| 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 |
| 600.1-a1 |
600.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
$1.53203$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.891621139$ |
$15.64258266$ |
2.013113201 |
\( \frac{21296}{15} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 2 a + 6\) , \( 3 a + 6\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a+6\right){x}+3a+6$ |
| 600.1-a2 |
600.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{4} \) |
$1.53203$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.445810569$ |
$15.64258266$ |
2.013113201 |
\( \frac{470596}{225} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -18 a - 29\) , \( 13 a + 23\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-18a-29\right){x}+13a+23$ |
| 600.1-a3 |
600.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{8} \) |
$1.53203$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.222905284$ |
$3.910645665$ |
2.013113201 |
\( \frac{136835858}{1875} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -138 a - 239\) , \( -1187 a - 2059\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-138a-239\right){x}-1187a-2059$ |
| 600.1-a4 |
600.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{8} \cdot 5^{2} \) |
$1.53203$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.222905284$ |
$15.64258266$ |
2.013113201 |
\( \frac{546718898}{405} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -218 a - 379\) , \( 2213 a + 3833\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-218a-379\right){x}+2213a+3833$ |
| 600.1-b1 |
600.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{16} \) |
$1.53203$ |
$(a+1), (a), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$2.911019061$ |
1.680677638 |
\( -\frac{27995042}{1171875} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 80 a - 141\) , \( -4420 a + 7659\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(80a-141\right){x}-4420a+7659$ |
| 600.1-b2 |
600.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{16} \cdot 5^{2} \) |
$1.53203$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.911019061$ |
1.680677638 |
\( \frac{54607676}{32805} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -80 a + 139\) , \( 70 a - 121\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-80a+139\right){x}+70a-121$ |
| 600.1-b3 |
600.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{4} \) |
$1.53203$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$11.64407624$ |
1.680677638 |
\( \frac{3631696}{2025} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 20 a - 36\) , \( 20 a - 36\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(20a-36\right){x}+20a-36$ |
| 600.1-b4 |
600.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{8} \) |
$1.53203$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$11.64407624$ |
1.680677638 |
\( \frac{868327204}{5625} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 200 a - 351\) , \( -1960 a + 3393\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(200a-351\right){x}-1960a+3393$ |
| 600.1-b5 |
600.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{2} \) |
$1.53203$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.822038123$ |
1.680677638 |
\( \frac{24918016}{45} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -15\) , \( -18\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-15{x}-18$ |
| 600.1-b6 |
600.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{4} \) |
$1.53203$ |
$(a+1), (a), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$11.64407624$ |
1.680677638 |
\( \frac{1770025017602}{75} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 3200 a - 5601\) , \( -129460 a + 224343\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(3200a-5601\right){x}-129460a+224343$ |
| 600.1-c1 |
600.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{16} \) |
$1.53203$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.805807860$ |
1.860933541 |
\( -\frac{27995042}{1171875} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 80 a - 140\) , \( 4500 a - 7800\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(80a-140\right){x}+4500a-7800$ |
| 600.1-c2 |
600.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{16} \cdot 5^{2} \) |
$1.53203$ |
$(a+1), (a), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$3.223231443$ |
1.860933541 |
\( \frac{54607676}{32805} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -80 a + 140\) , \( -150 a + 260\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-80a+140\right){x}-150a+260$ |
| 600.1-c3 |
600.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{4} \) |
$1.53203$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$12.89292577$ |
1.860933541 |
\( \frac{3631696}{2025} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 20 a - 35\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(20a-35\right){x}$ |
| 600.1-c4 |
600.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{8} \) |
$1.53203$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$3.223231443$ |
1.860933541 |
\( \frac{868327204}{5625} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 200 a - 350\) , \( 2160 a - 3744\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(200a-350\right){x}+2160a-3744$ |
| 600.1-c5 |
600.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{2} \) |
$1.53203$ |
$(a+1), (a), (5)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$25.78585154$ |
1.860933541 |
\( \frac{24918016}{45} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -15\) , \( 18\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-15{x}+18$ |
| 600.1-c6 |
600.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{4} \) |
$1.53203$ |
$(a+1), (a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.805807860$ |
1.860933541 |
\( \frac{1770025017602}{75} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 3200 a - 5600\) , \( 132660 a - 229944\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(3200a-5600\right){x}+132660a-229944$ |
| 600.1-d1 |
600.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
$1.53203$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.374384071$ |
$12.39841016$ |
2.679925586 |
\( \frac{21296}{15} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 4 a + 7\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(4a+7\right){x}$ |
| 600.1-d2 |
600.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{4} \) |
$1.53203$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.187192035$ |
$12.39841016$ |
2.679925586 |
\( \frac{470596}{225} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -16 a - 28\) , \( -30 a - 52\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-16a-28\right){x}-30a-52$ |
| 600.1-d3 |
600.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{8} \) |
$1.53203$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.374384071$ |
$12.39841016$ |
2.679925586 |
\( \frac{136835858}{1875} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -136 a - 238\) , \( 1050 a + 1820\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-136a-238\right){x}+1050a+1820$ |
| 600.1-d4 |
600.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{8} \cdot 5^{2} \) |
$1.53203$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.374384071$ |
$3.099602540$ |
2.679925586 |
\( \frac{546718898}{405} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -216 a - 378\) , \( -2430 a - 4212\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-216a-378\right){x}-2430a-4212$ |
*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.
