| 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 |
| 2304.1-a1 |
2304.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{8} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.690728597$ |
1.658422999 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 16 a + 24\) , \( 40 a + 56\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(16a+24\right){x}+40a+56$ |
| 2304.1-a2 |
2304.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$18.76291438$ |
1.658422999 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4 a - 6\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a-6\right){x}$ |
| 2304.1-a3 |
2304.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$18.76291438$ |
1.658422999 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -8 a - 12\) , \( -10 a - 14\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-8a-12\right){x}-10a-14$ |
| 2304.1-a4 |
2304.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$9.381457194$ |
1.658422999 |
\( \frac{7301384}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 64 a - 96\) , \( 300 a - 420\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(64a-96\right){x}+300a-420$ |
| 2304.1-b1 |
2304.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{4} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.319732820$ |
$11.50728806$ |
2.601628048 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 2\) , \( 2\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+2{x}+2$ |
| 2304.1-b2 |
2304.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.159866410$ |
$23.01457612$ |
2.601628048 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-3{x}+3$ |
| 2304.1-c1 |
2304.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{23} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$4.283776414$ |
$0.908836754$ |
2.752945917 |
\( -\frac{123062343233293457}{3} a + 58012144939294440 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -408 a - 1632\) , \( 18804 a + 13548\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-408a-1632\right){x}+18804a+13548$ |
| 2304.1-c2 |
2304.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{16} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.141888207$ |
$1.817673508$ |
2.752945917 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 32 a + 48\) , \( 900 a + 1260\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(32a+48\right){x}+900a+1260$ |
| 2304.1-c3 |
2304.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.070944103$ |
$14.54138807$ |
2.752945917 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a + 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+3\right){x}$ |
| 2304.1-c4 |
2304.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.535472051$ |
$14.54138807$ |
2.752945917 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 8 a - 12\) , \( -20 a + 28\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(8a-12\right){x}-20a+28$ |
| 2304.1-c5 |
2304.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.070944103$ |
$7.270694035$ |
2.752945917 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -48 a - 72\) , \( 180 a + 252\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-48a-72\right){x}+180a+252$ |
| 2304.1-c6 |
2304.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.070944103$ |
$7.270694035$ |
2.752945917 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -128 a - 192\) , \( -1100 a - 1540\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-128a-192\right){x}-1100a-1540$ |
| 2304.1-c7 |
2304.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{4} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.141888207$ |
$3.635347017$ |
2.752945917 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 768 a - 1152\) , \( 13860 a - 19404\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(768a-1152\right){x}+13860a-19404$ |
| 2304.1-c8 |
2304.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{23} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$4.283776414$ |
$1.817673508$ |
2.752945917 |
\( \frac{123062343233293457}{3} a + 58012144939294440 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 408 a - 1632\) , \( 18804 a - 13548\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(408a-1632\right){x}+18804a-13548$ |
| 2304.1-d1 |
2304.1-d |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{20} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$1.945878584$ |
1.719929928 |
\( -\frac{873722816}{59049} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -79\) , \( 231 a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}-79{x}+231a$ |
| 2304.1-d2 |
2304.1-d |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$9.729392922$ |
1.719929928 |
\( \frac{64}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( -a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+{x}-a$ |
| 2304.1-d3 |
2304.1-d |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$19.45878584$ |
1.719929928 |
\( \frac{85184}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -3\) , \( -3 a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}-3{x}-3a$ |
| 2304.1-d4 |
2304.1-d |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{10} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 5 \) |
$1$ |
$3.891757169$ |
1.719929928 |
\( \frac{58591911104}{243} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -323\) , \( 1477 a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}-323{x}+1477a$ |
| 2304.1-e1 |
2304.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{19} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$2.808387064$ |
1.985829537 |
\( -\frac{5779316804}{3} a + 2724397792 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 72 a + 96\) , \( -24 a - 48\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(72a+96\right){x}-24a-48$ |
| 2304.1-e2 |
2304.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{4} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$11.23354825$ |
1.985829537 |
\( -\frac{77248}{3} a + \frac{343328}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6 a - 8\) , \( 8 a - 12\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-8\right){x}+8a-12$ |
| 2304.1-e3 |
2304.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{19} \cdot 3^{8} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.616774128$ |
1.985829537 |
\( \frac{2321252}{27} a + \frac{9848176}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4 a - 8\) , \( 28 a - 28\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a-8\right){x}+28a-28$ |
| 2304.1-e4 |
2304.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$11.23354825$ |
1.985829537 |
\( \frac{359168}{3} a + 171392 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a - 5\) , \( -a + 1\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-5\right){x}-a+1$ |
| 2304.1-f1 |
2304.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{12} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.135844784$ |
$8.807833659$ |
2.538156107 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -6\) , \( 18\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-6{x}+18$ |
| 2304.1-f2 |
2304.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{6} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.067922392$ |
$17.61566731$ |
2.538156107 |
\( \frac{19056256}{27} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -35\) , \( 69\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-35{x}+69$ |
| 2304.1-g1 |
2304.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{19} \cdot 3^{8} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.698622027$ |
$5.078084327$ |
2.508575554 |
\( -\frac{2321252}{27} a + \frac{9848176}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 4 a - 8\) , \( 28 a + 28\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(4a-8\right){x}+28a+28$ |
| 2304.1-g2 |
2304.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.174655506$ |
