| 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 |
| 7938.3-a1 |
7938.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{16} \cdot 7^{2} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.913455777$ |
1.291821549 |
\( -\frac{7189057}{16128} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -36\) , \( -176\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-36{x}-176$ |
| 7938.3-a2 |
7938.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{44} \cdot 7^{4} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{6} \) |
$1$ |
$0.114181972$ |
1.291821549 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 3474\) , \( -31010\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+3474{x}-31010$ |
| 7938.3-a3 |
7938.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{28} \cdot 7^{8} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.228363944$ |
1.291821549 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -936\) , \( -3668\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-936{x}-3668$ |
| 7938.3-a4 |
7938.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{20} \cdot 7^{16} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.114181972$ |
1.291821549 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -8226\) , \( 286474\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-8226{x}+286474$ |
| 7938.3-a5 |
7938.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2 \cdot 3^{52} \cdot 7^{2} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.057090986$ |
1.291821549 |
\( -\frac{4649899211841477010577}{25942282643925774} a + \frac{175460189537451816680}{1853020188851841} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -5355 a + 38754\) , \( -2041263 a - 879494\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-5355a+38754\right){x}-2041263a-879494$ |
| 7938.3-a6 |
7938.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2 \cdot 3^{52} \cdot 7^{2} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.057090986$ |
1.291821549 |
\( \frac{4649899211841477010577}{25942282643925774} a + \frac{175460189537451816680}{1853020188851841} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 5355 a + 38754\) , \( 2041263 a - 879494\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(5355a+38754\right){x}+2041263a-879494$ |
| 7938.3-a7 |
7938.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{20} \cdot 7^{4} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.456727888$ |
1.291821549 |
\( \frac{65597103937}{63504} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -756\) , \( -7808\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-756{x}-7808$ |
| 7938.3-a8 |
7938.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{2} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.228363944$ |
1.291821549 |
\( \frac{268498407453697}{252} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -12096\) , \( -509036\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-12096{x}-509036$ |
| 7938.3-b1 |
7938.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{3} \cdot 3^{15} \cdot 7^{2} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.308398697$ |
$2.099685898$ |
5.494562463 |
\( -\frac{5017}{28} a + \frac{28405}{14} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 3 a + 10\) , \( -5 a - 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(3a+10\right){x}-5a-1$ |
| 7938.3-c1 |
7938.3-c |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{3} \cdot 3^{15} \cdot 7^{2} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.308398697$ |
$2.099685898$ |
5.494562463 |
\( \frac{5017}{28} a + \frac{28405}{14} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3 a + 10\) , \( 5 a - 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-3a+10\right){x}+5a-1$ |
| 7938.3-d1 |
7938.3-d |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{36} \cdot 3^{12} \cdot 7^{2} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$3.324049150$ |
$0.291805711$ |
5.487015846 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1535\) , \( 23591\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-1535{x}+23591$ |
| 7938.3-d2 |
7938.3-d |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 7^{2} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$0.369338794$ |
$2.626251405$ |
5.487015846 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -5\) , \( -7\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-5{x}-7$ |
| 7938.3-d3 |
7938.3-d |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 7^{6} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1.108016383$ |
$0.875417135$ |
5.487015846 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 40\) , \( 155\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+40{x}+155$ |
| 7938.3-d4 |
7938.3-d |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{12} \cdot 7^{12} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$2.216032767$ |
$0.437708567$ |
5.487015846 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -320\) , \( 1883\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-320{x}+1883$ |
| 7938.3-d5 |
7938.3-d |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{12} \cdot 7^{4} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$0.738677589$ |
$1.313125702$ |
5.487015846 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -95\) , \( -331\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-95{x}-331$ |
| 7938.3-d6 |
7938.3-d |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{12} \cdot 7^{4} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$6.648098301$ |
$0.145902855$ |
5.487015846 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -24575\) , \( 1488935\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-24575{x}+1488935$ |
*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.
