| 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 |
| 81.1-CMa2 |
81.1-CMa |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
81.1 |
\( 3^{4} \) |
\( 3^{10} \) |
$0.46432$ |
$(-2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-27$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$2.702876088$ |
0.346779163 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -30\) , \( 63\bigr] \) |
${y}^2+{y}={x}^{3}-30{x}+63$ |
| 324.1-a1 |
324.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{2} \cdot 3^{10} \) |
$0.65665$ |
$(-2a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$1.878378408$ |
0.722988186 |
\( -\frac{17268549}{2} a - 114659280 \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 91 a - 62\) , \( -276 a - 13\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(91a-62\right){x}-276a-13$ |
| 324.1-a2 |
324.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{2} \cdot 3^{10} \) |
$0.65665$ |
$(-2a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$1.878378408$ |
0.722988186 |
\( \frac{17268549}{2} a - \frac{246587109}{2} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 61 a - 92\) , \( 276 a - 289\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(61a-92\right){x}+276a-289$ |
| 324.1-a3 |
324.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{2} \cdot 3^{6} \) |
$0.65665$ |
$(-2a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$5.635135226$ |
0.722988186 |
\( -\frac{132651}{2} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -3 a + 3\) , \( 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-3a+3\right){x}+3$ |
| 361.2-a1 |
361.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
361.2 |
\( 19^{2} \) |
\( 19^{2} \) |
$0.67465$ |
$(-5a+3), (-5a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$2.033701819$ |
$0.935309008$ |
0.488089257 |
\( -\frac{50357871050752}{19} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -769\) , \( -8470\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-769{x}-8470$ |
| 361.2-a2 |
361.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
361.2 |
\( 19^{2} \) |
\( 19^{10} \) |
$0.67465$ |
$(-5a+3), (-5a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$0.225966868$ |
$0.935309008$ |
0.488089257 |
\( -\frac{14306161739497472}{322687697779} a - \frac{12817090105540608}{322687697779} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 31 a + 99\) , \( 498 a - 424\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(31a+99\right){x}+498a-424$ |
| 361.2-a3 |
361.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
361.2 |
\( 19^{2} \) |
\( 19^{10} \) |
$0.67465$ |
$(-5a+3), (-5a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$0.225966868$ |
$0.935309008$ |
0.488089257 |
\( \frac{14306161739497472}{322687697779} a - \frac{27123251845038080}{322687697779} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -99 a - 31\) , \( -498 a + 74\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-99a-31\right){x}-498a+74$ |
| 361.2-a5 |
361.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
361.2 |
\( 19^{2} \) |
\( 19^{2} \) |
$0.67465$ |
$(-5a+3), (-5a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$0.225966868$ |
$8.417781075$ |
0.488089257 |
\( \frac{32768}{19} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( a - 1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(a-1\right){x}$ |
| 441.1-CMa1 |
441.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{8} \) |
$0.70927$ |
$(-2a+1), (-3a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3, 7$ |
3B.1.1[2], 7Cs.6.1 |
$1$ |
\( 3 \) |
$1$ |
$2.215892550$ |
0.852897440 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -10 a + 14\bigr] \) |
${y}^2+a{y}={x}^{3}-10a+14$ |
| 441.3-CMa1 |
441.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
441.3 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{8} \) |
$0.70927$ |
$(-2a+1), (3a-2)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3, 7$ |
3B.1.1[2], 7Cs.6.1 |
$1$ |
\( 3 \) |
$1$ |
$2.215892550$ |
0.852897440 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( 9 a + 4\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+9a+4$ |
| 513.1-a1 |
513.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
513.1 |
\( 3^{3} \cdot 19 \) |
\( 3^{9} \cdot 19^{3} \) |
$0.73659$ |
$(-2a+1), (-5a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$2.326048010$ |
0.895296296 |
\( -\frac{189124608}{6859} a - \frac{266760192}{6859} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 9 a - 21\) , \( -22 a + 35\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(9a-21\right){x}-22a+35$ |
| 513.1-a2 |
513.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
513.1 |
\( 3^{3} \cdot 19 \) |
\( 3^{3} \cdot 19 \) |
$0.73659$ |
$(-2a+1), (-5a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$6.978144030$ |
0.895296296 |
\( \frac{331776}{19} a - \frac{552960}{19} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -a - 1\) , \( -a\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}-a$ |
| 513.2-a1 |
513.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
513.2 |
\( 3^{3} \cdot 19 \) |
\( 3^{9} \cdot 19^{3} \) |
$0.73659$ |
$(-2a+1), (-5a+2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$2.326048010$ |
0.895296296 |
