| 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 |
$4$ |
$6$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{2} \) |
$2.72508$ |
$(2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$9.768635228$ |
2.025920571 |
\( -\frac{1860867}{320} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 8 a - 33\) , \( -19 a + 109\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(8a-33\right){x}-19a+109$ |
| 100.1-a2 |
100.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{6} \) |
$2.72508$ |
$(2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$9.768635228$ |
2.025920571 |
\( \frac{804357}{500} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 5 a + 34\) , \( 11 a + 56\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a+34\right){x}+11a+56$ |
| 100.1-a3 |
100.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 5^{12} \) |
$2.72508$ |
$(2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$9.768635228$ |
2.025920571 |
\( \frac{57960603}{31250} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -25 a - 96\) , \( 7 a + 38\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-25a-96\right){x}+7a+38$ |
| 100.1-a4 |
100.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 5^{4} \) |
$2.72508$ |
$(2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$9.768635228$ |
2.025920571 |
\( \frac{8527173507}{200} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 128 a - 673\) , \( -1571 a + 8365\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(128a-673\right){x}-1571a+8365$ |
| 100.1-b1 |
100.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{2} \) |
$2.72508$ |
$(2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$9.768635228$ |
2.025920571 |
\( -\frac{1860867}{320} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -9 a - 25\) , \( 19 a + 90\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9a-25\right){x}+19a+90$ |
| 100.1-b2 |
100.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{6} \) |
$2.72508$ |
$(2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$9.768635228$ |
2.025920571 |
\( \frac{804357}{500} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -5 a + 39\) , \( -11 a + 67\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-5a+39\right){x}-11a+67$ |
| 100.1-b3 |
100.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 5^{12} \) |
$2.72508$ |
$(2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$9.768635228$ |
2.025920571 |
\( \frac{57960603}{31250} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 25 a - 121\) , \( -7 a + 45\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(25a-121\right){x}-7a+45$ |
| 100.1-b4 |
100.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 5^{4} \) |
$2.72508$ |
$(2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$9.768635228$ |
2.025920571 |
\( \frac{8527173507}{200} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -129 a - 545\) , \( 1571 a + 6794\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-129a-545\right){x}+1571a+6794$ |
*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.
