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 |
44563.1-a1 |
44563.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44563.1 |
\( 44563 \) |
\( 44563 \) |
$2.24876$ |
$(-239a+78)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.049752912$ |
$5.645758265$ |
2.594777623 |
\( -\frac{19503666}{44563} a + \frac{59761233}{44563} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -2 a + 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-2a+1\right){x}$ |
44563.2-a1 |
44563.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44563.2 |
\( 44563 \) |
\( 44563 \) |
$2.24876$ |
$(-239a+161)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.049752912$ |
$5.645758265$ |
2.594777623 |
\( \frac{19503666}{44563} a + \frac{40257567}{44563} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -2 a\) , \( -a\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}-2a{x}-a$ |
64783.1-a1 |
64783.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
64783.1 |
\( 64783 \) |
\( 64783 \) |
$2.46925$ |
$(-271a+37)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.057611185$ |
$5.509225935$ |
2.931951312 |
\( \frac{25189866}{64783} a - \frac{10010115}{64783} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -1\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}-a$ |
64783.2-a1 |
64783.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
64783.2 |
\( 64783 \) |
\( 64783 \) |
$2.46925$ |
$(271a-234)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.057611185$ |
$5.509225935$ |
2.931951312 |
\( -\frac{25189866}{64783} a + \frac{15179751}{64783} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -a + 1\) , \( a - 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-a+1\right){x}+a-1$ |
76729.2-a1 |
76729.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
76729.2 |
\( 277^{2} \) |
\( 277^{2} \) |
$2.57596$ |
$(19a-12), (-19a+7)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.068917871$ |
$5.485801888$ |
3.492459124 |
\( \frac{12167}{277} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -a\) , \( -1\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}-1$ |
82633.1-a1 |
82633.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
82633.1 |
\( 82633 \) |
\( 82633 \) |
$2.62414$ |
$(-331a+187)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.072824501$ |
$5.250856599$ |
3.532376894 |
\( -\frac{157933872}{82633} a + \frac{74370125}{82633} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 3 a - 1\) , \( a - 2\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a-1\right){x}+a-2$ |
82633.2-a1 |
82633.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
82633.2 |
\( 82633 \) |
\( 82633 \) |
$2.62414$ |
$(331a-144)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.072824501$ |
$5.250856599$ |
3.532376894 |
\( \frac{157933872}{82633} a - \frac{83563747}{82633} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -3 a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a+1\right){x}$ |
91612.2-a1 |
91612.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
91612.2 |
\( 2^{2} \cdot 37 \cdot 619 \) |
\( 2^{4} \cdot 37 \cdot 619 \) |
$2.69270$ |
$(-7a+4), (27a-22), (2)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.041767069$ |
$4.795638400$ |
3.700579893 |
\( \frac{3802059}{45806} a + \frac{13412547}{91612} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( a\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}-a$ |
91612.3-a1 |
91612.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
91612.3 |
\( 2^{2} \cdot 37 \cdot 619 \) |
\( 2^{4} \cdot 37 \cdot 619 \) |
$2.69270$ |
$(-7a+3), (-27a+5), (2)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.041767069$ |
$4.795638400$ |
3.700579893 |
\( -\frac{3802059}{45806} a + \frac{21016665}{91612} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( a - 1\) , \( a - 2\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(a-1\right){x}+a-2$ |
109579.1-a1 |
109579.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
109579.1 |
\( 109579 \) |
\( 109579 \) |
$2.81599$ |
$(358a-295)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.082468639$ |
$5.263234466$ |
4.009598630 |
\( -\frac{39984554}{109579} a + \frac{4876641}{109579} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( a - 1\) , \( -a\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}-a$ |
109579.2-a1 |
