11.85112914$ |
1.917440855 |
\( \frac{8120601}{3025} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 1541 a - 5197\) , \( 32926 a - 111036\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(1541a-5197\right){x}+32926a-111036$ |
| 275.1-b3 |
275.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
275.1 |
\( 5^{2} \cdot 11 \) |
\( 5^{2} \cdot 11^{8} \) |
$2.09040$ |
$(-4a-9), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.116179426$ |
$11.85112914$ |
1.917440855 |
\( \frac{2749884201}{73205} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -10741 a - 25481\) , \( 1005724 a + 2385860\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-10741a-25481\right){x}+1005724a+2385860$ |
| 275.1-b4 |
275.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
275.1 |
\( 5^{2} \cdot 11 \) |
\( 5^{8} \cdot 11^{2} \) |
$2.09040$ |
$(-4a-9), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.464717706$ |
$2.962782285$ |
1.917440855 |
\( \frac{22930509321}{6875} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 21781 a - 73452\) , \( 2959256 a - 9979444\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(21781a-73452\right){x}+2959256a-9979444$ |
*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.
