| 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 |
| 17600.2-a1 |
17600.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
17600.2 |
\( 2^{6} \cdot 5^{2} \cdot 11 \) |
\( 2^{22} \cdot 5^{10} \cdot 11^{2} \) |
$3.41360$ |
$(-a-1), (a-2), (-2a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1.815641955$ |
$0.645316789$ |
2.826160478 |
\( -\frac{4277626154}{21484375} a + \frac{98357937918}{21484375} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -78 a - 19\) , \( 273 a - 146\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-78a-19\right){x}+273a-146$ |
| 17600.2-b1 |
17600.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
17600.2 |
\( 2^{6} \cdot 5^{2} \cdot 11 \) |
\( 2^{16} \cdot 5^{12} \cdot 11^{2} \) |
$3.41360$ |
$(-a-1), (a-2), (-2a+1), (2)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.755606858$ |
$0.746548340$ |
6.322791243 |
\( \frac{2122416}{171875} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 17\) , \( -318\bigr] \) |
${y}^2={x}^{3}+17{x}-318$ |
| 17600.2-b2 |
17600.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
17600.2 |
\( 2^{6} \cdot 5^{2} \cdot 11 \) |
\( 2^{8} \cdot 5^{6} \cdot 11^{4} \) |
$3.41360$ |
$(-a-1), (a-2), (-2a+1), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.755606858$ |
$1.493096680$ |
6.322791243 |
\( \frac{379275264}{15125} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -38\) , \( -87\bigr] \) |
${y}^2={x}^{3}-38{x}-87$ |
| 17600.2-b3 |
17600.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
17600.2 |
\( 2^{6} \cdot 5^{2} \cdot 11 \) |
\( 2^{20} \cdot 5^{15} \cdot 11 \) |
$3.41360$ |
$(-a-1), (a-2), (-2a+1), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$7.022427434$ |
$0.373274170$ |
6.322791243 |
\( \frac{84964992917688}{2685546875} a + \frac{116907016674204}{2685546875} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -360 a + 637\) , \( -952 a - 7234\bigr] \) |
${y}^2={x}^{3}+\left(-360a+637\right){x}-952a-7234$ |
| 17600.2-b4 |
17600.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
17600.2 |
\( 2^{6} \cdot 5^{2} \cdot 11 \) |
\( 2^{20} \cdot 5^{15} \cdot 11 \) |
$3.41360$ |
$(-a-1), (a-2), (-2a+1), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$7.022427434$ |
$0.373274170$ |
6.322791243 |
\( -\frac{84964992917688}{2685546875} a + \frac{201872009591892}{2685546875} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 360 a + 277\) , \( 952 a - 8186\bigr] \) |
${y}^2={x}^{3}+\left(360a+277\right){x}+952a-8186$ |
| 17600.2-c1 |
17600.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
17600.2 |
\( 2^{6} \cdot 5^{2} \cdot 11 \) |
\( 2^{16} \cdot 5^{5} \cdot 11 \) |
$3.41360$ |
$(-a-1), (a-2), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.579555891$ |
$1.723122481$ |
3.282576040 |
\( \frac{510160032}{6875} a - \frac{617591088}{6875} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -15 a + 37\) , \( -28 a - 66\bigr] \) |
${y}^2={x}^{3}+\left(-15a+37\right){x}-28a-66$ |
| 17600.2-c2 |
17600.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
17600.2 |
\( 2^{6} \cdot 5^{2} \cdot 11 \) |
\( 2^{16} \cdot 5^{5} \cdot 11 \) |
$3.41360$ |
$(-a-1), (a-2), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.579555891$ |
$1.723122481$ |
3.282576040 |
\( -\frac{510160032}{6875} a - \frac{107431056}{6875} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15 a + 22\) , \( 28 a - 94\bigr] \) |
${y}^2={x}^{3}+\left(15a+22\right){x}+28a-94$ |
| 17600.2-c3 |
17600.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