109579.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
109579.2 |
\( 109579 \) |
\( 109579 \) |
$2.81599$ |
$(358a-63)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.082468639$ |
$5.263234466$ |
4.009598630 |
\( \frac{39984554}{109579} a - \frac{35107913}{109579} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -a\) , \( a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}-a{x}+a-1$ |
117049.2-a1 |
117049.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
117049.2 |
\( 67 \cdot 1747 \) |
\( 67 \cdot 1747 \) |
$2.86280$ |
$(9a-7), (47a-14)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.080567140$ |
$5.070008750$ |
3.773340634 |
\( -\frac{190644224}{117049} a - \frac{30572544}{117049} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( a + 1\) , \( -2 a + 1\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(a+1\right){x}-2a+1$ |
117049.3-a1 |
117049.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
117049.3 |
\( 67 \cdot 1747 \) |
\( 67 \cdot 1747 \) |
$2.86280$ |
$(9a-2), (-47a+33)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.080567140$ |
$5.070008750$ |
3.773340634 |
\( \frac{190644224}{117049} a - \frac{221216768}{117049} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -a + 2\) , \( 2 a - 1\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+2\right){x}+2a-1$ |
118857.1-a1 |
118857.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
118857.1 |
\( 3 \cdot 39619 \) |
\( 3^{2} \cdot 39619 \) |
$2.87379$ |
$(-2a+1), (-207a+190)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.051739241$ |
$4.731148459$ |
4.522473041 |
\( -\frac{25579250}{118857} a + \frac{71495307}{39619} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -4 a + 1\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a+1\right){x}-a$ |
118857.2-a1 |
118857.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
118857.2 |
\( 3 \cdot 39619 \) |
\( 3^{2} \cdot 39619 \) |
$2.87379$ |
$(-2a+1), (207a-17)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.051739241$ |
$4.731148459$ |
4.522473041 |
\( \frac{25579250}{118857} a + \frac{188906671}{118857} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 2 a - 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(2a-1\right){x}$ |
119989.1-a1 |
119989.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
119989.1 |
\( 97 \cdot 1237 \) |
\( 97 \cdot 1237 \) |
$2.88061$ |
$(-11a+3), (37a-33)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.101729443$ |
$4.808521183$ |
4.518742125 |
\( \frac{96309052}{119989} a + \frac{842067797}{119989} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -2 a + 4\) , \( a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+4\right){x}+a+1$ |
119989.4-a1 |
119989.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
119989.4 |
\( 97 \cdot 1237 \) |
\( 97 \cdot 1237 \) |
$2.88061$ |
$(-11a+8), (37a-4)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.101729443$ |
$4.808521183$ |
4.518742125 |
\( -\frac{96309052}{119989} a + \frac{938376849}{119989} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 2 a - 4\) , \( -2 a + 2\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(2a-4\right){x}-2a+2$ |
126793.1-a1 |
126793.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126793.1 |
\( 103 \cdot 1231 \) |
\( 103 \cdot 1231 \) |
$2.92061$ |
$(11a-9), (-39a+10)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.093508108$ |
$5.063912558$ |
4.374161601 |
\( \frac{74862592}{126793} a + \frac{284356608}{126793} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( -a + 2\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(-a+2\right){x}$ |
126793.4-a1 |
126793.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126793.4 |
\( 103 \cdot 1231 \) |
\( 103 \cdot 1231 \) |
$2.92061$ |
$(11a-2), (-39a+29)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.093508108$ |
$5.063912558$ |
4.374161601 |
\( -\frac{74862592}{126793} a + \frac{359219200}{126793} \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( -2 a + 1\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-2a+1\right){x}-a$ |
144193.1-a1 |
144193.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
144193.1 |
\( 7 \cdot 20599 \) |
\( 7^{2} \cdot 20599 \) |
$3.01603$ |
$(-3a+1), (145a-142)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.050407303$ |
$4.263788421$ |
3.970804128 |
