| 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 |
| 114.4-a4 |
114.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
114.4 |
\( 2 \cdot 3 \cdot 19 \) |
\( 2 \cdot 3^{3} \cdot 19 \) |
$0.82587$ |
$(a), (a-1), (3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$1.635434305$ |
1.156426687 |
\( \frac{1101457391617}{1026} a + \frac{8792832344816}{513} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 5 a + 170\) , \( -549 a + 68\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(5a+170\right){x}-549a+68$ |
| 912.4-a4 |
912.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
912.4 |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( 2^{13} \cdot 3^{3} \cdot 19 \) |
$1.38894$ |
$(a), (a-1), (3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.662191723$ |
$0.817717152$ |
2.297328544 |
\( \frac{1101457391617}{1026} a + \frac{8792832344816}{513} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 21 a + 682\) , \( -5074 a + 583\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(21a+682\right){x}-5074a+583$ |
| 3078.6-a4 |
3078.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3078.6 |
\( 2 \cdot 3^{4} \cdot 19 \) |
\( 2 \cdot 3^{15} \cdot 19 \) |
$1.88257$ |
$(a), (-a-1), (a-1), (3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$0.687516686$ |
$0.545144768$ |
2.120167050 |
\( \frac{1101457391617}{1026} a + \frac{8792832344816}{513} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 48 a + 1536\) , \( 16357 a - 1920\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(48a+1536\right){x}+16357a-1920$ |
| 6498.9-b4 |
6498.9-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6498.9 |
\( 2 \cdot 3^{2} \cdot 19^{2} \) |
\( 2 \cdot 3^{9} \cdot 19^{7} \) |
$2.26923$ |
$(a), (a-1), (3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.216618565$ |
2.450759305 |
\( \frac{1101457391617}{1026} a + \frac{8792832344816}{513} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 4997 a + 6696\) , \( -85682 a + 343713\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4997a+6696\right){x}-85682a+343713$ |
| 19494.6-b4 |
19494.6-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19494.6 |
\( 2 \cdot 3^{3} \cdot 19^{2} \) |
\( 2 \cdot 3^{9} \cdot 19^{7} \) |
$2.98647$ |
$(a), (-a-1), (a-1), (3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$2.380011608$ |
$0.216618565$ |
2.916417799 |
\( \frac{1101457391617}{1026} a + \frac{8792832344816}{513} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -6863 a - 769\) , \( 204609 a - 224238\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-6863a-769\right){x}+204609a-224238$ |
| 24624.6-k4 |
24624.6-k |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24624.6 |
\( 2^{4} \cdot 3^{4} \cdot 19 \) |
\( 2^{13} \cdot 3^{15} \cdot 19 \) |
$3.16609$ |
$(a), (-a-1), (a-1), (3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.272572384$ |
3.083804500 |
\( \frac{1101457391617}{1026} a + \frac{8792832344816}{513} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 192 a + 6144\) , \( 130856 a - 15360\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(192a+6144\right){x}+130856a-15360$ |
| 32946.12-e4 |
32946.12-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
32946.12 |
\( 2 \cdot 3 \cdot 17^{2} \cdot 19 \) |
\( 2 \cdot 3^{3} \cdot 17^{6} \cdot 19 \) |
$3.40513$ |
$(a), (a-1), (2a+3), (3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \cdot 3 \) |
$1.256288642$ |
$0.396651081$ |
4.228285700 |
\( \frac{1101457391617}{1026} a + \frac{8792832344816}{513} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 2052 a + 43\) , \( 29279 a + 42828\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(2052a+43\right){x}+29279a+42828$ |
| 32946.8-a4 |
32946.8-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
32946.8 |
\( 2 \cdot 3 \cdot 17^{2} \cdot 19 \) |
\( 2 \cdot 3^{3} \cdot 17^{6} \cdot 19 \) |
$3.40513$ |
$(a), (a-1), (-2a+3), (3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.396651081$ |
1.121898677 |
\( \frac{1101457391617}{1026} a + \frac{8792832344816}{513} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -2042 a + 299\) , \( 25921 a - 49441\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2042a+299\right){x}+25921a-49441$ |
| 41382.14-a4 |
41382.14-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41382.14 |
\( 2 \cdot 3^{2} \cdot 11^{2} \cdot 19 \) |
\( 2 \cdot 3^{9} \cdot 11^{6} \cdot 19 \) |
$3.60484$ |
$(a), (a-1), (a+3), (3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.155171443$ |
$0.284692570$ |
3.470826834 |
\( \frac{1101457391617}{1026} a + \frac{8792832344816}{513} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -3322 a + 3114\) , \( 11381 a + 166294\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-3322a+3114\right){x}+11381a+166294$ |
| 41382.18-c4 |
41382.18-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41382.18 |
\( 2 \cdot 3^{2} \cdot 11^{2} \cdot 19 \) |
\( 2 \cdot 3^{9} \cdot 11^{6} \cdot 19 \) |
$3.60484$ |
$(a), (a-1), (a-3), (3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$4.683765953$ |
$0.284692570$ |
7.543038215 |
\( \frac{1101457391617}{1026} a + \frac{8792832344816}{513} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -1531 a - 5205\) , \( 64576 a + 136549\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-1531a-5205\right){x}+64576a+136549$ |
| 43776.6-d4 |
43776.6-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
43776.6 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{25} \cdot 3^{9} \cdot 19 \) |
$3.65589$ |
$(a), (a-1), (3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.723661623$ |
$0.236054609$ |
3.821478575 |
\( \frac{1101457391617}{1026} a + \frac{8792832344816}{513} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -5546 a - 2389\) , \( -190362 a + 95806\bigr] \) |
${y}^2={x}^{3}+\left(-5546a-2389\right){x}-190362a+95806$ |
| 43776.6-g4 |
43776.6-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
43776.6 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{25} \cdot 3^{9} \cdot 19 \) |
$3.65589$ |
$(a), (a-1), (3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.236054609$ |
2.670653037 |
\( \frac{1101457391617}{1026} a + \frac{8792832344816}{513} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -5546 a - 2389\) , \( 190362 a - 95806\bigr] \) |
${y}^2={x}^{3}+\left(-5546a-2389\right){x}+190362a-95806$ |
*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.
