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 |
200.2-a3 |
200.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
200.2 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{8} \) |
$0.67209$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/4\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$2.996888981$ |
0.749222245 |
\( \frac{237276}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -4\) , \( -6 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}-4{x}-6i$ |
225.2-a6 |
225.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
225.2 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{8} \) |
$0.69217$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\Z/4\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$2.235701712$ |
0.558925428 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$ |
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 |
\( \frac{226834389543384}{59636082025} a + \frac{4972600364093721}{1490902050625} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -105 i + 39\) , \( 15 i - 399\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+\left(-105i+39\right){x}+15i-399$ |
5525.8-b9 |
5525.8-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5525.8 |
\( 5^{2} \cdot 13 \cdot 17 \) |
\( 5^{8} \cdot 13^{4} \cdot 17^{4} \) |
$1.54082$ |
$(-a-2), (2a+1), (2a+3), (a-4)$ |
$1$ |
$\Z/4\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1.125571825$ |
$0.734517914$ |
1.653505339 |
\( -\frac{226834389543384}{59636082025} a + \frac{4972600364093721}{1490902050625} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( 105 i + 39\) , \( -15 i - 399\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+\left(105i+39\right){x}-15i-399$ |
7650.3-d3 |
7650.3-d |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
7650.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 17 \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{12} \cdot 17^{4} \) |
$1.67141$ |
$(a+1), (-a-2), (2a+1), (a+4), (3)$ |
0 |
$\Z/4\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{11} \) |
$1$ |
$0.370147195$ |
2.961177564 |
\( -\frac{4726501092598558}{880885546875} a - \frac{81525979253294953}{10570626562500} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -455 i - 205\) , \( 4550 i - 500\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-455i-205\right){x}+4550i-500$ |
7650.4-d3 |
7650.4-d |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
7650.4 |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 17 \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{12} \cdot 17^{4} \) |
$1.67141$ |
$(a+1), (-a-2), (2a+1), (a-4), (3)$ |
0 |
$\Z/4\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{11} \) |
$1$ |
$0.370147195$ |
2.961177564 |
\( \frac{4726501092598558}{880885546875} a - \frac{81525979253294953}{10570626562500} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 455 i - 205\) , \( -4550 i - 500\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(455i-205\right){x}-4550i-500$ |
8450.5-c5 |
8450.5-c |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8450.5 |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{8} \cdot 13^{8} \) |
$1.71349$ |
$(a+1), (-a-2), (2a+1), (-3a-2), (2a+3)$ |
0 |
$\Z/4\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{10} \) |
$1$ |
$0.675991984$ |
2.703967938 |
\( -\frac{32798729601}{71402500} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -66\) , \( 441\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-66{x}+441$ |
22050.2-d5 |
22050.2-d |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
22050.2 |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 5^{16} \cdot 7^{8} \) |
$2.17781$ |
$(a+1), (-a-2), (2a+1), (3), (7)$ |
0 |
$\Z/4\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{13} \) |
$1$ |
$0.110519370$ |
3.536619863 |
\( \frac{47595748626367201}{1215506250000} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -7550\) , \( 247500\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-7550{x}+247500$ |
23400.3-c7 |
23400.3-c |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
23400.3 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 13 \) |
\( 2^{8} \cdot 3^{8} \cdot 5^{8} \cdot 13^{4} \) |
$2.21041$ |
$(a+1), (-a-2), (2a+1), (-3a-2), (3)$ |
0 |
$\Z/4\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{10} \) |
$1$ |
$0.586538713$ |
2.346154853 |
\( -\frac{180392107616}{96393375} a - \frac{1762911127684}{1445900625} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 140 i - 10\) , \( -500 i - 600\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+\left(140i-10\right){x}-500i-600$ |
23400.4-c7 |
23400.4-c |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
23400.4 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 13 \) |
\( 2^{8} \cdot 3^{8} \cdot 5^{8} \cdot 13^{4} \) |
$2.21041$ |
$(a+1), (-a-2), (2a+1), (2a+3), (3)$ |
0 |
$\Z/4\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{10} \) |
$1$ |
$0.586538713$ |
2.346154853 |
\( \frac{180392107616}{96393375} a - \frac{1762911127684}{1445900625} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( -140 i - 10\) , \( -500 i + 600\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+\left(-140i-10\right){x}-500i+600$ |
38025.5-a7 |
38025.5-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{8} \cdot 5^{8} \cdot 13^{8} \) |
$2.49566$ |
$(-a-2), (2a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/4\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{10} \) |
$1$ |
$0.370634167$ |
1.482536669 |
\( \frac{15551989015681}{1445900625} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -520\) , \( 4225\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-520{x}+4225$ |
84050.5-f1 |
84050.5-f |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84050.5 |
\( 2 \cdot 5^{2} \cdot 41^{2} \) |
\( 2^{12} \cdot 5^{16} \cdot 41^{8} \) |
$3.04301$ |
$(a+1), (-a-2), (2a+1), (-5a-4), (4a+5)$ |
0 |
$\Z/4\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{12} \cdot 3 \) |
$1$ |
$0.059517308$ |
2.856830815 |
\( -\frac{1106280483969259521}{70644025000000} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -21546\) , \( 1277381\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-21546{x}+1277381$ |
84825.5-b3 |
84825.5-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84825.5 |
\( 3^{2} \cdot 5^{2} \cdot 13 \cdot 29 \) |
\( 3^{8} \cdot 5^{12} \cdot 13^{4} \cdot 29^{4} \) |
$3.05000$ |
$(-a-2), (2a+1), (-3a-2), (-2a+5), (3)$ |
0 |
$\Z/4\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{11} \) |
$1$ |
$0.185677734$ |
1.485421873 |
\( \frac{15245709159221234008}{213053758323046875} a - \frac{49739276737014736007}{639161274969140625} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -35 i + 556\) , \( 20195 i - 5545\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}+\left(-35i+556\right){x}+20195i-5545$ |
84825.8-b3 |
84825.8-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84825.8 |
\( 3^{2} \cdot 5^{2} \cdot 13 \cdot 29 \) |
\( 3^{8} \cdot 5^{12} \cdot 13^{4} \cdot 29^{4} \) |
$3.05000$ |
$(-a-2), (2a+1), (2a+3), (2a+5), (3)$ |
0 |
$\Z/4\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{11} \) |
$1$ |
$0.185677734$ |
1.485421873 |
\( -\frac{15245709159221234008}{213053758323046875} a - \frac{49739276737014736007}{639161274969140625} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( 35 i + 556\) , \( -20195 i - 5545\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}+\left(35i+556\right){x}-20195i-5545$ |
*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.