\( \frac{339327630}{1009351} a + \frac{2403567459}{1009351} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -3 a - 1\) , \( -2 a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-3a-1\right){x}-2a+1$ |
144193.4-a1 |
144193.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
144193.4 |
\( 7 \cdot 20599 \) |
\( 7^{2} \cdot 20599 \) |
$3.01603$ |
$(3a-2), (145a-3)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.050407303$ |
$4.263788421$ |
3.970804128 |
\( -\frac{339327630}{1009351} a + \frac{2742895089}{1009351} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 2 a - 3\) , \( 2 a - 1\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a-3\right){x}+2a-1$ |
149187.2-a1 |
149187.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
149187.2 |
\( 3 \cdot 223^{2} \) |
\( 3^{2} \cdot 223^{2} \) |
$3.04181$ |
$(-2a+1), (-17a+6), (-17a+11)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.057856562$ |
$4.639410367$ |
4.959121729 |
\( -\frac{389017}{669} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -1\) , \( -2\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-{x}-2$ |
149533.1-a1 |
149533.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
149533.1 |
\( 149533 \) |
\( 149533 \) |
$3.04357$ |
$(-444a+181)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.097359941$ |
$4.977925300$ |
4.477009702 |
\( -\frac{246907308}{149533} a + \frac{441262055}{149533} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 3 a - 1\) , \( a - 2\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a-1\right){x}+a-2$ |
149533.2-a1 |
149533.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
149533.2 |
\( 149533 \) |
\( 149533 \) |
$3.04357$ |
$(444a-263)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.097359941$ |
$4.977925300$ |
4.477009702 |
\( \frac{246907308}{149533} a + \frac{194354747}{149533} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( a - 2\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-2\right){x}$ |
44402.2-a1 |
44402.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
44402.2 |
\( 2 \cdot 149^{2} \) |
\( 2^{2} \cdot 149^{2} \) |
$2.59429$ |
$(a+1), (10a-7), (7a-10)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.039519530$ |
$5.398034632$ |
3.413244711 |
\( \frac{59319}{298} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( 1\) , \( 1\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}+{x}+1$ |
52441.2-a1 |
52441.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52441.2 |
\( 229^{2} \) |
\( 229^{2} \) |
$2.70450$ |
$(-2a+15), (2a+15)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.081504763$ |
$5.335674696$ |
3.479063214 |
\( \frac{912673}{229} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-2{x}+1$ |
61562.1-a1 |
61562.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
61562.1 |
\( 2 \cdot 30781 \) |
\( 2^{2} \cdot 30781 \) |
$2.81512$ |
$(a+1), (-91a-150)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.045432724$ |
$5.247242173$ |
3.814344160 |
\( \frac{5169075}{30781} a + \frac{6271811}{61562} \) |
\( \bigl[1\) , \( -i - 1\) , \( i\) , \( -1\) , \( i + 1\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}+\left(-i-1\right){x}^{2}-{x}+i+1$ |
61562.2-a1 |
61562.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
61562.2 |
\( 2 \cdot 30781 \) |
\( 2^{2} \cdot 30781 \) |
$2.81512$ |
$(a+1), (-91a+150)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.045432724$ |
$5.247242173$ |
3.814344160 |
\( -\frac{5169075}{30781} a + \frac{6271811}{61562} \) |
\( \bigl[i\) , \( -i + 1\) , \( 1\) , \( -i - 1\) , \( i - 1\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-i-1\right){x}+i-1$ |
63773.1-a1 |
63773.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
63773.1 |
\( 63773 \) |
\( 63773 \) |
$2.84006$ |
$(-197a-158)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.068552342$ |
$5.420193804$ |
2.972535868 |
\( -\frac{30595072}{63773} a + \frac{124130240}{63773} \) |
\( \bigl[i + 1\) , \( -i\) , \( 1\) , \( -i + 1\) , \( 0\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}-i{x}^{2}+\left(-i+1\right){x}$ |
63773.2-a1 |
63773.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
63773.2 |
\( 63773 \) |
\( 63773 \) |
$2.84006$ |
$(158a+197)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.068552342$ |
$5.420193804$ |
2.972535868 |
\( \frac{30595072}{63773} a + \frac{124130240}{63773} \) |
