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 |
42588.2-a1 |
42588.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{24} \cdot 3^{14} \cdot 7^{4} \cdot 13^{2} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.324639593$ |
0.490808931 |
\( -\frac{461661588021041}{3895443062784} a + \frac{1507573920673103}{834737799168} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 170 a + 302\) , \( -970 a + 670\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(170a+302\right){x}-970a+670$ |
42588.2-b1 |
42588.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{24} \cdot 3^{14} \cdot 7^{4} \cdot 13^{2} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.324639593$ |
0.490808931 |
\( \frac{461661588021041}{3895443062784} a + \frac{19721050125360319}{11686329188352} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -171 a + 473\) , \( 969 a - 299\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-171a+473\right){x}+969a-299$ |
42588.2-c1 |
42588.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 7^{8} \cdot 13^{8} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.153886582$ |
$0.313083088$ |
1.748165624 |
\( \frac{7264187703863}{7406095788} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 403\) , \( 2756\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+403{x}+2756$ |
42588.2-c2 |
42588.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 7^{4} \cdot 13^{4} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.307773164$ |
$0.626166176$ |
1.748165624 |
\( \frac{281397674377}{96589584} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -137\) , \( 380\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-137{x}+380$ |
42588.2-c3 |
42588.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{6} \cdot 7^{2} \cdot 13^{2} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.153886582$ |
$1.252332353$ |
1.748165624 |
\( \frac{19968681097}{628992} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -57\) , \( -164\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-57{x}-164$ |
42588.2-c4 |
42588.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{24} \cdot 7^{2} \cdot 13^{2} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.615546328$ |
$0.313083088$ |
1.748165624 |
\( \frac{828279937799497}{193444524} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1957\) , \( 33140\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-1957{x}+33140$ |
42588.2-d1 |
42588.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{10} \cdot 7^{6} \cdot 13^{2} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$0.168079577$ |
$0.964296414$ |
2.450397098 |
\( -\frac{141339344329}{2167074} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -108\) , \( -486\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-108{x}-486$ |
42588.2-e1 |
42588.2-e |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{10} \cdot 3^{2} \cdot 7^{2} \cdot 13^{2} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.360406495$ |
$2.825005773$ |
3.078597526 |
\( -\frac{47045881}{8736} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -8\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-8{x}-10$ |
42588.2-f1 |
42588.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{5} \cdot 3^{4} \cdot 7^{4} \cdot 13^{2} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.308022967$ |
$0.392808501$ |
3.107185707 |
\( \frac{3440040594112169}{45864} a - \frac{6878875420624553}{45864} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 2496 a - 1\) , \( 15739 a + 69332\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(2496a-1\right){x}+15739a+69332$ |
42588.2-f2 |
42588.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{11} \cdot 3^{4} \cdot 7 \cdot 13^{8} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.308022967$ |
$0.785617002$ |
3.107185707 |
\( -\frac{77460685837}{460631808} a + \frac{17556307271}{230315904} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 2 a + 39\) , \( 168 a + 85\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(2a+39\right){x}+168a+85$ |
42588.2-f3 |
42588.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{10} \cdot 3^{8} \cdot 7^{2} \cdot 13^{4} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.654011483$ |
$0.785617002$ |
3.107185707 |
\( \frac{1679410751273}{6132672} a + \frac{673156175}{876096} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 156 a - 1\) , \( 295 a + 1004\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(156a-1\right){x}+295a+1004$ |
42588.2-f4 |
42588.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{14} \cdot 3^{16} \cdot 7 \cdot 13^{2} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.327005741$ |
$0.785617002$ |
3.107185707 |
\( \frac{72992335099}{815173632} a + \frac{3644142847061}{2445520896} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 34 a - 76\) , \( 22 a + 74\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(34a-76\right){x}+22a+74$ |
42588.2-g1 |
42588.2-g |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{54} \cdot 3^{2} \cdot 7^{2} \cdot 13^{2} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$0.099966647$ |
1.360218288 |
\( -\frac{1956469094246217097}{36641439744} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -26057\) , \( -1621108\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-26057{x}-1621108$ |
42588.2-g2 |
42588.2-g |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{18} \cdot 3^{6} \cdot 7^{6} \cdot 13^{6} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$0.299899943$ |
1.360218288 |
\( -\frac{198461344537}{10417365504} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -122\) , \( -4948\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-122{x}-4948$ |
