| 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 |
| 43264.2-a1 |
43264.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
43264.2 |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{18} \cdot 13^{6} \) |
$2.57751$ |
$(a+1), (-3a-2), (2a+3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.039180365$ |
$1.325034618$ |
4.153227228 |
\( -\frac{335147200}{371293} a + \frac{809589576}{371293} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 26 i + 11\) , \( -i + 51\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(26i+11\right){x}-i+51$ |
| 43264.2-a2 |
43264.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
43264.2 |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{18} \cdot 13^{6} \) |
$2.57751$ |
$(a+1), (-3a-2), (2a+3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.039180365$ |
$1.325034618$ |
4.153227228 |
\( \frac{335147200}{371293} a + \frac{809589576}{371293} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -26 i + 11\) , \( i + 51\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(-26i+11\right){x}+i+51$ |
| 43264.2-b1 |
43264.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
43264.2 |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{16} \cdot 13^{4} \) |
$2.57751$ |
$(a+1), (-3a-2), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.547256300$ |
$2.369310139$ |
2.593239803 |
\( \frac{432}{169} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 10 i\bigr] \) |
${y}^2={x}^{3}-{x}+10i$ |
| 43264.2-b2 |
43264.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
43264.2 |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{2} \) |
$2.57751$ |
$(a+1), (-3a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.094512601$ |
$4.738620278$ |
2.593239803 |
\( \frac{442368}{13} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 3 i\bigr] \) |
${y}^2={x}^{3}+4{x}+3i$ |
| 43264.2-b3 |
43264.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
43264.2 |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{20} \cdot 13^{5} \) |
$2.57751$ |
$(a+1), (-3a-2), (2a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.094512601$ |
$1.184655069$ |
2.593239803 |
\( -\frac{793539828}{28561} a + \frac{1773275112}{28561} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -60 i - 41\) , \( 234 i + 28\bigr] \) |
${y}^2={x}^{3}+\left(-60i-41\right){x}+234i+28$ |
| 43264.2-b4 |
43264.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
43264.2 |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{20} \cdot 13^{5} \) |
$2.57751$ |
$(a+1), (-3a-2), (2a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.094512601$ |
$1.184655069$ |
2.593239803 |
\( \frac{793539828}{28561} a + \frac{1773275112}{28561} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 60 i - 41\) , \( 234 i - 28\bigr] \) |
${y}^2={x}^{3}+\left(60i-41\right){x}+234i-28$ |
| 43264.2-c1 |
43264.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
43264.2 |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{18} \cdot 13^{2} \) |
$2.57751$ |
$(a+1), (-3a-2), (2a+3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.092906538$ |
$3.237581375$ |
4.812679665 |
\( -\frac{8}{13} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 0\) , \( 4 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+4i$ |
| 43264.2-d1 |
43264.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
43264.2 |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{16} \cdot 13^{4} \) |
$2.57751$ |
$(a+1), (-3a-2), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$2.271587909$ |
2.271587909 |
\( -\frac{258416}{2197} a + \frac{5960256}{2197} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 8 i + 6\) , \( -4 i + 10\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+\left(8i+6\right){x}-4i+10$ |
| 43264.2-e1 |
43264.2-e |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
43264.2 |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{22} \cdot 13^{2} \) |
$2.57751$ |
$(a+1), (-3a-2), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.236753544$ |
$2.194739176$ |
4.156898240 |
\( -\frac{235298}{13} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 16\) , \( 32 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+16{x}+32i$ |
| 43264.2-f1 |
43264.2-f |
$2$ |
$7$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
43264.2 |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{26} \cdot 13^{14} \) |
$2.57751$ |
$(a+1), (-3a-2), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$7$ |
7B.6.3 |
$1$ |
\( 2^{2} \cdot 7^{2} \) |
$0.089317794$ |
$0.140032125$ |
4.902885390 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3403\) , \( -83834 i\bigr] \) |
${y}^2={x}^{3}+3403{x}-83834i$ |
| 43264.2-f2 |
43264.2-f |
$2$ |
$7$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
43264.2 |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{38} \cdot 13^{2} \) |
$2.57751$ |
$(a+1), (-3a-2), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$7$ |
7B.6.1 |
$1$ |
\( 2^{2} \) |
$0.625224564$ |
$0.980224879$ |
4.902885390 |
\( -\frac{2146689}{1664} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 43\) , \( -166 i\bigr] \) |
${y}^2={x}^{3}+43{x}-166i$ |
| 43264.2-g1 |
43264.2-g |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
43264.2 |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{22} \cdot 13^{4} \) |
$2.57751$ |
$(a+1), (-3a-2), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.548399943$ |
3.096799887 |
\( \frac{10173824}{2197} a - \frac{428574}{2197} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -22 i - 9\) , \( 55 i - 23\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(-22i-9\right){x}+55i-23$ |
| 43264.2-h1 |
43264.2-h |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
43264.2 |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{16} \cdot 13^{2} \) |
$2.57751$ |
$(a+1), (-3a-2), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$3.196471962$ |
3.196471962 |
\( 2992 a - \frac{138816}{13} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 4 i - 6\) , \( -4 i + 6\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+\left(4i-6\right){x}-4i+6$ |
| 43264.2-i1 |
43264.2-i |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
43264.2 |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{16} \cdot 13^{4} \) |
$2.57751$ |
$(a+1), (-3a-2), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$2.271587909$ |
2.271587909 |
\( \frac{258416}{2197} a + \frac{5960256}{2197} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( -8 i + 6\) , \( 4 i + 10\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(-8i+6\right){x}+4i+10$ |
| 43264.2-j1 |
43264.2-j |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
43264.2 |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{22} \cdot 13^{4} \) |
$2.57751$ |
$(a+1), (-3a-2), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.548399943$ |
3.096799887 |
\( -\frac{10173824}{2197} a - \frac{428574}{2197} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 22 i - 9\) , \( -55 i - 23\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(22i-9\right){x}-55i-23$ |
| 43264.2-k1 |
43264.2-k |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
43264.2 |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{16} \cdot 13^{2} \) |
$2.57751$ |
$(a+1), (-3a-2), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$3.196471962$ |
3.196471962 |
\( -2992 a - \frac{138816}{13} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( -4 i - 6\) , \( 4 i + 6\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(-4i-6\right){x}+4i+6$ |
| 43264.2-l1 |
43264.2-l |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
43264.2 |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{42} \cdot 13^{2} \) |
$2.57751$ |
$(a+1), (-3a-2), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$2.977948821$ |
$0.224233532$ |
5.342047875 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 7352\) , \( -245104 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+7352{x}-245104i$ |
| 43264.2-l2 |
43264.2-l |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
43264.2 |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{30} \cdot 13^{6} \) |
$2.57751$ |
$(a+1), (-3a-2), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.992649607$ |
$0.672700598$ |
5.342047875 |
\( -\frac{10218313}{17576} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 72\) , \( -496 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+72{x}-496i$ |
| 43264.2-l3 |
43264.2-l |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
43264.2 |
\( 2^{8} \cdot 13^{2} \) |
\( 2^{26} \cdot 13^{2} \) |
$2.57751$ |
$(a+1), (-3a-2), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.330883202$ |
$2.018101794$ |
5.342047875 |
\( \frac{12167}{26} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( -8\) , \( 16 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}-8{x}+16i$ |
*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.
