| 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 |
| 28.2-a4 |
28.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( - 2^{8} \cdot 7^{12} \) |
$0.58140$ |
$(a), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.155441053$ |
0.571547619 |
\( \frac{29518306565684}{13841287201} a + \frac{41622722395132}{13841287201} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 9 a - 18\) , \( 320 a - 467\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(9a-18\right){x}+320a-467$ |
| 112.2-a4 |
112.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
112.2 |
\( 2^{4} \cdot 7 \) |
\( - 2^{8} \cdot 7^{12} \) |
$0.82222$ |
$(a), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$5.440006894$ |
0.961666441 |
\( \frac{29518306565684}{13841287201} a + \frac{41622722395132}{13841287201} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 7 a - 19\) , \( -312 a + 448\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(7a-19\right){x}-312a+448$ |
| 196.3-a4 |
196.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
196.3 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{8} \cdot 7^{18} \) |
$0.94569$ |
$(a), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.110440591$ |
1.177800108 |
\( \frac{29518306565684}{13841287201} a + \frac{41622722395132}{13841287201} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -6 a - 110\) , \( 2170 a - 2612\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-6a-110\right){x}+2170a-2612$ |
| 784.3-f4 |
784.3-f |
$8$ |
$12$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.3 |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{8} \cdot 7^{18} \) |
$1.33740$ |
$(a), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1.798389502$ |
$1.508489292$ |
1.918275556 |
\( \frac{29518306565684}{13841287201} a + \frac{41622722395132}{13841287201} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -6 a - 110\) , \( -2170 a + 2612\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a-110\right){x}-2170a+2612$ |
| 1372.1-b4 |
1372.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1372.1 |
\( 2^{2} \cdot 7^{3} \) |
\( - 2^{8} \cdot 7^{18} \) |
$1.53823$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.508489292$ |
1.599994511 |
\( \frac{29518306565684}{13841287201} a + \frac{41622722395132}{13841287201} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -321 a - 467\) , \( -3198 a - 4271\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-321a-467\right){x}-3198a-4271$ |
| 1792.2-b4 |
1792.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1792.2 |
\( 2^{8} \cdot 7 \) |
\( - 2^{20} \cdot 7^{12} \) |
$1.64444$ |
$(a), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.995543761$ |
2.116593788 |
\( \frac{29518306565684}{13841287201} a + \frac{41622722395132}{13841287201} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -60 a - 104\) , \( -468 a - 156\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-60a-104\right){x}-468a-156$ |
| 1792.2-g4 |
1792.2-g |
$8$ |
$12$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1792.2 |
\( 2^{8} \cdot 7 \) |
\( - 2^{20} \cdot 7^{12} \) |
$1.64444$ |
$(a), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$2.291195661$ |
$1.468974825$ |
2.379915478 |
\( \frac{29518306565684}{13841287201} a + \frac{41622722395132}{13841287201} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -60 a - 104\) , \( 468 a + 156\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-60a-104\right){x}+468a+156$ |
| 2268.2-b4 |
2268.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2268.2 |
\( 2^{2} \cdot 3^{4} \cdot 7 \) |
\( - 2^{8} \cdot 3^{12} \cdot 7^{12} \) |
$1.74419$ |
$(a), (2a+1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$1.813335631$ |
1.282221921 |
\( \frac{29518306565684}{13841287201} a + \frac{41622722395132}{13841287201} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 72 a - 174\) , \( -8662 a + 12416\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(72a-174\right){x}-8662a+12416$ |
*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.
