| 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 |
| 73.1-a1 |
73.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
73.1 |
\( 73 \) |
\( 73^{3} \) |
$0.45241$ |
$(-9a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$3.242334089$ |
0.311993743 |
\( \frac{60988685561}{389017} a - \frac{169775626841}{389017} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 6 a + 10\) , \( -11 a + 20\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a+10\right){x}-11a+20$ |
| 5329.1-a1 |
5329.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5329.1 |
\( 73^{2} \) |
\( 73^{9} \) |
$1.32239$ |
$(-9a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$2.486811560$ |
$0.379486501$ |
2.179408166 |
\( \frac{60988685561}{389017} a - \frac{169775626841}{389017} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 553 a + 535\) , \( 9628 a - 12840\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(553a+535\right){x}+9628a-12840$ |
| 12337.1-a1 |
12337.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12337.1 |
\( 13^{2} \cdot 73 \) |
\( 13^{6} \cdot 73^{3} \) |
$1.63118$ |
$(-4a+1), (-9a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2 \) |
$3.102706071$ |
$0.899261677$ |
3.221781549 |
\( \frac{60988685561}{389017} a - \frac{169775626841}{389017} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 141 a + 45\) , \( -389 a + 987\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(141a+45\right){x}-389a+987$ |
| 12337.5-c1 |
12337.5-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12337.5 |
\( 13^{2} \cdot 73 \) |
\( 13^{6} \cdot 73^{3} \) |
$1.63118$ |
$(4a-3), (-9a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.899261677$ |
3.115133830 |
\( \frac{60988685561}{389017} a - \frac{169775626841}{389017} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 180 a - 151\) , \( -1007 a + 266\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(180a-151\right){x}-1007a+266$ |
| 18688.1-e1 |
18688.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
18688.1 |
\( 2^{8} \cdot 73 \) |
\( 2^{24} \cdot 73^{3} \) |
$1.80963$ |
$(-9a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.810583522$ |
2.807943688 |
\( \frac{60988685561}{389017} a - \frac{169775626841}{389017} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -234 a + 77\) , \( 1113 a - 1050\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-234a+77\right){x}+1113a-1050$ |
| 32193.1-a1 |
32193.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32193.1 |
\( 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 3^{6} \cdot 7^{6} \cdot 73^{3} \) |
$2.07319$ |
$(-2a+1), (-3a+1), (-9a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1.049578337$ |
$0.707535304$ |
3.429985888 |
\( \frac{60988685561}{389017} a - \frac{169775626841}{389017} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -262 a - 16\) , \( 1736 a - 716\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-262a-16\right){x}+1736a-716$ |
| 32193.5-b1 |
32193.5-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32193.5 |
\( 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 3^{6} \cdot 7^{6} \cdot 73^{3} \) |
$2.07319$ |
$(-2a+1), (3a-2), (-9a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.707535304$ |
2.450974190 |
\( \frac{60988685561}{389017} a - \frac{169775626841}{389017} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -309 a + 204\) , \( 869 a - 2009\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-309a+204\right){x}+869a-2009$ |
| 45625.1-a1 |
45625.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
45625.1 |
\( 5^{4} \cdot 73 \) |
\( 5^{12} \cdot 73^{3} \) |
$2.26204$ |
$(-9a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2 \) |
$6.218135797$ |
$0.648466817$ |
4.656046711 |
\( \frac{60988685561}{389017} a - \frac{169775626841}{389017} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 245 a - 366\) , \( -2388 a + 2264\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(245a-366\right){x}-2388a+2264$ |
| 99937.1-a1 |
99937.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99937.1 |
\( 37^{2} \cdot 73 \) |
\( 37^{6} \cdot 73^{3} \) |
$2.75189$ |
$(-7a+4), (-9a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2 \) |
$5.493984262$ |
$0.533036440$ |
3.381533386 |
\( \frac{60988685561}{389017} a - \frac{169775626841}{389017} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -262 a - 290\) , \( -3103 a - 1420\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-262a-290\right){x}-3103a-1420$ |
| 99937.5-a1 |
99937.5-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99937.5 |
\( 37^{2} \cdot 73 \) |
\( 37^{6} \cdot 73^{3} \) |
$2.75189$ |
$(-7a+3), (-9a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2 \) |
$5.636818415$ |
$0.533036440$ |
3.469447446 |
\( \frac{60988685561}{389017} a - \frac{169775626841}{389017} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -426 a + 517\) , \( 1222 a + 3066\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-426a+517\right){x}+1222a+3066$ |
*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.