\( \frac{189124608}{6859} a - \frac{455884800}{6859} \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( -9 a - 12\) , \( 21 a + 13\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-9a-12\right){x}+21a+13$ |
| 513.2-a2 |
513.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
513.2 |
\( 3^{3} \cdot 19 \) |
\( 3^{3} \cdot 19 \) |
$0.73659$ |
$(-2a+1), (-5a+2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$6.978144030$ |
0.895296296 |
\( -\frac{331776}{19} a - \frac{221184}{19} \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( a - 2\) , \( -1\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-2\right){x}-1$ |
| 523.1-a1 |
523.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
523.1 |
\( 523 \) |
\( 523^{3} \) |
$0.74016$ |
$(-26a+9)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$2.284168151$ |
0.879176731 |
\( \frac{11489855124637}{143055667} a - \frac{6128833451203}{143055667} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 18 a - 22\) , \( -40 a + 39\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(18a-22\right){x}-40a+39$ |
| 523.1-a2 |
523.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
523.1 |
\( 523 \) |
\( 523 \) |
$0.74016$ |
$(-26a+9)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$6.852504454$ |
0.879176731 |
\( -\frac{19832319}{523} a + \frac{11332126}{523} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -2 a - 2\) , \( 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a-2\right){x}+1$ |
| 523.2-a1 |
523.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
523.2 |
\( 523 \) |
\( 523^{3} \) |
$0.74016$ |
$(-26a+17)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$2.284168151$ |
0.879176731 |
\( -\frac{11489855124637}{143055667} a + \frac{5361021673434}{143055667} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -16 a - 4\) , \( 23 a - 5\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-16a-4\right){x}+23a-5$ |
| 523.2-a2 |
523.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
523.2 |
\( 523 \) |
\( 523 \) |
$0.74016$ |
$(-26a+17)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$6.852504454$ |
0.879176731 |
\( \frac{19832319}{523} a - \frac{8500193}{523} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( a + 1\) , \( 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(a+1\right){x}+1$ |
| 532.2-b2 |
532.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
532.2 |
\( 2^{2} \cdot 7 \cdot 19 \) |
\( 2^{2} \cdot 7 \cdot 19 \) |
$0.74332$ |
$(-3a+1), (-5a+2), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$7.542892635$ |
0.967753576 |
\( \frac{1586601}{266} a + \frac{610835}{266} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -a\) , \( -1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}-a{x}-1$ |
| 532.2-b4 |
532.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
532.2 |
\( 2^{2} \cdot 7 \cdot 19 \) |
\( 2^{2} \cdot 7 \cdot 19^{9} \) |
$0.74332$ |
$(-3a+1), (-5a+2), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$0.838099181$ |
0.967753576 |
\( \frac{370224333190852179}{4517627768906} a + \frac{309374020241203618}{2258813884453} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 54 a - 195\) , \( -513 a + 1037\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(54a-195\right){x}-513a+1037$ |
| 532.2-b5 |
532.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
532.2 |
\( 2^{2} \cdot 7 \cdot 19 \) |
\( 2^{2} \cdot 7 \cdot 19 \) |
$0.74332$ |
$(-3a+1), (-5a+2), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$9$ |
\( 1 \) |
$1$ |
$0.838099181$ |
0.967753576 |
\( -\frac{579646309349518}{133} a + \frac{1352709098404281}{266} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 454 a - 1145\) , \( 7469 a - 13841\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(454a-1145\right){x}+7469a-13841$ |
| 532.3-b2 |
532.3-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
532.3 |
\( 2^{2} \cdot 7 \cdot 19 \) |
\( 2^{2} \cdot 7 \cdot 19 \) |
$0.74332$ |
$(3a-2), (-5a+3), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$7.542892635$ |
0.967753576 |
\( -\frac{1586601}{266} a + \frac{1098718}{133} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( -a\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}-a{x}-a$ |
| 532.3-b4 |
532.3-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
532.3 |
\( 2^{2} \cdot 7 \cdot 19 \) |
\( 2^{2} \cdot 7 \cdot 19^{9} \) |
$0.74332$ |
$(3a-2), (-5a+3), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$0.838099181$ |
0.967753576 |
\( -\frac{370224333190852179}{4517627768906} a + \frac{988972373673259415}{4517627768906} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 194 a - 55\) , \( 512 a + 525\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(194a-55\right){x}+512a+525$ |
| 532.3-b5 |
532.3-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
532.3 |
\( 2^{2} \cdot 7 \cdot 19 \) |
\( 2^{2} \cdot 7 \cdot 19 \) |
$0.74332$ |
$(3a-2), (-5a+3), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$9$ |
\( 1 \) |
$1$ |
$0.838099181$ |
0.967753576 |
\( \frac{579646309349518}{133} a + \frac{193416479705245}{266} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 1144 a - 455\) , \( -7470 a - 6371\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(1144a-455\right){x}-7470a-6371$ |
| 577.1-a1 |
577.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
577.1 |
\( 577 \) |