42588.2-g3 |
42588.2-g |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{6} \cdot 3^{18} \cdot 7^{2} \cdot 13^{2} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.899699829$ |
1.360218288 |
\( \frac{270840023}{14329224} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 13\) , \( 182\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+13{x}+182$ |
42588.2-h1 |
42588.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{5} \cdot 3^{4} \cdot 7^{4} \cdot 13^{2} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.308022967$ |
$0.392808501$ |
3.107185707 |
\( -\frac{3440040594112169}{45864} a - \frac{3673968831744}{49} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -2497 a + 2496\) , \( -15740 a + 85072\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2497a+2496\right){x}-15740a+85072$ |
42588.2-h2 |
42588.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{11} \cdot 3^{4} \cdot 7 \cdot 13^{8} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.308022967$ |
$0.785617002$ |
3.107185707 |
\( \frac{77460685837}{460631808} a - \frac{4705341255}{51181312} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -2 a + 41\) , \( -168 a + 253\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-2a+41\right){x}-168a+253$ |
42588.2-h3 |
42588.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{14} \cdot 3^{16} \cdot 7 \cdot 13^{2} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.327005741$ |
$0.785617002$ |
3.107185707 |
\( -\frac{72992335099}{815173632} a + \frac{148581532783}{94058496} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -34 a - 42\) , \( -22 a + 96\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-34a-42\right){x}-22a+96$ |
42588.2-h4 |
42588.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{10} \cdot 3^{8} \cdot 7^{2} \cdot 13^{4} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.654011483$ |
$0.785617002$ |
3.107185707 |
\( -\frac{1679410751273}{6132672} a + \frac{842061422249}{3066336} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -157 a + 156\) , \( -296 a + 1300\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-157a+156\right){x}-296a+1300$ |
42588.2-i1 |
42588.2-i |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{34} \cdot 3^{14} \cdot 7^{2} \cdot 13^{10} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \cdot 7 \cdot 17^{2} \) |
$0.011431035$ |
$0.034096494$ |
11.92071101 |
\( -\frac{112205650221491190337}{745029571313664} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -100484\) , \( -12372091\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-100484{x}-12372091$ |
42588.2-j1 |
42588.2-j |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{2} \cdot 7^{4} \cdot 13^{2} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
$0.019632690$ |
$1.501484892$ |
11.23084155 |
\( -\frac{462900251}{326144} a - \frac{399367313}{978432} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -a - 21\) , \( -11 a + 41\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a-21\right){x}-11a+41$ |
42588.2-k1 |
42588.2-k |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{2} \cdot 7^{4} \cdot 13^{2} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 7 \) |
$0.019632690$ |
$1.501484892$ |
11.23084155 |
\( \frac{462900251}{326144} a - \frac{894034033}{489216} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 2 a - 23\) , \( 8 a + 53\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-23\right){x}+8a+53$ |
42588.2-l1 |
42588.2-l |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{2} \cdot 13^{8} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.780402623$ |
4.719431462 |
\( \frac{8780064047}{32388174} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 43\) , \( 255\bigr] \) |
${y}^2+{x}{y}={x}^{3}+43{x}+255$ |
42588.2-l2 |
42588.2-l |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{4} \cdot 13^{4} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$1.560805247$ |
4.719431462 |
\( \frac{2181825073}{298116} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -27\) , \( 45\bigr] \) |
${y}^2+{x}{y}={x}^{3}-27{x}+45$ |
42588.2-l3 |
42588.2-l |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \cdot 13^{2} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$3.121610494$ |
4.719431462 |
\( \frac{38272753}{4368} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -7\) , \( -7\bigr] \) |
${y}^2+{x}{y}={x}^{3}-7{x}-7$ |
42588.2-l4 |
42588.2-l |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 7^{8} \cdot 13^{2} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.780402623$ |
4.719431462 |
\( \frac{8020417344913}{187278} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -417\) , \( 3243\bigr] \) |
${y}^2+{x}{y}={x}^{3}-417{x}+3243$ |
42588.2-m1 |
42588.2-m |
$2$ |
$7$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 13^{14} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.2[2] |
$49$ |
\( 2 \cdot 7 \) |
$1$ |
$0.016687499$ |
8.653591055 |
\( -\frac{5486773802537974663600129}{2635437714} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -3674496\) , \( -2711401518\bigr] \) |
${y}^2+{x}{y}={x}^{3}-3674496{x}-2711401518$ |
42588.2-m2 |
42588.2-m |
$2$ |
$7$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42588.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{14} \cdot 3^{14} \cdot 7^{14} \cdot 13^{2} \) |
$3.39633$ |
$(a), (-a+1), (-2a+1), (3), (13)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1[2] |
$1$ |
\( 2 \cdot 7^{4} \) |
$1$ |
$0.116812499$ |
8.653591055 |
\( \frac{40251338884511}{2997011332224} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 714\) , \( -82908\bigr] \) |
${y}^2+{x}{y}={x}^{3}+714{x}-82908$ |
*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.