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 |
283.1-a1 |
283.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
283.1 |
\( 283 \) |
\( 283 \) |
$0.63481$ |
$(19a-13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.020644019$ |
$8.749902689$ |
0.417154410 |
\( \frac{4374}{283} a + \frac{9477}{283} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -1\) , \( -a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}-{x}-a$ |
283.2-a1 |
283.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
283.2 |
\( 283 \) |
\( 283 \) |
$0.63481$ |
$(19a-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.020644019$ |
$8.749902689$ |
0.417154410 |
\( -\frac{4374}{283} a + \frac{13851}{283} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -a\) , \( 0\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}-a{x}$ |
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-a4 |
361.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
361.2 |
\( 19^{2} \) |
\( 19^{6} \) |
$0.67465$ |
$(-5a+3), (-5a+2)$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{2} \) |
$0.677900606$ |
$2.805927025$ |
0.488089257 |
\( -\frac{89915392}{6859} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -9 a + 9\) , \( -15\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-9a+9\right){x}-15$ |
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 |
\( \frac{32768}{19} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( a - 1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(a-1\right){x}$ |
379.1-a1 |
379.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
379.1 |
\( 379 \) |
\( 379 \) |
$0.68290$ |
$(22a-15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.026097731$ |
$8.419977107$ |
0.507473108 |
\( -\frac{113062}{379} a + \frac{420487}{379} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}$ |
379.2-a1 |
379.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
379.2 |
\( 379 \) |
\( 379 \) |
$0.68290$ |
$(22a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.026097731$ |
$8.419977107$ |
0.507473108 |
\( \frac{113062}{379} a + \frac{307425}{379} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}$ |
412.1-a1 |
412.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
412.1 |
\( 2^{2} \cdot 103 \) |
\( 2^{4} \cdot 103 \) |
$0.69731$ |
$(11a-9), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.014974092$ |
$7.480035602$ |
0.517337002 |
\( -\frac{22599}{412} a + \frac{272349}{412} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -a + 1\) , \( -a\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+1\right){x}-a$ |
412.2-a1 |
412.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
412.2 |
\( 2^{2} \cdot 103 \) |
\( 2^{4} \cdot 103 \) |
$0.69731$ |
$(11a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.014974092$ |
$7.480035602$ |
0.517337002 |
\( \frac{22599}{412} a + \frac{124875}{206} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}$ |
481.2-a1 |
481.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
481.2 |
\( 13 \cdot 37 \) |
\( 13 \cdot 37 \) |
$0.72483$ |
$(-4a+1), (-7a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.118200834$ |
$8.331786658$ |
0.568588478 |
\( -\frac{42208}{481} a - \frac{24959}{481} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}$ |
481.2-a2 |
481.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
481.2 |
\( 13 \cdot 37 \) |
\( 13^{2} \cdot 37^{2} \) |
$0.72483$ |
$(-4a+1), (-7a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.059100417$ |
$4.165893329$ |
0.568588478 |
\( -\frac{7617412112}{231361} a + \frac{4002184503}{231361} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 5\) , \( 3 a - 3\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+5{x}+3a-3$ |
481.3-a1 |
481.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
481.3 |
\( 13 \cdot 37 \) |
\( 13 \cdot 37 \) |
$0.72483$ |
$(4a-3), (-7a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.118200834$ |
$8.331786658$ |
0.568588478 |
\( \frac{42208}{481} a - \frac{67167}{481} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( a\) , \( 0\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}$ |
481.3-a2 |
481.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
481.3 |
\( 13 \cdot 37 \) |
\( 13^{2} \cdot 37^{2} \) |
$0.72483$ |
$(4a-3), (-7a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.059100417$ |
$4.165893329$ |
0.568588478 |
\( \frac{7617412112}{231361} a - \frac{3615227609}{231361} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( a + 5\) , \( -3 a + 5\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+5\right){x}-3a+5$ |
507.2-a1 |
507.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
507.2 |
\( 3 \cdot 13^{2} \) |
\( 3^{2} \cdot 13^{2} \) |
$0.73443$ |
$(-2a+1), (-4a+1), (4a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.282583906$ |
$7.561180171$ |
0.616802873 |
\( \frac{12167}{39} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+{x}$ |
507.2-a2 |
507.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
507.2 |
\( 3 \cdot 13^{2} \) |
\( 3^{4} \cdot 13^{4} \) |
$0.73443$ |
$(-2a+1), (-4a+1), (4a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.141291953$ |
$3.780590085$ |
0.616802873 |
\( \frac{10218313}{1521} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-4{x}-5$ |
507.2-a3 |
507.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
507.2 |
\( 3 \cdot 13^{2} \) |
\( 3^{2} \cdot 13^{8} \) |
$0.73443$ |
$(-2a+1), (-4a+1), (4a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.070645976$ |
$1.890295042$ |
0.616802873 |
\( \frac{822656953}{85683} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -19\) , \( 22\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-19{x}+22$ |
507.2-a4 |
507.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
507.2 |
\( 3 \cdot 13^{2} \) |
