| 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 |
| 3675.2-a4 |
3675.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3675.2 |
\( 3 \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{2} \cdot 5^{8} \cdot 7^{2} \) |
$1.20507$ |
$(-2a+1), (-3a+1), (3a-2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.259415011$ |
$1.393647371$ |
1.669849624 |
\( \frac{157551496201}{13125} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -113\) , \( -469\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-113{x}-469$ |
| 99225.2-a4 |
99225.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
99225.2 |
\( 3^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{14} \cdot 5^{8} \cdot 7^{2} \) |
$3.17193$ |
$(-a-2), (2a+1), (3), (7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.522107791$ |
$0.464549123$ |
3.880715476 |
\( \frac{157551496201}{13125} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -1012\) , \( -12656\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-1012{x}-12656$ |
| 14175.1-a4 |
14175.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14175.1 |
\( 3^{4} \cdot 5^{2} \cdot 7 \) |
\( 3^{14} \cdot 5^{8} \cdot 7^{2} \) |
$2.57969$ |
$(-2a+1), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.259415011$ |
$0.464549123$ |
1.457564248 |
\( \frac{157551496201}{13125} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1013\) , \( 12656\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-1013{x}+12656$ |
| 735.1-a4 |
735.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-15}) \) |
$2$ |
$[0, 1]$ |
735.1 |
\( 3 \cdot 5 \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{8} \cdot 7^{2} \) |
$1.80201$ |
$(3,a+1), (5,a+2), (7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.475046402$ |
$1.393647371$ |
1.367518754 |
\( \frac{157551496201}{13125} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 111 a + 339\) , \( -1407 a + 3282\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(111a+339\right){x}-1407a+3282$ |
| 525.2-b4 |
525.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-21}) \) |
$2$ |
$[0, 1]$ |
525.2 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{14} \cdot 5^{8} \cdot 7^{2} \) |
$3.92029$ |
$(3,a), (5,a+2), (5,a+3), (7,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$0.259415011$ |
$1.393647371$ |
2.524575333 |
\( \frac{157551496201}{13125} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1013\) , \( 12656\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-1013{x}+12656$ |
| 735.1-b4 |
735.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
735.1 |
\( 3 \cdot 5 \cdot 7^{2} \) |
\( 3^{14} \cdot 5^{8} \cdot 7^{2} \) |
$5.09684$ |
$(3,a), (5,a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$0.259415011$ |
$1.393647371$ |
2.112211265 |
\( \frac{157551496201}{13125} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1013\) , \( 12656\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-1013{x}+12656$ |
| 3675.1-b4 |
3675.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3675.1 |
\( 3 \cdot 5^{2} \cdot 7^{2} \) |
\( 3^{2} \cdot 5^{8} \cdot 7^{2} \) |
$2.41015$ |
$(a), (5), (7)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.347904379$ |
$14.46234780$ |
2.904946046 |
\( \frac{157551496201}{13125} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -114\) , \( 468\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-114{x}+468$ |
| 525.1-e5 |
525.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{2} \cdot 5^{8} \cdot 7^{2} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.259415011$ |
$14.46234780$ |
1.637397992 |
\( \frac{157551496201}{13125} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 562 a - 1576\) , \( -10688 a + 29830\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(562a-1576\right){x}-10688a+29830$ |
*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.
