| 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 |
| 67600.1-CMb1 |
67600.1-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 5^{6} \cdot 13^{9} \) |
$2.88174$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$13$ |
13Cs.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.449098830$ |
0.449098830 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 174 i - 157\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(174i-157\right){x}$ |
| 67600.1-CMa1 |
67600.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 5^{3} \cdot 13^{6} \) |
$2.88174$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$5$ |
5Cs.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1.275176390$ |
1.275176390 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 22 i + 19\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(22i+19\right){x}$ |
| 67600.1-a1 |
67600.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{7} \cdot 13^{9} \) |
$2.88174$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.623798259$ |
0.623798259 |
\( \frac{256}{5} a + \frac{8048}{5} \) |
\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( -93 i - 74\) , \( 48 i - 112\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-93i-74\right){x}+48i-112$ |
| 67600.1-a2 |
67600.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{8} \cdot 13^{9} \) |
$2.88174$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.311899129$ |
0.623798259 |
\( -\frac{4439964}{25} a + \frac{3656648}{25} \) |
\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( -878 i - 944\) , \( -16162 i - 7582\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-878i-944\right){x}-16162i-7582$ |
| 67600.1-b1 |
67600.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{3} \cdot 13^{7} \) |
$2.88174$ |
$(a+1), (-a-2), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.299396318$ |
$1.314767969$ |
3.149093514 |
\( -\frac{2224}{13} a + \frac{356}{13} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -12 i - 4\) , \( 54 i + 28\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-12i-4\right){x}+54i+28$ |
| 67600.1-b2 |
67600.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{10} \cdot 5^{3} \cdot 13^{8} \) |
$2.88174$ |
$(a+1), (-a-2), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.598792636$ |
$0.657383984$ |
3.149093514 |
\( \frac{47776420}{169} a + \frac{17266442}{169} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -232 i - 194\) , \( 2070 i + 540\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-232i-194\right){x}+2070i+540$ |
| 67600.1-c1 |
67600.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{10} \cdot 5^{9} \cdot 13^{10} \) |
$2.88174$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.153739610$ |
0.614958440 |
\( \frac{10359522503116}{3570125} a - \frac{4364617727362}{3570125} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( 3290 i - 7061\) , \( 159838 i - 210616\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(3290i-7061\right){x}+159838i-210616$ |
| 67600.1-c2 |
67600.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{10} \cdot 5^{18} \cdot 13^{7} \) |
$2.88174$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.153739610$ |
0.614958440 |
\( -\frac{2896194844812}{3173828125} a + \frac{3398200522034}{3173828125} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -1470 i + 1119\) , \( 14542 i - 22988\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-1470i+1119\right){x}+14542i-22988$ |
| 67600.1-c3 |
67600.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{12} \cdot 13^{8} \) |
$2.88174$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.307479220$ |
0.614958440 |
\( \frac{3643553424}{2640625} a + \frac{4710369332}{2640625} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( 270 i - 451\) , \( 1258 i - 3426\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(270i-451\right){x}+1258i-3426$ |
| 67600.1-c4 |
67600.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{9} \cdot 13^{7} \) |
$2.88174$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.614958440$ |
0.614958440 |
\( -\frac{50931328}{1625} a + \frac{11807696}{1625} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( 190 i - 136\) , \( -1388 i + 127\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(190i-136\right){x}-1388i+127$ |
| 67600.1-d1 |
67600.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{6} \cdot 13^{2} \) |
$2.88174$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cn |
$1$ |
\( 1 \) |
$1$ |
$2.533498384$ |
2.533498384 |
\( -512 a + 768 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 2 i + 6\) , \( 6 i + 5\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(2i+6\right){x}+6i+5$ |
| 67600.1-e1 |
67600.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 5^{9} \cdot 13^{9} \) |
$2.88174$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cn |
$1$ |
\( 2^{5} \) |
$1$ |
$0.302143887$ |
2.417151103 |
\( -\frac{906876}{2197} a + \frac{1118799}{2197} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 29 i - 379\) , \( -3876 i + 1497\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(29i-379\right){x}-3876i+1497$ |
| 67600.1-e2 |
67600.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 5^{9} \cdot 13^{12} \) |
$2.88174$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cn |
$4$ |
\( 2^{4} \) |
$1$ |
$0.151071943$ |
2.417151103 |
\( \frac{10047446145}{4826809} a + \frac{17756992962}{4826809} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 649 i + 2461\) , \( -33648 i + 20493\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(649i+2461\right){x}-33648i+20493$ |
| 67600.1-f1 |
67600.1-f |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{13} \cdot 5^{16} \cdot 13^{3} \) |
$2.88174$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.359365980$ |
2.874927842 |
\( \frac{80398914857}{19531250} a - \frac{197826917099}{19531250} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( 307 i - 452\) , \( -4378 i + 3383\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(307i-452\right){x}-4378i+3383$ |
| 67600.1-f2 |
67600.1-f |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 5^{11} \cdot 13^{3} \) |
$2.88174$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.718731960$ |
2.874927842 |
\( -\frac{10462207}{6250} a - \frac{2706038}{3125} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( 87 i + 8\) , \( 130 i + 339\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(87i+8\right){x}+130i+339$ |
| 67600.1-f3 |
67600.1-f |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{22} \cdot 5^{7} \cdot 13^{3} \) |
$2.88174$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.718731960$ |
2.874927842 |
\( \frac{523313}{160} a + \frac{424661}{40} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( -61 i + 125\) , \( -484 i - 365\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+\left(-61i+125\right){x}-484i-365$ |
| 67600.1-f4 |
67600.1-f |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{17} \cdot 5^{8} \cdot 13^{3} \) |
$2.88174$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.359365980$ |
2.874927842 |
\( \frac{12916359143}{200} a + \frac{17274394699}{200} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( -941 i + 1965\) , \( -31012 i - 24461\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+\left(-941i+1965\right){x}-31012i-24461$ |
| 67600.1-g1 |
67600.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{10} \cdot 5^{9} \cdot 13^{7} \) |
$2.88174$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.518674966$ |
4.149399729 |
\( \frac{109298}{1625} a + \frac{1963264}{1625} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( 133 i - 84\) , \( 20 i - 593\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(133i-84\right){x}+20i-593$ |
| 67600.1-g2 |
67600.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{11} \cdot 5^{12} \cdot 13^{8} \) |
$2.88174$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.259337483$ |
4.149399729 |
\( -\frac{321047281}{2640625} a + \frac{6395175767}{2640625} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( -657 i + 386\) , \( 190 i - 3903\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-657i+386\right){x}+190i-3903$ |
*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.
