| 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 |
| 363.1-a1 |
363.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( - 3^{3} \cdot 11^{10} \) |
$1.35116$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.468126413$ |
1.289836993 |
\( -\frac{430559510626058357323}{1929229929} a + \frac{82861216372529232360}{214358881} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 645 a - 1226\) , \( -12039 a + 21843\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(645a-1226\right){x}-12039a+21843$ |
| 363.1-a2 |
363.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( 3^{24} \cdot 11^{2} \) |
$1.35116$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$2.234063206$ |
1.289836993 |
\( \frac{9090072503}{5845851} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 44\) , \( 55\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+44{x}+55$ |
| 363.1-a3 |
363.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( 3^{12} \cdot 11^{4} \) |
$1.35116$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$8.936252827$ |
1.289836993 |
\( \frac{169112377}{88209} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -11\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-11{x}$ |
| 363.1-a4 |
363.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( 3^{6} \cdot 11^{2} \) |
$1.35116$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.936252827$ |
1.289836993 |
\( \frac{30664297}{297} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 365 a - 633\) , \( 4716 a - 8169\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(365a-633\right){x}+4716a-8169$ |
| 363.1-a5 |
363.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( 3^{6} \cdot 11^{8} \) |
$1.35116$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$8.936252827$ |
1.289836993 |
\( \frac{347873904937}{395307} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -146\) , \( 621\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-146{x}+621$ |
| 363.1-a6 |
363.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( - 3^{3} \cdot 11^{10} \) |
$1.35116$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.468126413$ |
1.289836993 |
\( \frac{430559510626058357323}{1929229929} a + \frac{82861216372529232360}{214358881} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -645 a - 1226\) , \( 12039 a + 21843\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-645a-1226\right){x}+12039a+21843$ |
| 363.1-b1 |
363.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( - 3^{3} \cdot 11^{10} \) |
$1.35116$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.932777014$ |
$0.470813266$ |
1.576126501 |
\( -\frac{430559510626058357323}{1929229929} a + \frac{82861216372529232360}{214358881} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 645 a - 1227\) , \( 12684 a - 23070\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(645a-1227\right){x}+12684a-23070$ |
| 363.1-b2 |
363.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( 3^{24} \cdot 11^{2} \) |
$1.35116$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.966388507$ |
$1.883253066$ |
1.576126501 |
\( \frac{9090072503}{5845851} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 43\) , \( -12\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+43{x}-12$ |
| 363.1-b3 |
363.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( 3^{12} \cdot 11^{4} \) |
$1.35116$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.483194253$ |
$7.533012266$ |
1.576126501 |
\( \frac{169112377}{88209} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -12\) , \( -12\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-12{x}-12$ |
| 363.1-b4 |
363.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( 3^{6} \cdot 11^{2} \) |
$1.35116$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.241597126$ |
$30.13204906$ |
1.576126501 |
\( \frac{30664297}{297} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 365 a - 632\) , \( -4716 a + 8168\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(365a-632\right){x}-4716a+8168$ |
| 363.1-b5 |
363.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( 3^{6} \cdot 11^{8} \) |
$1.35116$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.966388507$ |
$1.883253066$ |
1.576126501 |
\( \frac{347873904937}{395307} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -147\) , \( -768\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-147{x}-768$ |
| 363.1-b6 |
363.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( - 3^{3} \cdot 11^{10} \) |
$1.35116$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.932777014$ |
$0.470813266$ |
1.576126501 |
\( \frac{430559510626058357323}{1929229929} a + \frac{82861216372529232360}{214358881} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -645 a - 1227\) , \( -12684 a - 23070\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-645a-1227\right){x}-12684a-23070$ |
*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.
