| 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 |
| 441.1-a1 |
441.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{10} \cdot 7^{2} \) |
$2.00611$ |
$(a+3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.412632664$ |
$6.010951247$ |
5.920505431 |
\( -\frac{2762656000}{63} a + \frac{966760000}{9} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( 13 a - 39\) , \( 40 a - 103\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(13a-39\right){x}+40a-103$ |
| 441.1-a2 |
441.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{4} \) |
$2.00611$ |
$(a+3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.206316332$ |
$12.02190249$ |
5.920505431 |
\( \frac{31456000}{21} a + \frac{541624000}{147} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 353 a - 861\) , \( 5203 a - 12743\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(353a-861\right){x}+5203a-12743$ |
| 441.1-b1 |
441.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{7} \cdot 7^{2} \) |
$2.00611$ |
$(a+3), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.140022263$ |
$13.44459085$ |
3.074178280 |
\( -\frac{4211}{21} a + \frac{2917}{7} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -a + 3\) , \( a - 2\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+3\right){x}+a-2$ |
| 441.1-c1 |
441.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{10} \cdot 7^{2} \) |
$2.00611$ |
$(a+3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.268934374$ |
$14.58796887$ |
1.601642260 |
\( -\frac{2762656000}{63} a + \frac{966760000}{9} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -162 a - 399\) , \( -1477 a - 3618\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-162a-399\right){x}-1477a-3618$ |
| 441.1-c2 |
441.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{4} \) |
$2.00611$ |
$(a+3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.537868749$ |
$7.293984436$ |
1.601642260 |
\( \frac{31456000}{21} a + \frac{541624000}{147} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -2 a - 21\) , \( -27 a - 34\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-2a-21\right){x}-27a-34$ |
| 441.1-d1 |
441.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{4} \) |
$2.00611$ |
$(a+3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.767262781$ |
$8.450487594$ |
2.646977654 |
\( -\frac{1728}{49} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( a - 6\) , \( -11 a + 24\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-6\right){x}-11a+24$ |
| 441.1-d2 |
441.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{2} \) |
$2.00611$ |
$(a+3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.383631390$ |
$16.90097518$ |
2.646977654 |
\( \frac{1259712}{7} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -14 a - 36\) , \( -50 a - 123\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-14a-36\right){x}-50a-123$ |
| 441.1-e1 |
441.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{7} \cdot 7^{2} \) |
$2.00611$ |
$(a+3), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.183842358$ |
$8.340063935$ |
2.503798229 |
\( \frac{4211}{21} a + \frac{2917}{7} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 8 a - 20\) , \( 98 a - 240\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(8a-20\right){x}+98a-240$ |
| 441.1-f1 |
441.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{7} \cdot 7^{2} \) |
$2.00611$ |
$(a+3), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.140022263$ |
$13.44459085$ |
3.074178280 |
\( \frac{4211}{21} a + \frac{2917}{7} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( a + 3\) , \( -a - 2\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+3\right){x}-a-2$ |
| 441.1-g1 |
441.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{4} \) |
$2.00611$ |
$(a+3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.767262781$ |
$8.450487594$ |
2.646977654 |
\( -\frac{1728}{49} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -2 a - 6\) , \( 10 a + 24\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-2a-6\right){x}+10a+24$ |
| 441.1-g2 |
441.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{2} \) |
$2.00611$ |
$(a+3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.383631390$ |
$16.90097518$ |
2.646977654 |
\( \frac{1259712}{7} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 13 a - 36\) , \( 49 a - 123\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(13a-36\right){x}+49a-123$ |
| 441.1-h1 |
441.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{4} \) |
$2.00611$ |
$(a+3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.537868749$ |
$7.293984436$ |
1.601642260 |
\( -\frac{31456000}{21} a + \frac{541624000}{147} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( a - 21\) , \( 27 a - 34\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(a-21\right){x}+27a-34$ |
| 441.1-h2 |
441.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{10} \cdot 7^{2} \) |
$2.00611$ |
$(a+3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.268934374$ |
$14.58796887$ |
1.601642260 |
\( \frac{2762656000}{63} a + \frac{966760000}{9} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 161 a - 399\) , \( 1476 a - 3618\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(161a-399\right){x}+1476a-3618$ |
| 441.1-i1 |
441.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{4} \) |
$2.00611$ |
$(a+3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.206316332$ |
$12.02190249$ |
5.920505431 |
\( -\frac{31456000}{21} a + \frac{541624000}{147} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -354 a - 861\) , \( -5203 a - 12743\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-354a-861\right){x}-5203a-12743$ |
| 441.1-i2 |
441.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{10} \cdot 7^{2} \) |
$2.00611$ |
$(a+3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.412632664$ |
$6.010951247$ |
5.920505431 |
\( \frac{2762656000}{63} a + \frac{966760000}{9} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -14 a - 39\) , \( -41 a - 103\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-14a-39\right){x}-41a-103$ |
| 441.1-j1 |
441.1-j |
$1$ |
$1$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{7} \cdot 7^{2} \) |
$2.00611$ |
$(a+3), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.183842358$ |
$8.340063935$ |
2.503798229 |
\( -\frac{4211}{21} a + \frac{2917}{7} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -9 a - 20\) , \( -98 a - 240\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9a-20\right){x}-98a-240$ |
*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.