\( \bigl[i + 1\) , \( 0\) , \( 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+{x}$ |
83129.2-a1 |
83129.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83129.2 |
\( 97 \cdot 857 \) |
\( 97 \cdot 857 \) |
$3.03464$ |
$(-4a+9), (4a+29)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.078013512$ |
$5.348866758$ |
3.338271088 |
\( \frac{55140352}{83129} a - \frac{4861952}{83129} \) |
\( \bigl[0\) , \( i + 1\) , \( i\) , \( 1\) , \( i + 1\bigr] \) |
${y}^2+i{y}={x}^{3}+\left(i+1\right){x}^{2}+{x}+i+1$ |
83129.3-a1 |
83129.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83129.3 |
\( 97 \cdot 857 \) |
\( 97 \cdot 857 \) |
$3.03464$ |
$(4a+9), (-4a+29)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.078013512$ |
$5.348866758$ |
3.338271088 |
\( -\frac{55140352}{83129} a - \frac{4861952}{83129} \) |
\( \bigl[0\) , \( -i + 1\) , \( i\) , \( 1\) , \( -i + 1\bigr] \) |
${y}^2+i{y}={x}^{3}+\left(-i+1\right){x}^{2}+{x}-i+1$ |
85753.2-a1 |
85753.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
85753.2 |
\( 29 \cdot 2957 \) |
\( 29 \cdot 2957 \) |
$3.05831$ |
$(-2a+5), (-46a+29)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.077560119$ |
$5.339228538$ |
3.312889630 |
\( -\frac{56217600}{85753} a + \frac{630784}{85753} \) |
\( \bigl[0\) , \( -i\) , \( i\) , \( i - 1\) , \( i + 1\bigr] \) |
${y}^2+i{y}={x}^{3}-i{x}^{2}+\left(i-1\right){x}+i+1$ |
85753.3-a1 |
85753.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
85753.3 |
\( 29 \cdot 2957 \) |
\( 29 \cdot 2957 \) |
$3.05831$ |
$(2a+5), (-29a+46)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.077560119$ |
$5.339228538$ |
3.312889630 |
\( \frac{56217600}{85753} a + \frac{630784}{85753} \) |
\( \bigl[0\) , \( -i\) , \( 1\) , \( -i - 1\) , \( i - 1\bigr] \) |
${y}^2+{y}={x}^{3}-i{x}^{2}+\left(-i-1\right){x}+i-1$ |
86337.2-a1 |
86337.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
86337.2 |
\( 3^{2} \cdot 53 \cdot 181 \) |
\( 3^{4} \cdot 53 \cdot 181 \) |
$3.06350$ |
$(-2a+7), (9a+10), (3)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.046208829$ |
$4.444374442$ |
3.285909470 |
\( \frac{52523008}{86337} a + \frac{73441280}{86337} \) |
\( \bigl[0\) , \( i - 1\) , \( 1\) , \( -i + 2\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-i+2\right){x}$ |
86337.3-a1 |
86337.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
86337.3 |
\( 3^{2} \cdot 53 \cdot 181 \) |
\( 3^{4} \cdot 53 \cdot 181 \) |
$3.06350$ |
$(2a+7), (-10a-9), (3)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.046208829$ |
$4.444374442$ |
3.285909470 |
\( -\frac{52523008}{86337} a + \frac{73441280}{86337} \) |
\( \bigl[0\) , \( -i - 1\) , \( 1\) , \( i + 2\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(i+2\right){x}$ |
89234.1-a1 |
89234.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
89234.1 |
\( 2 \cdot 44617 \) |
\( 2^{2} \cdot 44617 \) |
$3.08888$ |
$(a+1), (-171a+124)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.054460669$ |
$5.086482828$ |
4.432212166 |
\( \frac{10931499}{89234} a - \frac{3259790}{44617} \) |
\( \bigl[i\) , \( i + 1\) , \( i\) , \( 1\) , \( i + 1\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(i+1\right){x}^{2}+{x}+i+1$ |
89234.2-a1 |
89234.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
89234.2 |
\( 2 \cdot 44617 \) |
\( 2^{2} \cdot 44617 \) |
$3.08888$ |
$(a+1), (-124a+171)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.054460669$ |
$5.086482828$ |
4.432212166 |
\( -\frac{10931499}{89234} a - \frac{3259790}{44617} \) |
\( \bigl[1\) , \( i - 1\) , \( 1\) , \( 0\) , \( i - 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(i-1\right){x}^{2}+i-1$ |
91592.1-a1 |
91592.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
91592.1 |
\( 2^{3} \cdot 107^{2} \) |
\( 2^{8} \cdot 107^{2} \) |
$3.10909$ |
$(a+1), (107)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.043175467$ |
$4.060484670$ |
5.610026370 |
\( -\frac{4}{107} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 0\) , \( -2 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}-2i$ |
92233.1-a1 |
92233.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92233.1 |
\( 92233 \) |
\( 92233 \) |
$3.11451$ |
$(168a+253)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.089493719$ |
$4.957701315$ |
3.549465054 |
