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
55.1-c3
55.1-c
$4$
$6$
4.4.5125.1
$4$
$[4, 0]$
55.1
\( 5 \cdot 11 \)
\( 5^{3} \cdot 11^{3} \)
$10.55676$
$(-a^3+a^2+4a+1), (-a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$4$
\( 1 \)
$1$
$117.3818148$
1.639660313
\( \frac{133990069789633150033955762628}{6655} a^{3} + \frac{94645515348052450445056005699}{6655} a^{2} - \frac{547795377221621290762673298852}{6655} a - \frac{544602192760246793271514751626}{6655} \)
\( \bigl[a^{3} - 5 a - 3\) , \( -a^{3} + 6 a + 4\) , \( a^{3} - 4 a - 3\) , \( 149 a^{3} + 15 a^{2} - 859 a - 806\) , \( 2623 a^{3} + 320 a^{2} - 15049 a - 13499\bigr] \)
${y}^2+\left(a^{3}-5a-3\right){x}{y}+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(-a^{3}+6a+4\right){x}^{2}+\left(149a^{3}+15a^{2}-859a-806\right){x}+2623a^{3}+320a^{2}-15049a-13499$
55.1-d3
55.1-d
$4$
$6$
4.4.5125.1
$4$
$[4, 0]$
55.1
\( 5 \cdot 11 \)
\( 5^{3} \cdot 11^{3} \)
$10.55676$
$(-a^3+a^2+4a+1), (-a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$36$
\( 1 \)
$1$
$8.259790245$
1.038399794
\( \frac{133990069789633150033955762628}{6655} a^{3} + \frac{94645515348052450445056005699}{6655} a^{2} - \frac{547795377221621290762673298852}{6655} a - \frac{544602192760246793271514751626}{6655} \)
\( \bigl[a + 1\) , \( 0\) , \( a^{3} - 4 a - 3\) , \( -191 a^{3} + 389 a^{2} + 555 a - 1139\) , \( -2260 a^{3} + 4761 a^{2} + 6611 a - 13813\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(-191a^{3}+389a^{2}+555a-1139\right){x}-2260a^{3}+4761a^{2}+6611a-13813$
275.1-g2
275.1-g
$4$
$6$
4.4.5125.1
$4$
$[4, 0]$
275.1
\( 5^{2} \cdot 11 \)
\( 5^{9} \cdot 11^{3} \)
$12.90928$
$(-a^3+a^2+4a+1), (-a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \cdot 3 \)
$0.965324358$
$23.49504118$
3.801752031
\( \frac{133990069789633150033955762628}{6655} a^{3} + \frac{94645515348052450445056005699}{6655} a^{2} - \frac{547795377221621290762673298852}{6655} a - \frac{544602192760246793271514751626}{6655} \)
\( \bigl[a^{2} - 3\) , \( a\) , \( 1\) , \( -56 a^{3} + 51 a^{2} + 125 a - 257\) , \( 604 a^{3} + 1027 a^{2} - 3261 a - 5613\bigr] \)
${y}^2+\left(a^{2}-3\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-56a^{3}+51a^{2}+125a-257\right){x}+604a^{3}+1027a^{2}-3261a-5613$
275.1-l3
275.1-l
$4$
$6$
4.4.5125.1
$4$
$[4, 0]$
275.1
\( 5^{2} \cdot 11 \)
\( 5^{9} \cdot 11^{3} \)
$12.90928$
$(-a^3+a^2+4a+1), (-a)$
$0 \le r \le 1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
\( 2^{2} \cdot 3 \)
$1$
$8.253223834$
3.977414736
\( \frac{133990069789633150033955762628}{6655} a^{3} + \frac{94645515348052450445056005699}{6655} a^{2} - \frac{547795377221621290762673298852}{6655} a - \frac{544602192760246793271514751626}{6655} \)
\( \bigl[a^{2} - 4\) , \( a^{2} - 5\) , \( a^{3} - 5 a - 4\) , \( 388 a^{3} - 1883 a^{2} + 2299 a - 119\) , \( -13237 a^{3} + 62213 a^{2} - 67828 a - 9718\bigr] \)
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{3}-5a-4\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(388a^{3}-1883a^{2}+2299a-119\right){x}-13237a^{3}+62213a^{2}-67828a-9718$
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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.