| 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 |
| 98.1-a1 |
98.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$0.79523$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$0.436190660$ |
0.693975091 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$ |
| 98.1-a2 |
98.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$0.79523$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$35.33144352$ |
0.693975091 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}$ |
| 98.1-a3 |
98.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$0.79523$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$3.925715946$ |
0.693975091 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$ |
| 98.1-a4 |
98.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2 \cdot 7^{5} \) |
$0.79523$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$17.66572176$ |
0.693975091 |
\( -\frac{2928743223192875}{4802} a + \frac{2070934198465000}{2401} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 55 a - 91\) , \( -290 a + 416\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(55a-91\right){x}-290a+416$ |
| 98.1-a5 |
98.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$0.79523$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3Cs.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$3.925715946$ |
0.693975091 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$ |
| 98.1-a6 |
98.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{3} \cdot 7^{15} \) |
$0.79523$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$1.962857973$ |
0.693975091 |
\( -\frac{392127492092318125}{55365148804} a + \frac{138814532776321000}{13841287201} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 130 a - 356\) , \( 2000 a - 2038\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(130a-356\right){x}+2000a-2038$ |
| 98.1-a7 |
98.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{9} \cdot 7^{5} \) |
$0.79523$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$0.218095330$ |
0.693975091 |
\( -\frac{218768831290078842857759125}{76832} a + \frac{9668307757341907702465000}{2401} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 14480 a - 23211\) , \( 1224480 a - 1786730\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(14480a-23211\right){x}+1224480a-1786730$ |
| 98.1-a8 |
98.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$0.79523$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$35.33144352$ |
0.693975091 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$ |
| 98.1-a9 |
98.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{3} \cdot 7^{15} \) |
$0.79523$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$1.962857973$ |
0.693975091 |
\( \frac{392127492092318125}{55365148804} a + \frac{138814532776321000}{13841287201} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -130 a - 356\) , \( -2000 a - 2038\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-130a-356\right){x}-2000a-2038$ |
| 98.1-a10 |
98.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$0.79523$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{3} \) |
$1$ |
$0.436190660$ |
0.693975091 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$ |
| 98.1-a11 |
98.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2 \cdot 7^{5} \) |
$0.79523$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$17.66572176$ |
0.693975091 |
\( \frac{2928743223192875}{4802} a + \frac{2070934198465000}{2401} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -55 a - 91\) , \( 290 a + 416\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-55a-91\right){x}+290a+416$ |
| 98.1-a12 |
98.1-a |
$12$ |
$36$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{9} \cdot 7^{5} \) |
$0.79523$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$0.218095330$ |
0.693975091 |
\( \frac{218768831290078842857759125}{76832} a + \frac{9668307757341907702465000}{2401} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -14480 a - 23211\) , \( -1224480 a - 1786730\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-14480a-23211\right){x}-1224480a-1786730$ |
*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.