\( 577^{3} \) |
$0.75857$ |
$(-27a+19)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$2.618055143$ |
1.007689894 |
\( -\frac{1230241558528}{192100033} a + \frac{1127925596160}{192100033} \) |
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( 9 a - 9\) , \( 14 a - 8\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(9a-9\right){x}+14a-8$ |
| 577.1-a2 |
577.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
577.1 |
\( 577 \) |
\( 577 \) |
$0.75857$ |
$(-27a+19)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$7.854165429$ |
1.007689894 |
\( \frac{700416}{577} a + \frac{1368064}{577} \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( a\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+a{x}-a$ |
| 577.2-a1 |
577.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
577.2 |
\( 577 \) |
\( 577^{3} \) |
$0.75857$ |
$(27a-8)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$2.618055143$ |
1.007689894 |
\( \frac{1230241558528}{192100033} a - \frac{102315962368}{192100033} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -9 a\) , \( -15 a + 7\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}-9a{x}-15a+7$ |
| 577.2-a2 |
577.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
577.2 |
\( 577 \) |
\( 577 \) |
$0.75857$ |
$(27a-8)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$7.854165429$ |
1.007689894 |
\( -\frac{700416}{577} a + \frac{2068480}{577} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( -1\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}-{x}$ |
| 613.1-a1 |
613.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
613.1 |
\( 613 \) |
\( 613 \) |
$0.77013$ |
$(28a-19)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$7.390956618$ |
0.948260176 |
\( \frac{3577833}{613} a + \frac{2506987}{613} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 2 a\) , \( a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+2a{x}+a$ |
| 613.1-a2 |
613.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
613.1 |
\( 613 \) |
\( 613^{3} \) |
$0.77013$ |
$(28a-19)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$2.463652206$ |
0.948260176 |
\( -\frac{1278850555981}{230346397} a + \frac{3648159129780}{230346397} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -3 a - 10\) , \( 2 a + 9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-3a-10\right){x}+2a+9$ |
| 613.2-a1 |
613.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
613.2 |
\( 613 \) |
\( 613 \) |
$0.77013$ |
$(28a-9)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$7.390956618$ |
0.948260176 |
\( -\frac{3577833}{613} a + \frac{6084820}{613} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -a + 2\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a+2\right){x}$ |
| 613.2-a2 |
613.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
613.2 |
\( 613 \) |
\( 613^{3} \) |
$0.77013$ |
$(28a-9)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$2.463652206$ |
0.948260176 |
\( \frac{1278850555981}{230346397} a + \frac{2369308573799}{230346397} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 4 a - 13\) , \( -6 a + 25\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a-13\right){x}-6a+25$ |
| 676.2-b1 |
676.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{18} \cdot 13^{2} \) |
$0.78920$ |
$(-4a+1), (4a-3), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$0.896934130$ |
1.035690323 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -460\) , \( -3830\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-460{x}-3830$ |
| 676.2-b3 |
676.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 13^{2} \) |
$0.78920$ |
$(-4a+1), (4a-3), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$8.072407178$ |
1.035690323 |
\( \frac{12167}{26} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}-{x}$ |
| 676.2-b4 |
676.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 13^{10} \) |
$0.78920$ |
$(-4a+1), (4a-3), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$0.896934130$ |
1.035690323 |
\( -\frac{1824558573109097}{21208998746} a + \frac{26221448217163305}{21208998746} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 135 a + 94\) , \( 724 a - 1240\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(135a+94\right){x}+724a-1240$ |
| 676.2-b5 |
676.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 13^{10} \) |
$0.78920$ |
$(-4a+1), (4a-3), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$0.896934130$ |
1.035690323 |
\( \frac{1824558573109097}{21208998746} a + \frac{12198444822027104}{10604499373} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -95 a - 136\) , \( -724 a - 516\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-95a-136\right){x}-724a-516$ |
| 703.2-a1 |
703.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
703.2 |
\( 19 \cdot 37 \) |
\( 19^{3} \cdot 37^{3} \) |
$0.79696$ |
$(-5a+3), (-7a+3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$0.113802202$ |
$2.673687979$ |
0.702685116 |
\( \frac{200000710493}{347428927} a - \frac{176021954063}{347428927} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -5 a\) , \( -8 a + 7\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-5a{x}-8a+7$ |
| 703.2-a2 |
703.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
703.2 |
\( 19 \cdot 37 \) |
\( 19 \cdot 37 \) |
$0.79696$ |
