| 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 |
| 5525.5-a1 |
5525.5-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5525.5 |
\( 5^{2} \cdot 13 \cdot 17 \) |
\( 5^{3} \cdot 13^{2} \cdot 17^{2} \) |
$1.54082$ |
$(-a-2), (2a+1), (-3a-2), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.121163146$ |
$2.959933985$ |
1.434539657 |
\( \frac{37004480699}{1221025} a - \frac{80300939102}{1221025} \) |
\( \bigl[1\) , \( -i\) , \( 1\) , \( -6 i - 11\) , \( 14 i + 8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-i{x}^{2}+\left(-6i-11\right){x}+14i+8$ |
| 5525.5-a2 |
5525.5-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5525.5 |
\( 5^{2} \cdot 13 \cdot 17 \) |
\( 5^{3} \cdot 13 \cdot 17 \) |
$1.54082$ |
$(-a-2), (2a+1), (-3a-2), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.242326292$ |
$5.919867971$ |
1.434539657 |
\( \frac{1621356}{5525} a + \frac{1618663}{5525} \) |
\( \bigl[i\) , \( i\) , \( i\) , \( -i\) , \( 0\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+i{x}^{2}-i{x}$ |
| 5525.5-b1 |
5525.5-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5525.5 |
\( 5^{2} \cdot 13 \cdot 17 \) |
\( 5^{2} \cdot 13 \cdot 17^{4} \) |
$1.54082$ |
$(-a-2), (2a+1), (-3a-2), (a+4)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$4.502287300$ |
$0.183629478$ |
1.653505339 |
\( -\frac{1745448433835905844163}{5428865} a - \frac{1750959281176604212878}{5428865} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -25680 i + 10614\) , \( 343455 i - 1745489\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+\left(-25680i+10614\right){x}+343455i-1745489$ |
| 5525.5-b2 |
5525.5-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5525.5 |
\( 5^{2} \cdot 13 \cdot 17 \) |
\( 5^{17} \cdot 13^{4} \cdot 17 \) |
$1.54082$ |
$(-a-2), (2a+1), (-3a-2), (a+4)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1.125571825$ |
$0.183629478$ |
1.653505339 |
\( -\frac{6490200321008653523650362}{74087066650390625} a - \frac{4221279326334621864710259}{74087066650390625} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -8295 i - 591\) , \( -229305 i + 183071\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+\left(-8295i-591\right){x}-229305i+183071$ |
| 5525.5-b3 |
5525.5-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5525.5 |
\( 5^{2} \cdot 13 \cdot 17 \) |
\( 5^{4} \cdot 13^{2} \cdot 17^{8} \) |
$1.54082$ |
$(-a-2), (2a+1), (-3a-2), (a+4)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$2.251143650$ |
$0.367258957$ |
1.653505339 |
\( \frac{581265201029275534788}{29472575188225} a - \frac{9608380177127950125}{1178903007529} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1605 i + 663\) , \( -5065 i + 27149\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-1605i+663\right){x}-5065i+27149$ |
| 5525.5-b4 |
5525.5-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5525.5 |
\( 5^{2} \cdot 13 \cdot 17 \) |
\( 5^{5} \cdot 13 \cdot 17 \) |
$1.54082$ |
$(-a-2), (2a+1), (-3a-2), (a+4)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.125571825$ |
$2.938071658$ |
1.653505339 |
\( \frac{77770489824}{138125} a - \frac{50461131843}{138125} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( 15 i + 9\) , \( 3 i - 25\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+\left(15i+9\right){x}+3i-25$ |
| 5525.5-b5 |
5525.5-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5525.5 |
\( 5^{2} \cdot 13 \cdot 17 \) |
\( 5^{17} \cdot 13 \cdot 17 \) |
$1.54082$ |
$(-a-2), (2a+1), (-3a-2), (a+4)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.125571825$ |
$0.734517914$ |
1.653505339 |
\( -\frac{267792000683486904}{33721923828125} a - \frac{1521451863867966597}{33721923828125} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 135 i - 112\) , \( -915 i + 251\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(135i-112\right){x}-915i+251$ |
| 5525.5-b6 |
5525.5-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5525.5 |
\( 5^{2} \cdot 13 \cdot 17 \) |
\( 5^{2} \cdot 13 \cdot 17^{16} \) |
$1.54082$ |
$(-a-2), (2a+1), (-3a-2), (a+4)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$4.502287300$ |
$0.183629478$ |
1.653505339 |
\( -\frac{12036726557935967494824957}{3162977471918346451265} a - \frac{5845390968758645234655522}{3162977471918346451265} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1530 i + 713\) , \( -7875 i + 28309\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-1530i+713\right){x}-7875i+28309$ |
| 5525.5-b7 |
5525.5-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5525.5 |
\( 5^{2} \cdot 13 \cdot 17 \) |
\( 5^{5} \cdot 13^{16} \cdot 17 \) |
$1.54082$ |
$(-a-2), (2a+1), (-3a-2), (a+4)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1.125571825$ |
$0.183629478$ |
1.653505339 |
\( \frac{1532265513206391380076282}{7070051472571285810625} a - \frac{433520938539899132774301}{7070051472571285810625} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( 525 i - 501\) , \( -12333 i + 17155\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+\left(525i-501\right){x}-12333i+17155$ |
| 5525.5-b8 |
5525.5-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5525.5 |
\( 5^{2} \cdot 13 \cdot 17 \) |
\( 5^{10} \cdot 13^{2} \cdot 17^{2} \) |
$1.54082$ |
$(-a-2), (2a+1), (-3a-2), (a+4)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.562785912$ |
$1.469035829$ |
1.653505339 |
\( -\frac{10227040701264}{19078515625} a + \frac{4248414065673}{19078515625} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 15 i + 3\) , \( -17 i + 35\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(15i+3\right){x}-17i+35$ |
| 5525.5-b9 |
5525.5-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5525.5 |
\( 5^{2} \cdot 13 \cdot 17 \) |
\( 5^{8} \cdot 13^{4} \cdot 17^{4} \) |
$1.54082$ |
$(-a-2), (2a+1), (-3a-2), (a+4)$ |
$1$ |
$\Z/4\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1.125571825$ |
$0.734517914$ |
1.653505339 |
\( \frac{226834389543384}{59636082025} a + \frac{4972600364093721}{1490902050625} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -105 i + 39\) , \( 15 i - 399\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+\left(-105i+39\right){x}+15i-399$ |
| 5525.5-b10 |
5525.5-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5525.5 |
\( 5^{2} \cdot 13 \cdot 17 \) |
\( 5^{10} \cdot 13^{8} \cdot 17^{2} \) |
$1.54082$ |
$(-a-2), (2a+1), (-3a-2), (a+4)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$0.562785912$ |
$0.367258957$ |
1.653505339 |
\( -\frac{825889105879790573124}{92088350925390625} a + \frac{518245358544105049557}{92088350925390625} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -525 i - 26\) , \( -3723 i + 2635\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+\left(-525i-26\right){x}-3723i+2635$ |
*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.