\( -\frac{43081728}{92233} a + \frac{591081472}{92233} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -2 i + 2\) , \( -i - 1\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+\left(-2i+2\right){x}-i-1$ |
92233.2-a1 |
92233.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92233.2 |
\( 92233 \) |
\( 92233 \) |
$3.11451$ |
$(253a+168)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.089493719$ |
$4.957701315$ |
3.549465054 |
\( \frac{43081728}{92233} a + \frac{591081472}{92233} \) |
\( \bigl[0\) , \( -1\) , \( i\) , \( 2 i + 2\) , \( -i + 1\bigr] \) |
${y}^2+i{y}={x}^{3}-{x}^{2}+\left(2i+2\right){x}-i+1$ |
45378.1-a1 |
45378.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
45378.1 |
\( 2 \cdot 3^{2} \cdot 2521 \) |
\( 2^{2} \cdot 3^{4} \cdot 2521 \) |
$3.45063$ |
$(a), (-32a+43), (3)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.032531134$ |
$4.483068269$ |
3.527812688 |
\( \frac{10973375}{90756} a - \frac{2225125}{90756} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( a - 2\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a-2\right){x}$ |
45378.4-a1 |
45378.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
45378.4 |
\( 2 \cdot 3^{2} \cdot 2521 \) |
\( 2^{2} \cdot 3^{4} \cdot 2521 \) |
$3.45063$ |
$(-a+1), (-32a-11), (3)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.032531134$ |
$4.483068269$ |
3.527812688 |
\( -\frac{10973375}{90756} a + \frac{4374125}{45378} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -a - 1\) , \( -2 a + 2\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-a-1\right){x}-2a+2$ |
22898.2-a1 |
22898.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
22898.2 |
\( 2 \cdot 107^{2} \) |
\( 2^{2} \cdot 107^{2} \) |
$3.10909$ |
$(a), (7a+3), (7a-3)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.054776727$ |
$5.624169012$ |
3.485454604 |
\( \frac{357911}{214} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}$ |
24964.1-a1 |
24964.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24964.1 |
\( 2^{2} \cdot 79^{2} \) |
\( 2^{4} \cdot 79^{2} \) |
$3.17696$ |
$(a), (79)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 3 \) |
$0.041712789$ |
$5.249013259$ |
3.715721447 |
\( \frac{148176}{79} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -1\) , \( 1\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-{x}+1$ |
27848.2-a1 |
27848.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27848.2 |
\( 2^{3} \cdot 59^{2} \) |
\( 2^{8} \cdot 59^{2} \) |
$3.26499$ |
$(a), (-5a+3), (-5a-3)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.039143184$ |
$4.414919187$ |
3.910334407 |
\( \frac{55296}{59} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( 1\bigr] \) |
${y}^2={x}^{3}+2{x}+1$ |
32441.1-a1 |
32441.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
32441.1 |
\( 32441 \) |
\( 32441 \) |
$3.39201$ |
$(40a-171)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.097013233$ |
$5.720880151$ |
3.139560225 |
\( -\frac{22835200}{32441} a + \frac{51867648}{32441} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( a - 1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(a-1\right){x}$ |
32441.2-a1 |
32441.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
32441.2 |
\( 32441 \) |
\( 32441 \) |
$3.39201$ |
$(-40a-171)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.097013233$ |
$5.720880151$ |
3.139560225 |
\( \frac{22835200}{32441} a + \frac{51867648}{32441} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-a-1\right){x}$ |
34225.1-b1 |
34225.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
34225.1 |
\( 5^{2} \cdot 37^{2} \) |
\( 5^{4} \cdot 37^{2} \) |
$3.43771$ |
$(5), (37)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.131565918$ |
$3.860390354$ |
5.746185051 |
\( \frac{16777216}{925} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -5\) , \( 6\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-5{x}+6$ |
40401.5-a1 |
40401.5-a |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
40401.5 |
\( 3^{2} \cdot 67^{2} \) |
\( 3^{4} \cdot 67^{2} \) |
$3.58329$ |
$(-a-1), (a-1), (-3a+7), (3a+7)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.037307963$ |
$4.761045369$ |
4.019192869 |
\( \frac{512000}{603} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 2\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+2{x}$ |
*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.