| 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 |
| 14.1-a2 |
14.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$1.29349$ |
$(-a+4), (-2a+7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1.403390075$ |
$35.33144352$ |
1.472425245 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}$ |
| 14.1-b2 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$1.29349$ |
$(-a+4), (-2a+7)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.027708105$ |
0.939116998 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 62 a - 229\) , \( 960 a - 3591\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(62a-229\right){x}+960a-3591$ |
| 98.1-a2 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{8} \) |
$2.10397$ |
$(-a+4), (-2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1.634316204$ |
$5.955778371$ |
2.601420732 |
\( -\frac{15625}{28} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 13 a - 46\) , \( -88 a + 330\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(13a-46\right){x}-88a+330$ |
| 98.1-b2 |
98.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{8} \) |
$2.10397$ |
$(-a+4), (-2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1.634316204$ |
$5.955778371$ |
2.601420732 |
\( -\frac{15625}{28} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -13 a - 46\) , \( 88 a + 330\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-13a-46\right){x}+88a+330$ |
| 112.1-a2 |
112.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
112.1 |
\( 2^{4} \cdot 7 \) |
\( 2^{16} \cdot 7^{2} \) |
$2.17539$ |
$(-a+4), (-2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.389689685$ |
$17.66572176$ |
3.679732717 |
\( -\frac{15625}{28} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -5\) , \( -2\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-5{x}-2$ |
| 112.1-f2 |
112.1-f |
$6$ |
$18$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
112.1 |
\( 2^{4} \cdot 7 \) |
\( 2^{16} \cdot 7^{2} \) |
$2.17539$ |
$(-a+4), (-2a+7)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.513854052$ |
0.939116998 |
\( -\frac{15625}{28} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 247 a - 924\) , \( 9108 a - 34079\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(247a-924\right){x}+9108a-34079$ |
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*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.
