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
55.2-a1
55.2-a
$2$
$2$
4.4.5125.1
$4$
$[4, 0]$
55.2
\( 5 \cdot 11 \)
\( 5^{2} \cdot 11^{2} \)
$10.55676$
$(-a^3+a^2+4a+1), (a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$134.2078364$
1.874696378
\( \frac{287491768525988172527}{605} a^{3} + \frac{203073306864646217091}{605} a^{2} - \frac{235072139333994482191}{121} a - \frac{106228121417968802248}{55} \)
\( \bigl[a^{3} - 4 a - 4\) , \( -a - 1\) , \( a\) , \( 64 a^{3} - a^{2} - 383 a - 342\) , \( 655 a^{3} + 104 a^{2} - 3702 a - 3363\bigr] \)
${y}^2+\left(a^{3}-4a-4\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(64a^{3}-a^{2}-383a-342\right){x}+655a^{3}+104a^{2}-3702a-3363$
55.2-f1
55.2-f
$2$
$2$
4.4.5125.1
$4$
$[4, 0]$
55.2
\( 5 \cdot 11 \)
\( 5^{2} \cdot 11^{2} \)
$10.55676$
$(-a^3+a^2+4a+1), (a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$70.55402936$
0.985541431
\( \frac{287491768525988172527}{605} a^{3} + \frac{203073306864646217091}{605} a^{2} - \frac{235072139333994482191}{121} a - \frac{106228121417968802248}{55} \)
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a + 1\) , \( 219 a^{3} - 805 a^{2} + 81 a + 1343\) , \( 3458 a^{3} - 12790 a^{2} + 996 a + 22447\bigr] \)
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(219a^{3}-805a^{2}+81a+1343\right){x}+3458a^{3}-12790a^{2}+996a+22447$
275.2-f2
275.2-f
$2$
$2$
4.4.5125.1
$4$
$[4, 0]$
275.2
\( 5^{2} \cdot 11 \)
\( 5^{8} \cdot 11^{2} \)
$12.90928$
$(-a^3+a^2+4a+1), (a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$2.630873448$
$13.28471173$
3.905666397
\( \frac{287491768525988172527}{605} a^{3} + \frac{203073306864646217091}{605} a^{2} - \frac{235072139333994482191}{121} a - \frac{106228121417968802248}{55} \)
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{2} + a + 3\) , \( a^{2} - 4\) , \( 190 a^{3} - 751 a^{2} + 279 a + 970\) , \( -5407 a^{3} + 19582 a^{2} + 444 a - 37455\bigr] \)
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(190a^{3}-751a^{2}+279a+970\right){x}-5407a^{3}+19582a^{2}+444a-37455$
275.2-q2
275.2-q
$2$
$2$
4.4.5125.1
$4$
$[4, 0]$
275.2
\( 5^{2} \cdot 11 \)
\( 5^{8} \cdot 11^{2} \)
$12.90928$
$(-a^3+a^2+4a+1), (a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$0.216192880$
$142.5533925$
3.443990916
\( \frac{287491768525988172527}{605} a^{3} + \frac{203073306864646217091}{605} a^{2} - \frac{235072139333994482191}{121} a - \frac{106228121417968802248}{55} \)
\( \bigl[a + 1\) , \( a^{3} - 4 a - 4\) , \( a + 1\) , \( -107 a^{3} - 78 a^{2} + 403 a + 374\) , \( 1448 a^{3} + 944 a^{2} - 6037 a - 5860\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-4a-4\right){x}^{2}+\left(-107a^{3}-78a^{2}+403a+374\right){x}+1448a^{3}+944a^{2}-6037a-5860$
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*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.