| 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 |
$4$ |
$6$ |
\(\Q(\sqrt{19}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{12} \) |
$2.46346$ |
$(-3a+13), (2a+9), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.898413785$ |
$10.34365470$ |
6.395800016 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -120440 a - 524985\) , \( 71628793 a + 312222670\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-120440a-524985\right){x}+71628793a+312222670$ |
| 100.1-a2 |
100.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{19}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$2.46346$ |
$(-3a+13), (2a+9), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$2.695241356$ |
$10.34365470$ |
6.395800016 |
\( \frac{21296}{25} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 12160 a + 53005\) , \( -1497775 a - 6528650\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(12160a+53005\right){x}-1497775a-6528650$ |
| 100.1-a3 |
100.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{19}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$2.46346$ |
$(-3a+13), (2a+9), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$5.390482712$ |
$20.68730941$ |
6.395800016 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-{x}$ |
| 100.1-a4 |
100.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{19}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$2.46346$ |
$(-3a+13), (2a+9), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1.796827570$ |
$20.68730941$ |
6.395800016 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -41\) , \( 116\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-41{x}+116$ |
| 100.1-b1 |
100.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{19}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{12} \) |
$2.46346$ |
$(-3a+13), (2a+9), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$2.304605724$ |
$1.772687765$ |
0.937242735 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -120441 a - 524988\) , \( -72515124 a - 316086098\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-120441a-524988\right){x}-72515124a-316086098$ |
| 100.1-b2 |
100.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{19}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$2.46346$ |
$(-3a+13), (2a+9), (-2a+9)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.768201908$ |
$15.95418988$ |
0.937242735 |
\( \frac{21296}{25} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 12159 a + 53002\) , \( 1587234 a + 6918592\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(12159a+53002\right){x}+1587234a+6918592$ |
| 100.1-b3 |
100.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{19}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$2.46346$ |
$(-3a+13), (2a+9), (-2a+9)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1.536403816$ |
$31.90837977$ |
0.937242735 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-{x}$ |
| 100.1-b4 |
100.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{19}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$2.46346$ |
$(-3a+13), (2a+9), (-2a+9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$4.609211449$ |
$3.545375530$ |
0.937242735 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-41{x}-116$ |
*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.