\( 3^{8} \cdot 13^{2} \) |
$0.73443$ |
$(-2a+1), (-4a+1), (4a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.282583906$ |
$1.890295042$ |
0.616802873 |
\( \frac{37159393753}{1053} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -69\) , \( -252\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-69{x}-252$ |
553.2-a1 |
553.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
553.2 |
\( 7 \cdot 79 \) |
\( 7 \cdot 79 \) |
$0.75055$ |
$(-3a+1), (10a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.032459368$ |
$8.244746797$ |
0.618040249 |
\( \frac{45056}{553} a + \frac{65536}{553} \) |
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( 0\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}-a$ |
553.3-a1 |
553.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
553.3 |
\( 7 \cdot 79 \) |
\( 7 \cdot 79 \) |
$0.75055$ |
$(3a-2), (10a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.032459368$ |
$8.244746797$ |
0.618040249 |
\( -\frac{45056}{553} a + \frac{110592}{553} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}$ |
579.1-a1 |
579.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
579.1 |
\( 3 \cdot 193 \) |
\( 3^{2} \cdot 193 \) |
$0.75922$ |
$(-2a+1), (16a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.075774335$ |
$7.505847337$ |
0.656736620 |
\( -\frac{12224}{579} a - \frac{9867}{193} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -1\) , \( -a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}-{x}-a$ |
579.1-a2 |
579.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
579.1 |
\( 3 \cdot 193 \) |
\( 3 \cdot 193^{2} \) |
$0.75922$ |
$(-2a+1), (16a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.151548671$ |
$3.752923668$ |
0.656736620 |
\( \frac{4604240642}{111747} a + \frac{23890776935}{111747} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 10 a - 6\) , \( -10 a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(10a-6\right){x}-10a$ |
579.2-a1 |
579.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
579.2 |
\( 3 \cdot 193 \) |
\( 3^{2} \cdot 193 \) |
$0.75922$ |
$(-2a+1), (-16a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.075774335$ |
$7.505847337$ |
0.656736620 |
\( \frac{12224}{579} a - \frac{41825}{579} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -a\) , \( 0\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}-a{x}$ |
579.2-a2 |
579.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
579.2 |
\( 3 \cdot 193 \) |
\( 3 \cdot 193^{2} \) |
$0.75922$ |
$(-2a+1), (-16a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.151548671$ |
$3.752923668$ |
0.656736620 |
\( -\frac{4604240642}{111747} a + \frac{28495017577}{111747} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -11 a + 5\) , \( 9 a - 9\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-11a+5\right){x}+9a-9$ |
673.1-a1 |
673.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
673.1 |
\( 673 \) |
\( 673 \) |
$0.78832$ |
$(29a-8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.039416036$ |
$7.914920287$ |
0.720474911 |
\( -\frac{950272}{673} a + \frac{688128}{673} \) |
\( \bigl[0\) , \( a\) , \( a\) , \( a - 1\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(a-1\right){x}$ |
673.2-a1 |
673.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
673.2 |
\( 673 \) |
\( 673 \) |
$0.78832$ |
$(-29a+21)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.039416036$ |
$7.914920287$ |
0.720474911 |
\( \frac{950272}{673} a - \frac{262144}{673} \) |
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -a\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}-a{x}-a$ |
679.2-a1 |
679.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
679.2 |
\( 7 \cdot 97 \) |
\( 7 \cdot 97 \) |
$0.79007$ |
$(-3a+1), (-11a+8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.034929906$ |
$7.994668168$ |
0.644907208 |
\( \frac{71037}{679} a + \frac{993465}{679} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}$ |
679.3-a1 |
679.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
679.3 |
\( 7 \cdot 97 \) |
\( 7 \cdot 97 \) |
$0.79007$ |
$(3a-2), (-11a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.034929906$ |
$7.994668168$ |
0.644907208 |
\( -\frac{71037}{679} a + \frac{1064502}{679} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}$ |
700.1-a1 |
700.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
700.1 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
$0.79611$ |
$(-3a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.050710775$ |
$5.988646760$ |
0.701339516 |
\( \frac{152207}{196} a + \frac{317396}{245} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( a - 1\) , \( -a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}-a$ |
700.1-a2 |
700.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
700.1 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{2} \cdot 5^{4} \cdot 7^{4} \) |
$0.79611$ |
$(-3a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.101421550$ |
$2.994323380$ |
0.701339516 |
\( -\frac{1668770723}{24010} a + \frac{6868996887}{120050} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 11 a - 1\) , \( a + 14\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(11a-1\right){x}+a+14$ |
700.2-a1 |
700.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
$0.79611$ |
$(3a-2), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.050710775$ |
$5.988646760$ |
0.701339516 |
\( -\frac{152207}{196} a + \frac{2030619}{980} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -2 a + 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-2a+1\right){x}$ |
700.2-a2 |
700.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{2} \cdot 5^{4} \cdot 7^{4} \) |
$0.79611$ |
$(3a-2), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.101421550$ |
$2.994323380$ |
