| 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 |
| 324.1-a1 |
324.1-a |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{12} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$4.549688489$ |
1.261856548 |
\( -\frac{1250637664527933}{32} a - \frac{1629300280935823}{32} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -257 a + 13\) , \( 1140 a + 2856\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-257a+13\right){x}+1140a+2856$ |
| 324.1-a2 |
324.1-a |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{2} \cdot 3^{12} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$4.549688489$ |
1.261856548 |
\( -\frac{461373}{2} a - \frac{601423}{2} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -14 a - 18\) , \( -34 a - 44\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-14a-18\right){x}-34a-44$ |
| 324.1-a3 |
324.1-a |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{30} \cdot 3^{12} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3Cs, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$4.549688489$ |
1.261856548 |
\( -\frac{1680914269}{32768} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 669 a - 1560\) , \( -13229 a + 30488\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(669a-1560\right){x}-13229a+30488$ |
| 324.1-a4 |
324.1-a |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{2} \cdot 3^{12} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$4.549688489$ |
1.261856548 |
\( \frac{461373}{2} a - 531398 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 13 a - 32\) , \( 33 a - 78\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(13a-32\right){x}+33a-78$ |
| 324.1-a5 |
324.1-a |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{12} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3Cs, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$4.549688489$ |
1.261856548 |
\( \frac{1331}{8} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -6 a + 15\) , \( 37 a - 85\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-6a+15\right){x}+37a-85$ |
| 324.1-a6 |
324.1-a |
$6$ |
$45$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{12} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$4.549688489$ |
1.261856548 |
\( \frac{1250637664527933}{32} a - \frac{719984486365939}{8} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 256 a - 243\) , \( -1141 a + 3997\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(256a-243\right){x}-1141a+3997$ |
| 324.1-b1 |
324.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{16} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.168787711$ |
$5.155137791$ |
1.930631613 |
\( -\frac{4653908}{3} a - \frac{387700105}{192} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -155 a + 346\) , \( 49 a - 102\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-155a+346\right){x}+49a-102$ |
| 324.1-b2 |
324.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{12} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.056262570$ |
$15.46541337$ |
1.930631613 |
\( \frac{344113}{108} a - \frac{198007}{27} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( a + 1\) , \( 19 a + 25\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(a+1\right){x}+19a+25$ |
| 324.1-b3 |
324.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{2} \cdot 3^{15} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.112525140$ |
$15.46541337$ |
1.930631613 |
\( -\frac{60298633043}{1458} a + \frac{138901252937}{1458} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -59 a - 89\) , \( 307 a + 421\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-59a-89\right){x}+307a+421$ |
| 324.1-b4 |
324.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{17} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.337575422$ |
$5.155137791$ |
1.930631613 |
\( \frac{312258622128767}{36} a + \frac{813605851286657}{72} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 565 a - 1454\) , \( 121 a + 474\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(565a-1454\right){x}+121a+474$ |
| 324.1-c1 |
324.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{18} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$2.980924615$ |
1.653519468 |
\( -\frac{344113}{108} a - \frac{149305}{36} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3 a + 3\) , \( -41 a + 92\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-3a+3\right){x}-41a+92$ |
| 324.1-c2 |
324.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{10} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$8.942773845$ |
1.653519468 |
\( \frac{4653908}{3} a - \frac{228516739}{64} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 29 a + 33\) , \( -10 a - 11\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(29a+33\right){x}-10a-11$ |
| 324.1-c3 |
324.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{11} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$8.942773845$ |
1.653519468 |
\( -\frac{312258622128767}{36} a + \frac{479374365181397}{24} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -91 a - 207\) , \( -34 a + 229\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-91a-207\right){x}-34a+229$ |
| 324.1-c4 |
324.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{2} \cdot 3^{21} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$2.980924615$ |
1.653519468 |
\( \frac{60298633043}{1458} a + \frac{13100436649}{243} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 87 a - 267\) , \( -851 a + 1766\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(87a-267\right){x}-851a+1766$ |
| 324.1-d1 |
324.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{12} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.056262570$ |
$15.46541337$ |
1.930631613 |
\( -\frac{344113}{108} a - \frac{149305}{36} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -2 a + 3\) , \( -19 a + 44\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-2a+3\right){x}-19a+44$ |
| 324.1-d2 |
324.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{16} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.168787711$ |
$5.155137791$ |
1.930631613 |
