| 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 |
| 18.3-a2 |
18.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{21} \cdot 3^{9} \) |
$1.16409$ |
$(2,a), (3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$4.276400154$ |
1.352316467 |
\( \frac{454513}{2048} a + \frac{260987}{256} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 17 a + 53\) , \( 29 a + 92\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(17a+53\right){x}+29a+92$ |
| 18.3-d2 |
18.3-d |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
18.3 |
\( 2 \cdot 3^{2} \) |
\( 2^{33} \cdot 3^{9} \) |
$1.16409$ |
$(2,a), (3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 7 \) |
$0.031792900$ |
$4.276400154$ |
1.805750669 |
\( \frac{454513}{2048} a + \frac{260987}{256} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 70 a + 221\) , \( 165 a + 526\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(70a+221\right){x}+165a+526$ |
| 144.2-b2 |
144.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{45} \cdot 3^{9} \) |
$1.95776$ |
$(2,a), (3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.523091040$ |
1.926574708 |
\( \frac{454513}{2048} a + \frac{260987}{256} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 274 a + 886\) , \( 118 a + 298\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(274a+886\right){x}+118a+298$ |
| 144.2-k2 |
144.2-k |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{33} \cdot 3^{9} \) |
$1.95776$ |
$(2,a), (3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.523091040$ |
0.963287354 |
\( \frac{454513}{2048} a + \frac{260987}{256} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 66 a + 223\) , \( -29 a - 81\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(66a+223\right){x}-29a-81$ |
| 162.1-b2 |
162.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( 2^{33} \cdot 3^{9} \) |
$2.01626$ |
$(2,a), (3,a+1), (3,a+2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \cdot 7 \) |
$1$ |
$3.046182080$ |
2.247670493 |
\( \frac{454513}{2048} a + \frac{260987}{256} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 1362 a + 4303\) , \( -2358 a - 7459\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(1362a+4303\right){x}-2358a-7459$ |
| 162.1-k2 |
162.1-k |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( 2^{21} \cdot 3^{9} \) |
$2.01626$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1.450494984$ |
$3.046182080$ |
2.794486951 |
\( \frac{454513}{2048} a + \frac{260987}{256} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 340 a + 1077\) , \( -465 a - 1473\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(340a+1077\right){x}-465a-1473$ |
| 450.3-i2 |
450.3-i |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{21} \cdot 3^{3} \cdot 5^{6} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 7 \) |
$0.159128273$ |
$3.258409817$ |
6.886560190 |
\( \frac{454513}{2048} a + \frac{260987}{256} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 22\) , \( -15 a + 31\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+22{x}-15a+31$ |
| 450.3-v2 |
450.3-v |
$2$ |
$3$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.3 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{33} \cdot 3^{3} \cdot 5^{6} \) |
$2.60299$ |
$(2,a), (3,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$3.258409817$ |
1.030399657 |
\( \frac{454513}{2048} a + \frac{260987}{256} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 5 a + 80\) , \( -40 a + 275\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(5a+80\right){x}-40a+275$ |
*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.
