| 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 |
| 5.1-a1 |
5.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{9} \) |
$0.99994$ |
$(-a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 1 \) |
$1$ |
$11.70663218$ |
1.564364528 |
\( \frac{534684321}{1953125} a + \frac{3601913643}{1953125} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -15 a - 54\) , \( -33 a - 127\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-15a-54\right){x}-33a-127$ |
| 5.1-b1 |
5.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{9} \) |
$0.99994$ |
$(-a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 3^{2} \) |
$0.053182667$ |
$11.35679518$ |
1.452795207 |
\( \frac{534684321}{1953125} a + \frac{3601913643}{1953125} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -8 a + 30\) , \( 27 a - 101\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-8a+30\right){x}+27a-101$ |
| 80.1-b1 |
80.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( - 2^{12} \cdot 5^{9} \) |
$1.99989$ |
$(-a+4), (-a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Nn |
$1$ |
\( 2 \) |
$1$ |
$5.678397592$ |
1.517615592 |
\( \frac{534684321}{1953125} a + \frac{3601913643}{1953125} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -32 a + 126\) , \( 152 a - 566\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-32a+126\right){x}+152a-566$ |
| 80.1-h1 |
80.1-h |
$1$ |
$1$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( - 2^{12} \cdot 5^{9} \) |
$1.99989$ |
$(-a+4), (-a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Nn |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.101752226$ |
$5.853316092$ |
2.865196318 |
\( \frac{534684321}{1953125} a + \frac{3601913643}{1953125} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -58 a - 210\) , \( -380 a - 1418\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-58a-210\right){x}-380a-1418$ |
| 245.1-a1 |
245.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
245.1 |
\( 5 \cdot 7^{2} \) |
\( - 5^{9} \cdot 7^{6} \) |
$2.64560$ |
$(-a+3), (-2a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Nn |
$1$ |
\( 3^{2} \) |
$1$ |
$3.543269039$ |
4.261403177 |
\( \frac{534684321}{1953125} a + \frac{3601913643}{1953125} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -1672 a + 6274\) , \( 76992 a - 288053\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-1672a+6274\right){x}+76992a-288053$ |
| 245.1-f1 |
245.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
245.1 |
\( 5 \cdot 7^{2} \) |
\( - 5^{9} \cdot 7^{6} \) |
$2.64560$ |
$(-a+3), (-2a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Nn |
$1$ |
\( 1 \) |
$2.155418876$ |
$5.360256812$ |
3.087829141 |
\( \frac{534684321}{1953125} a + \frac{3601913643}{1953125} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -2 a + 9\) , \( -4 a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-2a+9\right){x}-4a-3$ |
*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.