$20.31233730$ |
2.508575554 |
\( -\frac{359168}{3} a + 171392 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a - 5\) , \( -a - 1\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-5\right){x}-a-1$ |
| 2304.1-g3 |
2304.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{4} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.349311013$ |
$20.31233730$ |
2.508575554 |
\( \frac{77248}{3} a + \frac{343328}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -6 a - 8\) , \( 8 a + 12\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a-8\right){x}+8a+12$ |
| 2304.1-g4 |
2304.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{19} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.698622027$ |
$10.15616865$ |
2.508575554 |
\( \frac{5779316804}{3} a + 2724397792 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -72 a + 96\) , \( -24 a + 48\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-72a+96\right){x}-24a+48$ |
| 2304.1-h1 |
2304.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.595685243$ |
1.624820099 |
\( \frac{3328}{3} a + \frac{128}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 4 a - 4\) , \( 8 a - 12\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(4a-4\right){x}+8a-12$ |
| 2304.1-h2 |
2304.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$9.191370486$ |
1.624820099 |
\( -\frac{5197888}{3} a + 2452192 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -12 a - 18\) , \( -12 a - 18\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-12a-18\right){x}-12a-18$ |
| 2304.1-i1 |
2304.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.595685243$ |
1.624820099 |
\( -\frac{3328}{3} a + \frac{128}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -4 a - 4\) , \( -8 a - 12\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-4a-4\right){x}-8a-12$ |
| 2304.1-i2 |
2304.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$9.191370486$ |
1.624820099 |
\( \frac{5197888}{3} a + 2452192 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 12 a - 18\) , \( 12 a - 18\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(12a-18\right){x}+12a-18$ |
| 2304.1-j1 |
2304.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.337851468$ |
0.590054352 |
\( -\frac{8000}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a - 4\) , \( -18 a - 26\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-4\right){x}-18a-26$ |
| 2304.1-j2 |
2304.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.337851468$ |
0.590054352 |
\( -\frac{98115010000}{3} a + 46251861000 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -24 a - 64\) , \( 36 a - 44\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-24a-64\right){x}+36a-44$ |
| 2304.1-j3 |
2304.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$6.675702937$ |
0.590054352 |
\( \frac{2744000}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -24 a - 34\) , \( -72 a - 104\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-24a-34\right){x}-72a-104$ |
| 2304.1-j4 |
2304.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.337851468$ |
0.590054352 |
\( \frac{98115010000}{3} a + 46251861000 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 24 a - 64\) , \( -36 a - 44\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(24a-64\right){x}-36a-44$ |
| 2304.1-k1 |
2304.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.163799660$ |
$12.18018650$ |
2.821512200 |
\( -\frac{3328}{3} a + \frac{128}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -4 a - 4\) , \( 8 a + 12\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-4a-4\right){x}+8a+12$ |
| 2304.1-k2 |
2304.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.327599320$ |
$24.36037300$ |
2.821512200 |
\( \frac{5197888}{3} a + 2452192 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 12 a - 18\) , \( -12 a + 18\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(12a-18\right){x}-12a+18$ |
| 2304.1-l1 |
2304.1-l |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$13.47682996$ |
2.382389464 |
\( -\frac{8000}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a - 4\) , \( 18 a + 26\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a-4\right){x}+18a+26$ |
| 2304.1-l2 |
2304.1-l |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$13.47682996$ |
2.382389464 |
\( -\frac{98115010000}{3} a + 46251861000 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -24 a - 64\) , \( -36 a + 44\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-24a-64\right){x}-36a+44$ |
| 2304.1-l3 |
2304.1-l |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$26.95365992$ |
2.382389464 |
\( \frac{2744000}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -24 a - 34\) , \( 72 a + 104\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-24a-34\right){x}+72a+104$ |
| 2304.1-l4 |
2304.1-l |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$13.47682996$ |
2.382389464 |
\( \frac{98115010000}{3} a + 46251861000 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 24 a - 64\) , \( 36 a + 44\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(24a-64\right){x}+36a+44$ |
| 2304.1-m1 |
2304.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{19} \cdot 3^{8} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.616774128$ |
1.985829537 |
\( -\frac{2321252}{27} a + \frac{9848176}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 4 a - 8\) , \( -28 a - 28\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(4a-8\right){x}-28a-28$ |
| 2304.1-m2 |
2304.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$11.23354825$ |
1.985829537 |
\( -\frac{359168}{3} a + 171392 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a - 5\) , \( a + 1\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a-5\right){x}+a+1$ |
| 2304.1-m3 |
2304.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{4} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$11.23354825$ |
1.985829537 |
\( \frac{77248}{3} a + \frac{343328}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -6 a - 8\) , \( -8 a - 12\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a-8\right){x}-8a-12$ |
| 2304.1-m4 |
2304.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{19} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$2.808387064$ |
1.985829537 |
\( \frac{5779316804}{3} a + 2724397792 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -72 a + 96\) , \( 24 a - 48\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-72a+96\right){x}+24a-48$ |
| 2304.1-n1 |
2304.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{4} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.405092923$ |
2.264542320 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 2\) , \( -2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+2{x}-2$ |
| 2304.1-n2 |
2304.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$12.81018584$ |
2.264542320 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -3\) , \( -3\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-3{x}-3$ |
| 2304.1-o1 |
2304.1-o |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{19} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.698622027$ |
$10.15616865$ |
2.508575554 |
\( -\frac{5779316804}{3} a + 2724397792 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 72 a + 96\) , \( 24 a + 48\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(72a+96\right){x}+24a+48$ |
| 2304.1-o2 |
2304.1-o |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{4} \) |
$1.75107$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.349311013$ |
$20.31233730$ |
2.508575554 |
\( -\frac{77248}{3} a + \frac{343328}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6 a - 8\) , \( -8 a + 12\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a-8\right){x}-8a+12$ |
*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.
