| 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 |
| 100.1-a1 |
100.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{12} \) |
$1.49526$ |
$(a+3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$10.34365470$ |
2.932150499 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -434 a - 1147\) , \( 11367 a + 30074\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-434a-1147\right){x}+11367a+30074$ |
| 100.1-a2 |
100.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$1.49526$ |
$(a+3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$10.34365470$ |
2.932150499 |
\( \frac{21296}{25} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 46 a + 123\) , \( -173 a - 458\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(46a+123\right){x}-173a-458$ |
| 100.1-a3 |
100.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$1.49526$ |
$(a+3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$20.68730941$ |
2.932150499 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-{x}$ |
| 100.1-a4 |
100.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$1.49526$ |
$(a+3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$20.68730941$ |
2.932150499 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -41\) , \( 116\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-41{x}+116$ |
| 100.1-b1 |
100.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{2} \) |
$1.49526$ |
$(a+3), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 3 \) |
$0.117724536$ |
$16.70104037$ |
2.229373069 |
\( \frac{8192}{5} \) |
\( \bigl[0\) , \( a\) , \( a + 1\) , \( 3\) , \( -2\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+3{x}-2$ |
| 100.1-c1 |
100.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{2} \) |
$1.49526$ |
$(a+3), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 3 \) |
$0.117724536$ |
$16.70104037$ |
2.229373069 |
\( \frac{8192}{5} \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 3\) , \( -a - 2\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+3{x}-a-2$ |
| 100.1-d1 |
100.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{12} \) |
$1.49526$ |
$(a+3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.772687765$ |
0.502509747 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -435 a - 1148\) , \( -12954 a - 34274\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-435a-1148\right){x}-12954a-34274$ |
| 100.1-d2 |
100.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$1.49526$ |
$(a+3), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$15.95418988$ |
0.502509747 |
\( \frac{21296}{25} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 45 a + 122\) , \( 336 a + 888\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(45a+122\right){x}+336a+888$ |
| 100.1-d3 |
100.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$1.49526$ |
$(a+3), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$31.90837977$ |
0.502509747 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-{x}$ |
| 100.1-d4 |
100.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$1.49526$ |
$(a+3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$3.545375530$ |
0.502509747 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-41{x}-116$ |
*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.