\( \frac{4653908}{3} a - \frac{228516739}{64} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 154 a + 192\) , \( -50 a - 52\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(154a+192\right){x}-50a-52$ |
| 324.1-d3 |
324.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{17} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.337575422$ |
$5.155137791$ |
1.930631613 |
\( -\frac{312258622128767}{36} a + \frac{479374365181397}{24} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -566 a - 888\) , \( -122 a + 596\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-566a-888\right){x}-122a+596$ |
| 324.1-d4 |
324.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{2} \cdot 3^{15} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.112525140$ |
$15.46541337$ |
1.930631613 |
\( \frac{60298633043}{1458} a + \frac{13100436649}{243} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( 58 a - 147\) , \( -307 a + 728\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(58a-147\right){x}-307a+728$ |
| 324.1-e1 |
324.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{10} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$8.942773845$ |
1.653519468 |
\( -\frac{4653908}{3} a - \frac{387700105}{192} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -31 a + 63\) , \( 9 a - 20\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-31a+63\right){x}+9a-20$ |
| 324.1-e2 |
324.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{18} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$2.980924615$ |
1.653519468 |
\( \frac{344113}{108} a - \frac{198007}{27} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 3 a\) , \( 41 a + 51\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+3a{x}+41a+51$ |
| 324.1-e3 |
324.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{2} \cdot 3^{21} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$2.980924615$ |
1.653519468 |
\( -\frac{60298633043}{1458} a + \frac{138901252937}{1458} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -87 a - 180\) , \( 851 a + 915\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-87a-180\right){x}+851a+915$ |
| 324.1-e4 |
324.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{11} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$8.942773845$ |
1.653519468 |
\( \frac{312258622128767}{36} a + \frac{813605851286657}{72} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 89 a - 297\) , \( 33 a + 196\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(89a-297\right){x}+33a+196$ |
| 324.1-f1 |
324.1-f |
$8$ |
$20$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{40} \cdot 3^{14} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$2.085842366$ |
1.157017170 |
\( -\frac{4395631034341}{3145728} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 9214 a - 21500\) , \( -657647 a + 1516071\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(9214a-21500\right){x}-657647a+1516071$ |
| 324.1-f2 |
324.1-f |
$8$ |
$20$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{22} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$2.085842366$ |
1.157017170 |
\( \frac{5735339}{3888} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -101 a + 235\) , \( 343 a - 789\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-101a+235\right){x}+343a-789$ |
| 324.1-f3 |
324.1-f |
$8$ |
$20$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{32} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B.4.1 |
$1$ |
\( 2^{5} \) |
$1$ |
$2.085842366$ |
1.157017170 |
\( \frac{476379541}{236196} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 439 a - 1025\) , \( 2431 a - 5613\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(439a-1025\right){x}+2431a-5613$ |
| 324.1-f4 |
324.1-f |
$8$ |
$20$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{2} \cdot 3^{37} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{4} \) |
$1$ |
$1.042921183$ |
1.157017170 |
\( -\frac{1025795879759761}{3486784401} a + \frac{5304841542920801}{6973568802} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -3770 a - 5085\) , \( 172133 a + 223258\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-3770a-5085\right){x}+172133a+223258$ |
| 324.1-f5 |
324.1-f |
$8$ |
$20$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{2} \cdot 3^{37} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{4} \) |
$1$ |
$1.042921183$ |
1.157017170 |
\( \frac{1025795879759761}{3486784401} a + \frac{1084416594467093}{2324522934} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 3769 a - 8855\) , \( -172133 a + 395391\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(3769a-8855\right){x}-172133a+395391$ |
| 324.1-f6 |
324.1-f |
$8$ |
$20$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{17} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$1.042921183$ |
1.157017170 |
\( -\frac{1373276865151726904870180471}{1296} a + \frac{2108232339288241560240379517}{864} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -128735 a - 239805\) , \( 39888431 a + 59374840\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-128735a-239805\right){x}+39888431a+59374840$ |
| 324.1-f7 |
324.1-f |
$8$ |
$20$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{16} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2Cs, 5B.4.2 |
$1$ |
\( 2^{5} \) |
$1$ |
$2.085842366$ |
1.157017170 |
\( \frac{18013780041269221}{9216} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 147454 a - 344060\) , \( -41926895 a + 96662055\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(147454a-344060\right){x}-41926895a+96662055$ |
| 324.1-f8 |
324.1-f |
$8$ |
$20$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{17} \) |
$1.36693$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$1.042921183$ |
1.157017170 |
\( \frac{1373276865151726904870180471}{1296} a + \frac{3578143287561270870980777609}{2592} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 128734 a - 368540\) , \( -39888431 a + 99263271\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(128734a-368540\right){x}-39888431a+99263271$ |
*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.
