| 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 |
| 4225.3-CMb1 |
4225.3-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
4225.3 |
\( 5^{2} \cdot 13^{2} \) |
\( 5^{9} \cdot 13^{6} \) |
$1.44087$ |
$(-a-2), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$5$ |
5Cs.4.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$1.140552436$ |
2.281104873 |
\( 1728 \) |
\( \bigl[i + 1\) , \( i\) , \( 1\) , \( -31 i - 21\) , \( -10 i + 15\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-31i-21\right){x}-10i+15$ |
| 4225.3-CMa1 |
4225.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
4225.3 |
\( 5^{2} \cdot 13^{2} \) |
\( 5^{6} \cdot 13^{3} \) |
$1.44087$ |
$(-a-2), (2a+3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$13$ |
13Cs.4.1 |
$1$ |
\( 2^{3} \) |
$0.046240206$ |
$3.238497722$ |
1.197990421 |
\( 1728 \) |
\( \bigl[i + 1\) , \( i\) , \( i\) , \( 4 i\) , \( -2\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+4i{x}-2$ |
| 4225.3-a1 |
4225.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
4225.3 |
\( 5^{2} \cdot 13^{2} \) |
\( 5^{15} \cdot 13^{8} \) |
$1.44087$ |
$(-a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$4.566902086$ |
$0.105483683$ |
1.926934617 |
\( -\frac{157034896049234432}{330078125} a - \frac{128574568523373376}{330078125} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( i\) , \( 30270 i + 232\) , \( 1427002 i + 1454927\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(30270i+232\right){x}+1427002i+1454927$ |
| 4225.3-a2 |
4225.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
4225.3 |
\( 5^{2} \cdot 13^{2} \) |
\( 5^{12} \cdot 13^{9} \) |
$1.44087$ |
$(-a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \) |
$0.761150347$ |
$0.316451050$ |
1.926934617 |
\( -\frac{2088753403392}{34328125} a - \frac{1627055822656}{34328125} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 1\) , \( -731 i - 739\) , \( -11543 i - 5045\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-731i-739\right){x}-11543i-5045$ |
| 4225.3-a3 |
4225.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
4225.3 |
\( 5^{2} \cdot 13^{2} \) |
\( 5^{8} \cdot 13^{7} \) |
$1.44087$ |
$(-a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.253716782$ |
$0.949353151$ |
1.926934617 |
\( \frac{732672}{325} a - \frac{3306304}{325} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 1\) , \( 44 i - 64\) , \( -225 i + 206\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(44i-64\right){x}-225i+206$ |
| 4225.3-a4 |
4225.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
4225.3 |
\( 5^{2} \cdot 13^{2} \) |
\( 5^{24} \cdot 13^{7} \) |
$1.44087$ |
$(-a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$2.283451043$ |
$0.105483683$ |
1.926934617 |
\( \frac{1110974116587520512}{49591064453125} a - \frac{489671365797093184}{49591064453125} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 1\) , \( -7536 i - 124\) , \( 182088 i - 183203\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-7536i-124\right){x}+182088i-183203$ |
| 4225.3-a5 |
4225.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
4225.3 |
\( 5^{2} \cdot 13^{2} \) |
\( 5^{7} \cdot 13^{8} \) |
$1.44087$ |
$(-a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.507433565$ |
$0.949353151$ |
1.926934617 |
\( -\frac{1183232}{845} a - \frac{851776}{845} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( i\) , \( -50 i - 8\) , \( -189 i + 40\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-50i-8\right){x}-189i+40$ |
| 4225.3-a6 |
4225.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
4225.3 |
\( 5^{2} \cdot 13^{2} \) |
\( 5^{9} \cdot 13^{12} \) |
$1.44087$ |
$(-a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \) |
$1.522300695$ |
$0.316451050$ |
1.926934617 |
\( \frac{356394317312}{603351125} a + \frac{580261889216}{603351125} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( i\) , \( 395 i + 107\) , \( 3005 i + 723\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(395i+107\right){x}+3005i+723$ |
*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.