0.701339516 |
\( \frac{1668770723}{24010} a - \frac{737428364}{60025} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -12 a + 11\) , \( -2 a + 16\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-12a+11\right){x}-2a+16$ |
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 |
\( \frac{328275}{703} a + \frac{30959}{703} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -a\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}-a{x}-a$ |
721.2-a1 |
721.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
721.2 |
\( 7 \cdot 103 \) |
\( 7^{2} \cdot 103 \) |
$0.80202$ |
$(-3a+1), (11a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.024305426$ |
$6.476558615$ |
0.727071148 |
\( -\frac{16418226}{5047} a + \frac{20582839}{5047} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( a - 1\) , \( a - 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(a-1\right){x}+a-1$ |
721.3-a1 |
721.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
721.3 |
\( 7 \cdot 103 \) |
\( 7^{2} \cdot 103 \) |
$0.80202$ |
$(3a-2), (11a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.024305426$ |
$6.476558615$ |
0.727071148 |
\( \frac{16418226}{5047} a + \frac{4164613}{5047} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -a\) , \( -a\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-a{x}-a$ |
723.1-a1 |
723.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
723.1 |
\( 3 \cdot 241 \) |
\( 3^{2} \cdot 241 \) |
$0.80257$ |
$(-2a+1), (-16a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.022130156$ |
$7.253556061$ |
0.741420883 |
\( -\frac{4096}{241} a + \frac{1183744}{723} \) |
\( \bigl[0\) , \( -a + 1\) , \( a\) , \( -1\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}-{x}$ |
723.2-a1 |
723.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
723.2 |
\( 3 \cdot 241 \) |
\( 3^{2} \cdot 241 \) |
$0.80257$ |
$(-2a+1), (16a-15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.022130156$ |
$7.253556061$ |
0.741420883 |
\( \frac{4096}{241} a + \frac{1171456}{723} \) |
\( \bigl[0\) , \( a\) , \( a + 1\) , \( -1\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}-{x}-a$ |
793.1-a1 |
793.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
793.1 |
\( 13 \cdot 61 \) |
\( 13 \cdot 61 \) |
$0.82133$ |
$(-4a+1), (-9a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.159905183$ |
$8.015887349$ |
0.740037145 |
\( -\frac{67529}{793} a + \frac{53952}{793} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( a\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}$ |
793.1-a2 |
793.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
793.1 |
\( 13 \cdot 61 \) |
\( 13^{2} \cdot 61^{2} \) |
$0.82133$ |
$(-4a+1), (-9a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.079952591$ |
$4.007943674$ |
0.740037145 |
\( \frac{5372259095}{628849} a + \frac{5563211089}{628849} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -4 a\) , \( 7 a - 4\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}-4a{x}+7a-4$ |
793.4-a1 |
793.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
793.4 |
\( 13 \cdot 61 \) |
\( 13 \cdot 61 \) |
$0.82133$ |
$(4a-3), (-9a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.159905183$ |
$8.015887349$ |
0.740037145 |
\( \frac{67529}{793} a - \frac{13577}{793} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( a\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}$ |
793.4-a2 |
793.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
793.4 |
\( 13 \cdot 61 \) |
\( 13^{2} \cdot 61^{2} \) |
$0.82133$ |
$(4a-3), (-9a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.079952591$ |
$4.007943674$ |
0.740037145 |
\( -\frac{5372259095}{628849} a + \frac{10935470184}{628849} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 6 a - 5\) , \( -2 a - 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-5\right){x}-2a-2$ |
832.1-a1 |
832.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
832.1 |
\( 2^{6} \cdot 13 \) |
\( 2^{8} \cdot 13 \) |
$0.83125$ |
$(-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.096512155$ |
$6.962250664$ |
0.775891583 |
\( \frac{13568}{13} a + \frac{5632}{13} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}-{x}$ |
832.1-a2 |
832.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
832.1 |
\( 2^{6} \cdot 13 \) |
\( 2^{16} \cdot 13^{2} \) |
$0.83125$ |
$(-4a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.048256077$ |
$3.481125332$ |
0.775891583 |
\( -\frac{301712}{169} a + \frac{465744}{169} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 4\) , \( -4 a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+4{x}-4a$ |
832.2-a1 |
832.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
832.2 |
\( 2^{6} \cdot 13 \) |
\( 2^{8} \cdot 13 \) |
$0.83125$ |
$(4a-3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.096512155$ |
$6.962250664$ |
0.775891583 |
\( -\frac{13568}{13} a + \frac{19200}{13} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-{x}$ |
832.2-a2 |
832.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
832.2 |
\( 2^{6} \cdot 13 \) |
\( 2^{16} \cdot 13^{2} \) |
$0.83125$ |
$(4a-3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.048256077$ |
$3.481125332$ |
0.775891583 |
\( \frac{301712}{169} a + \frac{164032}{169} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 4\) , \( 4 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+4{x}+4a-4$ |
837.1-a1 |
837.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
837.1 |
\( 3^{3} \cdot 31 \) |
\( 3^{5} \cdot 31 \) |
$0.83249$ |
$(-2a+1), (-6a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \) |
$0.018108707$ |
$6.605155465$ |
0.828688140 |
\( \frac{5324}{31} a + \frac{9317}{31} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}-{x}$ |
*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.