| 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 |
| 225.2-a5 |
225.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-31}) \) |
$2$ |
$[0, 1]$ |
225.2 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{4} \) |
$1.92693$ |
$(5,a+1), (5,a+3), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$4.471403425$ |
0.803087762 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$ |
| 45.2-a5 |
45.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-155}) \) |
$2$ |
$[0, 1]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{16} \) |
$2.88143$ |
$(3,a), (3,a+2), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$4.471403425$ |
2.873214126 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( 523\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-126{x}+523$ |
| 75.1-c5 |
75.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-93}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{4} \) |
$5.07195$ |
$(3,a), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{3} \) |
$0.650156421$ |
$4.471403425$ |
4.823254967 |
\( \frac{13997521}{225} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 135\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^3+135{x}$ |
| 75.2-d5 |
75.2-d |
$8$ |
$16$ |
\(\Q(\sqrt{-651}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{4} \cdot 13^{12} \) |
$6.70956$ |
$(3,a+1), (5,a+1), (5,a+3)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{4} \) |
$1$ |
$8.942806850$ |
5.607939751 |
\( \frac{13997521}{225} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -8 a + 1215\) , \( -414 a - 7711\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+\left(a+1\right){x}^2+\left(-8a+1215\right){x}-414a-7711$ |
| 75.2-b5 |
75.2-b |
$8$ |
$16$ |
\(\Q(\sqrt{-186}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{4} \cdot 31^{12} \) |
$7.17283$ |
$(3,a), (5,a+2), (5,a+3)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{4} \) |
$1$ |
$8.942806850$ |
5.245747299 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -4825\) , \( -127600\bigr] \) |
${y}^2+{x}{y}={x}^3-4825{x}-127600$ |
| 15.1-d5 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-465}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \cdot 31^{12} \) |
$7.58434$ |
$(3,a), (5,a)$ |
$1 \le r \le 3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{4} \) |
$1.200487677$ |
$8.942806850$ |
7.965720493 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -4825\) , \( -127600\bigr] \) |
${y}^2+{x}{y}={x}^3-4825{x}-127600$ |
| 75.1-a5 |
75.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{4} \) |
$2.53598$ |
$(a+4), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$10.19195692$ |
2.113713401 |
\( \frac{13997521}{225} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 439 a - 2316\) , \( 11311 a - 60156\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(439a-2316\right){x}+11311a-60156$ |
*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.
