| 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 |
| 124.1-a1 |
124.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{2} \cdot 31^{2} \) |
$2.87565$ |
$(3a-17), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.622822806$ |
$14.11688118$ |
3.646882609 |
\( -\frac{27}{62} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 2 a + 4\) , \( 9 a + 35\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(2a+4\right){x}+9a+35$ |
| 124.1-b1 |
124.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{2} \cdot 31^{3} \) |
$2.87565$ |
$(3a-17), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$3.650323415$ |
0.378520905 |
\( -\frac{11452023}{1922} a - \frac{49539843}{1922} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -21 a - 89\) , \( -341 a - 1474\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-21a-89\right){x}-341a-1474$ |
| 124.1-b2 |
124.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{6} \cdot 31 \) |
$2.87565$ |
$(3a-17), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$3.650323415$ |
0.378520905 |
\( \frac{776885175}{124} a - \frac{8268589269}{248} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 21 a - 63\) , \( 87 a - 392\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(21a-63\right){x}+87a-392$ |
| 124.1-c1 |
124.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{8} \cdot 31^{2} \) |
$2.87565$ |
$(3a-17), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.277796173$ |
$19.66889363$ |
4.645723052 |
\( -\frac{35937}{496} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-{x}+1$ |
| 124.1-c2 |
124.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{2} \cdot 31^{8} \) |
$2.87565$ |
$(3a-17), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$9.111184694$ |
$4.917223407$ |
4.645723052 |
\( \frac{3196010817}{1847042} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-31{x}+5$ |
| 124.1-c3 |
124.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{4} \cdot 31^{4} \) |
$2.87565$ |
$(3a-17), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$4.555592347$ |
$19.66889363$ |
4.645723052 |
\( \frac{979146657}{3844} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -21\) , \( 41\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-21{x}+41$ |
| 124.1-c4 |
124.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{2} \cdot 31^{2} \) |
$2.87565$ |
$(3a-17), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.277796173$ |
$19.66889363$ |
4.645723052 |
\( \frac{3999236143617}{62} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -331\) , \( 2397\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-331{x}+2397$ |
| 124.1-d1 |
124.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{6} \cdot 31 \) |
$2.87565$ |
$(3a-17), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$3.650323415$ |
0.378520905 |
\( -\frac{776885175}{124} a - \frac{6714818919}{248} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -7 a - 30\) , \( -149 a - 644\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-7a-30\right){x}-149a-644$ |
| 124.1-d2 |
124.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{2} \cdot 31^{3} \) |
$2.87565$ |
$(3a-17), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$3.650323415$ |
0.378520905 |
\( \frac{11452023}{1922} a - \frac{30495933}{961} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 35 a - 135\) , \( 207 a - 1031\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(35a-135\right){x}+207a-1031$ |
| 124.1-e1 |
124.1-e |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{10} \cdot 31^{6} \) |
$2.87565$ |
$(3a-17), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$2.774006076$ |
0.575302060 |
\( -\frac{458314011}{953312} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 49 a - 249\) , \( -799 a + 4259\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(49a-249\right){x}-799a+4259$ |
| 124.1-e2 |
124.1-e |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{30} \cdot 31^{2} \) |
$2.87565$ |
$(3a-17), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$2.774006076$ |
0.575302060 |
\( \frac{406869021}{1015808} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 45 a + 209\) , \( 743 a + 3220\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(45a+209\right){x}+743a+3220$ |
| 124.1-f1 |
124.1-f |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{6} \cdot 31 \) |
$2.87565$ |
$(3a-17), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$24.23594038$ |
2.513149945 |
\( -\frac{776885175}{124} a - \frac{6714818919}{248} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -8 a + 91\) , \( -29 a + 224\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-8a+91\right){x}-29a+224$ |
| 124.1-f2 |
124.1-f |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{2} \cdot 31^{3} \) |
$2.87565$ |
$(3a-17), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$24.23594038$ |
2.513149945 |
\( \frac{11452023}{1922} a - \frac{30495933}{961} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 8 a + 36\) , \( 19 a + 82\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(8a+36\right){x}+19a+82$ |
| 124.1-g1 |
124.1-g |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{2} \cdot 31^{3} \) |
$2.87565$ |
$(3a-17), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$24.23594038$ |
2.513149945 |
\( -\frac{11452023}{1922} a - \frac{49539843}{1922} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 6 a + 19\) , \( a + 64\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(6a+19\right){x}+a+64$ |
| 124.1-g2 |
124.1-g |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{6} \cdot 31 \) |
$2.87565$ |
$(3a-17), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$24.23594038$ |
2.513149945 |
\( \frac{776885175}{124} a - \frac{8268589269}{248} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 22 a + 95\) , \( 121 a + 523\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(22a+95\right){x}+121a+523$ |
| 124.1-h1 |
124.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{8} \cdot 31^{2} \) |
$2.87565$ |
$(3a-17), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$9.445571402$ |
$5.013606122$ |
4.910627291 |
\( -\frac{35937}{496} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -63 a - 239\) , \( -2815 a - 12129\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-63a-239\right){x}-2815a-12129$ |
| 124.1-h2 |
124.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{2} \cdot 31^{8} \) |
$2.87565$ |
$(3a-17), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$9.445571402$ |
$5.013606122$ |
4.910627291 |
\( \frac{3196010817}{1847042} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -2673 a - 11519\) , \( 3605 a + 15617\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2673a-11519\right){x}+3605a+15617$ |
| 124.1-h3 |
124.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{4} \cdot 31^{4} \) |
$2.87565$ |
$(3a-17), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$18.89114280$ |
$5.013606122$ |
4.910627291 |
\( \frac{979146657}{3844} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -1803 a - 7759\) , \( -92615 a - 400229\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1803a-7759\right){x}-92615a-400229$ |
| 124.1-h4 |
124.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{2} \cdot 31^{2} \) |
$2.87565$ |
$(3a-17), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$37.78228561$ |
$1.253401530$ |
4.910627291 |
\( \frac{3999236143617}{62} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -28773 a - 124319\) , \( -5859235 a - 25322555\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-28773a-124319\right){x}-5859235a-25322555$ |
| 124.1-i1 |
124.1-i |
$1$ |
$1$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{2} \cdot 31^{2} \) |
$2.87565$ |
$(3a-17), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.622822806$ |
$14.11688118$ |
3.646882609 |
\( -\frac{27}{62} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -4 a + 7\) , \( -10 a + 44\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a+7\right){x}-10a+44$ |
| 124.1-j1 |
124.1-j |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{10} \cdot 31^{6} \) |
$2.87565$ |
$(3a-17), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$2.774006076$ |
0.575302060 |
\( -\frac{458314011}{953312} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -49 a - 200\) , \( 799 a + 3460\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-49a-200\right){x}+799a+3460$ |
| 124.1-j2 |
124.1-j |
$2$ |
$3$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{30} \cdot 31^{2} \) |
$2.87565$ |
$(3a-17), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$2.774006076$ |
0.575302060 |
\( \frac{406869021}{1015808} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -46 a + 255\) , \( -743 a + 3963\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-46a+255\right){x}-743a+3963$ |
*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.
