| 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 |
| 98.2-a1 |
98.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2 \) |
$5.504475848$ |
$1.750834270$ |
1.697055907 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-171{x}-874$ |
| 98.2-a2 |
98.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2 \) |
$5.504475848$ |
$15.75750843$ |
1.697055907 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}$ |
| 98.2-a3 |
98.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2 \cdot 3^{2} \) |
$1.834825282$ |
$5.252502811$ |
1.697055907 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+4{x}-6$ |
| 98.2-a4 |
98.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$3.669650565$ |
$2.626251405$ |
1.697055907 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-36{x}-70$ |
| 98.2-a5 |
98.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{3} \) |
$11.00895169$ |
$7.878754216$ |
1.697055907 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-11{x}+12$ |
| 98.2-a6 |
98.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{3} \) |
$11.00895169$ |
$0.875417135$ |
1.697055907 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2731{x}-55146$ |
| 98.2-b1 |
98.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
|
\( 2 \) |
$1$ |
$1.750834270$ |
3.716531963 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 198\) , \( 1388\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+198{x}+1388$ |
| 98.2-b2 |
98.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
|
\( 2 \) |
$1$ |
$15.75750843$ |
3.716531963 |
\( -\frac{15625}{28} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 368\) , \( -1356\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+368{x}-1356$ |
| 98.2-b3 |
98.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
|
\( 2 \) |
$1$ |
$5.252502811$ |
3.716531963 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 373\) , \( -1405\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+373{x}-1405$ |
| 98.2-b4 |
98.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
|
\( 2^{3} \) |
$1$ |
$2.626251405$ |
3.716531963 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 333\) , \( -901\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+333{x}-901$ |
| 98.2-b5 |
98.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
|
\( 2^{3} \) |
$1$ |
$7.878754216$ |
3.716531963 |
\( \frac{128787625}{98} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 358\) , \( -1258\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+358{x}-1258$ |
| 98.2-b6 |
98.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
|
\( 2^{3} \) |
$1$ |
$0.875417135$ |
3.716531963 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -2362\) , \( 83820\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2-2362{x}+83820$ |
| 98.2-c1 |
98.2-c |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{36} \cdot 3^{12} \cdot 7^{2} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$36$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$1.750834270$ |
2.774742516 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1535\) , \( 23591\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-1535{x}+23591$ |
| 98.2-c2 |
98.2-c |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 7^{2} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2^{2} \) |
$1$ |
$15.75750843$ |
2.774742516 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -5\) , \( -7\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-5{x}-7$ |
| 98.2-c3 |
98.2-c |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 7^{6} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$5.252502811$ |
2.774742516 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 40\) , \( 155\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2+40{x}+155$ |
| 98.2-c4 |
98.2-c |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{12} \cdot 7^{12} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2^{3} \cdot 3^{3} \) |
$1$ |
$2.626251405$ |
2.774742516 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -320\) , \( 1883\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-320{x}+1883$ |
| 98.2-c5 |
98.2-c |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{12} \cdot 7^{4} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2^{3} \) |
$1$ |
$7.878754216$ |
2.774742516 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -95\) , \( -331\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-95{x}-331$ |
| 98.2-c6 |
98.2-c |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{12} \cdot 7^{4} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$36$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.875417135$ |
2.774742516 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -24575\) , \( 1488935\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-24575{x}+1488935$ |
| 98.2-d1 |
98.2-d |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{36} \cdot 3^{12} \cdot 7^{2} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$9.645424961$ |
$1.750834270$ |
26.76357072 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -1188\) , \( -7952\bigr] \) |
${y}^2+a{x}{y}={x}^3-1188{x}-7952$ |
| 98.2-d2 |
98.2-d |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 7^{2} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \) |
$9.645424961$ |
$15.75750843$ |
26.76357072 |
\( -\frac{15625}{28} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 342\) , \( -1184\bigr] \) |
${y}^2+a{x}{y}={x}^3+342{x}-1184$ |
| 98.2-d3 |
98.2-d |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 7^{6} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$9.645424961$ |
$5.252502811$ |
26.76357072 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 387\) , \( -1841\bigr] \) |
${y}^2+a{x}{y}={x}^3+387{x}-1841$ |
| 98.2-d4 |
98.2-d |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{12} \cdot 7^{12} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$9.645424961$ |
$2.626251405$ |
26.76357072 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 27\) , \( 391\bigr] \) |
${y}^2+a{x}{y}={x}^3+27{x}+391$ |
| 98.2-d5 |
98.2-d |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{12} \cdot 7^{4} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \) |
$9.645424961$ |
$7.878754216$ |
26.76357072 |
\( \frac{128787625}{98} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 252\) , \( 130\bigr] \) |
${y}^2+a{x}{y}={x}^3+252{x}+130$ |
| 98.2-d6 |
98.2-d |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{12} \cdot 7^{4} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$9.645424961$ |
$0.875417135$ |
26.76357072 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -24228\) , \( -1219856\bigr] \) |
${y}^2+a{x}{y}={x}^3-24228{x}-1219856$ |
*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.