$(-5a+3), (-7a+3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$0.341406607$ |
$8.021063937$ |
0.702685116 |
\( -\frac{328275}{703} a + \frac{359234}{703} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -a\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}-a{x}$ |
| 703.3-a1 |
703.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
703.3 |
\( 19 \cdot 37 \) |
\( 19^{3} \cdot 37^{3} \) |
$0.79696$ |
$(-5a+2), (-7a+4)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$0.113802202$ |
$2.673687979$ |
0.702685116 |
\( -\frac{200000710493}{347428927} a + \frac{23978756430}{347428927} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 4 a - 5\) , \( 7 a - 1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(4a-5\right){x}+7a-1$ |
| 703.3-a2 |
703.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
703.3 |
\( 19 \cdot 37 \) |
\( 19 \cdot 37 \) |
$0.79696$ |
$(-5a+2), (-7a+4)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$0.341406607$ |
$8.021063937$ |
0.702685116 |
\( \frac{328275}{703} a + \frac{30959}{703} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -a\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}-a{x}-a$ |
| 729.1-CMb1 |
729.1-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
729.1 |
\( 3^{6} \) |
\( 3^{6} \) |
$0.80423$ |
$(-2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$8.108628264$ |
1.040337491 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a$ |
| 729.1-CMa1 |
729.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
729.1 |
\( 3^{6} \) |
\( 3^{6} \) |
$0.80423$ |
$(-2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$8.108628264$ |
1.040337491 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}$ |
| 729.1-a1 |
729.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
729.1 |
\( 3^{6} \) |
\( 3^{6} \) |
$0.80423$ |
$(-2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$6.976113039$ |
0.895035720 |
\( -18981 a + 13149 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -2 a\) , \( a\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}-2a{x}+a$ |
| 729.1-a2 |
729.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
729.1 |
\( 3^{6} \) |
\( 3^{6} \) |
$0.80423$ |
$(-2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$6.976113039$ |
0.895035720 |
\( 18981 a - 5832 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( a - 2\) , \( -2 a + 1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(a-2\right){x}-2a+1$ |
| 756.1-a1 |
756.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
756.1 |
\( 2^{2} \cdot 3^{3} \cdot 7 \) |
\( 2^{2} \cdot 3^{11} \cdot 7 \) |
$0.81158$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$9$ |
\( 1 \) |
$1$ |
$0.851435750$ |
0.983153319 |
\( \frac{94629827885}{14} a - \frac{179449637977}{14} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 699 a - 305\) , \( -4326 a - 2344\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(699a-305\right){x}-4326a-2344$ |
| 756.1-a2 |
756.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
756.1 |
\( 2^{2} \cdot 3^{3} \cdot 7 \) |
\( 2^{18} \cdot 3^{11} \cdot 7 \) |
$0.81158$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$0.851435750$ |
0.983153319 |
\( \frac{2250281123}{896} a - \frac{12902619235}{3584} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 249 a - 260\) , \( 1740 a - 922\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(249a-260\right){x}+1740a-922$ |
| 756.1-a3 |
756.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
756.1 |
\( 2^{2} \cdot 3^{3} \cdot 7 \) |
\( 2^{2} \cdot 3^{3} \cdot 7 \) |
$0.81158$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$7.662921756$ |
0.983153319 |
\( \frac{40743}{14} a - \frac{1674}{7} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -a\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-a{x}$ |
| 756.1-a5 |
756.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
756.1 |
\( 2^{2} \cdot 3^{3} \cdot 7 \) |
\( 2^{2} \cdot 3^{11} \cdot 7^{9} \) |
$0.81158$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$0.851435750$ |
0.983153319 |
\( -\frac{1490704436330}{40353607} a + \frac{4279363666973}{80707214} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -111 a + 145\) , \( -186 a - 472\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-111a+145\right){x}-186a-472$ |
| 756.2-a1 |
756.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
756.2 |
\( 2^{2} \cdot 3^{3} \cdot 7 \) |
\( 2^{2} \cdot 3^{11} \cdot 7 \) |
$0.81158$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$9$ |
\( 1 \) |
$1$ |
$0.851435750$ |
0.983153319 |
\( -\frac{94629827885}{14} a - \frac{42409905046}{7} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -699 a + 394\) , \( 4326 a - 6670\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-699a+394\right){x}+4326a-6670$ |
| 756.2-a2 |
756.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
756.2 |
\( 2^{2} \cdot 3^{3} \cdot 7 \) |
\( 2^{18} \cdot 3^{11} \cdot 7 \) |
$0.81158$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$0.851435750$ |
0.983153319 |
\( -\frac{2250281123}{896} a - \frac{3901494743}{3584} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -249 a - 11\) , \( -1740 a + 818\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-249a-11\right){x}-1740a+818$ |
*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.