17600.2 |
\( 2^{6} \cdot 5^{2} \cdot 11 \) |
\( 2^{8} \cdot 5^{4} \cdot 11^{2} \) |
$3.41360$ |
$(-a-1), (a-2), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.789777945$ |
$3.446244963$ |
3.282576040 |
\( \frac{55296}{275} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( -3\bigr] \) |
${y}^2={x}^{3}+2{x}-3$ |
| 17600.2-c4 |
17600.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
17600.2 |
\( 2^{6} \cdot 5^{2} \cdot 11 \) |
\( 2^{16} \cdot 5^{2} \cdot 11^{4} \) |
$3.41360$ |
$(-a-1), (a-2), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.394888972$ |
$1.723122481$ |
3.282576040 |
\( \frac{5256144}{605} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -23\) , \( -38\bigr] \) |
${y}^2={x}^{3}-23{x}-38$ |
| 17600.2-d1 |
17600.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
17600.2 |
\( 2^{6} \cdot 5^{2} \cdot 11 \) |
\( 2^{20} \cdot 5^{24} \cdot 11^{4} \) |
$3.41360$ |
$(-a-1), (a-2), (-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \cdot 3^{2} \) |
$1$ |
$0.079165717$ |
1.718594068 |
\( -\frac{1957960715364}{29541015625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2627\) , \( 269646\bigr] \) |
${y}^2={x}^{3}-2627{x}+269646$ |
| 17600.2-d2 |
17600.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
17600.2 |
\( 2^{6} \cdot 5^{2} \cdot 11 \) |
\( 2^{20} \cdot 5^{6} \cdot 11^{16} \) |
$3.41360$ |
$(-a-1), (a-2), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.079165717$ |
1.718594068 |
\( \frac{46424454082884}{26794860125} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7547\) , \( -12986\bigr] \) |
${y}^2={x}^{3}-7547{x}-12986$ |
| 17600.2-d3 |
17600.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
17600.2 |
\( 2^{6} \cdot 5^{2} \cdot 11 \) |
\( 2^{16} \cdot 5^{12} \cdot 11^{8} \) |
$3.41360$ |
$(-a-1), (a-2), (-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$0.158331435$ |
1.718594068 |
\( \frac{55537159171536}{228765625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -5047\) , \( 137514\bigr] \) |
${y}^2={x}^{3}-5047{x}+137514$ |
| 17600.2-d4 |
17600.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
17600.2 |
\( 2^{6} \cdot 5^{2} \cdot 11 \) |
\( 2^{8} \cdot 5^{6} \cdot 11^{4} \) |
$3.41360$ |
$(-a-1), (a-2), (-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.316662871$ |
1.718594068 |
\( \frac{885956203616256}{15125} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -5042\) , \( 137801\bigr] \) |
${y}^2={x}^{3}-5042{x}+137801$ |
| 17600.2-e1 |
17600.2-e |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
17600.2 |
\( 2^{6} \cdot 5^{2} \cdot 11 \) |
\( 2^{22} \cdot 5^{10} \cdot 11^{2} \) |
$3.41360$ |
$(-a-1), (a-2), (-2a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1.815641955$ |
$0.645316789$ |
2.826160478 |
\( \frac{4277626154}{21484375} a + \frac{94080311764}{21484375} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 78 a - 97\) , \( -273 a + 127\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(78a-97\right){x}-273a+127$ |
| 17600.2-f1 |
17600.2-f |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
17600.2 |
\( 2^{6} \cdot 5^{2} \cdot 11 \) |
\( 2^{22} \cdot 5^{6} \cdot 11^{2} \) |
$3.41360$ |
$(-a-1), (a-2), (-2a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$1.035496722$ |
11.23970432 |
\( -\frac{16241202}{1375} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -67\) , \( -226\bigr] \) |
${y}^2={x}^{3}-67{x}-226$ |
*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.
