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 |
2475.9-b2 |
2475.9-b |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2475.9 |
\( 3^{2} \cdot 5^{2} \cdot 11 \) |
\( 3^{9} \cdot 5^{4} \cdot 11^{9} \) |
$2.09040$ |
$(a-1), (a-2), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.576638824$ |
0.695452588 |
\( -\frac{116936704}{161051} a + \frac{282554368}{161051} \) |
\( \bigl[0\) , \( -a + 1\) , \( a\) , \( 46 a + 95\) , \( 276 a - 231\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(46a+95\right){x}+276a-231$ |
2475.9-f2 |
2475.9-f |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2475.9 |
\( 3^{2} \cdot 5^{2} \cdot 11 \) |
\( 3^{9} \cdot 5^{10} \cdot 11^{9} \) |
$2.09040$ |
$(a-1), (a-2), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.257880721$ |
2.799142674 |
\( -\frac{116936704}{161051} a + \frac{282554368}{161051} \) |
\( \bigl[0\) , \( a - 1\) , \( a\) , \( -380 a + 512\) , \( -1979 a + 6075\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-380a+512\right){x}-1979a+6075$ |
22275.9-e2 |
22275.9-e |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{9} \cdot 5^{10} \cdot 11^{9} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.257880721$ |
0.622031705 |
\( -\frac{116936704}{161051} a + \frac{282554368}{161051} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -327 a - 291\) , \( -2441 a - 3169\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-327a-291\right){x}-2441a-3169$ |
22275.9-m2 |
22275.9-m |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.9 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{9} \cdot 5^{4} \cdot 11^{9} \) |
$3.62067$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$0.576638824$ |
4.172715533 |
\( -\frac{116936704}{161051} a + \frac{282554368}{161051} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -48 a + 141\) , \( 35 a + 514\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-48a+141\right){x}+35a+514$ |
27225.9-b2 |
27225.9-b |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.9 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{3} \cdot 5^{10} \cdot 11^{15} \) |
$3.80695$ |
$(a-1), (a-2), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.134673814$ |
0.324845463 |
\( -\frac{116936704}{161051} a + \frac{282554368}{161051} \) |
\( \bigl[0\) , \( -a + 1\) , \( a\) , \( -1555 a + 487\) , \( 25084 a - 16217\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1555a+487\right){x}+25084a-16217$ |
27225.9-e2 |
27225.9-e |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.9 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{3} \cdot 5^{4} \cdot 11^{15} \) |
$3.80695$ |
$(a-1), (a-2), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.920706491$ |
$0.301139804$ |
8.025355133 |
\( -\frac{116936704}{161051} a + \frac{282554368}{161051} \) |
\( \bigl[0\) , \( a - 1\) , \( a\) , \( -4 a + 520\) , \( -1715 a - 1288\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a+520\right){x}-1715a-1288$ |
*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.