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
4.1-a2
4.1-a
$6$
$45$
4.4.10512.1
$4$
$[4, 0]$
4.1
\( 2^{2} \)
\( 2^{2} \)
$10.89529$
$(a^3-a^2-5a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3, 5$
3B.1.2 , 5B.4.1
$9$
\( 1 \)
$0.645493086$
$8.845515909$
2.004816315
\( -34209743891669426 a^{3} + \frac{85596887776772763}{2} a^{2} + \frac{371849567703010955}{2} a - \frac{54689211566783959}{2} \)
\( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{3} - 5 a - 5\) , \( -96 a^{3} + 122 a^{2} + 523 a - 91\) , \( -697 a^{3} + 877 a^{2} + 3789 a - 585\bigr] \)
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{3}-5a-5\right){y}={x}^{3}+a{x}^{2}+\left(-96a^{3}+122a^{2}+523a-91\right){x}-697a^{3}+877a^{2}+3789a-585$
4.1-b2
4.1-b
$6$
$45$
4.4.10512.1
$4$
$[4, 0]$
4.1
\( 2^{2} \)
\( 2^{2} \)
$10.89529$
$(a^3-a^2-5a)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3, 5$
3B.1.1 , 5B.4.1
$1$
\( 1 \)
$0.645493086$
$716.4867886$
2.004816315
\( -34209743891669426 a^{3} + \frac{85596887776772763}{2} a^{2} + \frac{371849567703010955}{2} a - \frac{54689211566783959}{2} \)
\( \bigl[a^{3} - 6 a - 4\) , \( a^{3} - 6 a - 6\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -96 a^{3} + 123 a^{2} + 526 a - 90\) , \( 723 a^{3} - 903 a^{2} - 3931 a + 590\bigr] \)
${y}^2+\left(a^{3}-6a-4\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(a^{3}-6a-6\right){x}^{2}+\left(-96a^{3}+123a^{2}+526a-90\right){x}+723a^{3}-903a^{2}-3931a+590$
4.1-c1
4.1-c
$6$
$45$
4.4.10512.1
$4$
$[4, 0]$
4.1
\( 2^{2} \)
\( 2^{2} \)
$10.89529$
$(a^3-a^2-5a)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3, 5$
3B , 5B.4.1
$9$
\( 1 \)
$1$
$17.53722959$
1.539433102
\( -34209743891669426 a^{3} + \frac{85596887776772763}{2} a^{2} + \frac{371849567703010955}{2} a - \frac{54689211566783959}{2} \)
\( \bigl[a^{3} - 5 a - 5\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( a^{3} - a^{2} - 4 a\) , \( 37 a^{3} - 35 a^{2} - 174 a - 89\) , \( 49 a^{3} - 134 a^{2} - 66 a + 221\bigr] \)
${y}^2+\left(a^{3}-5a-5\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+4\right){x}^{2}+\left(37a^{3}-35a^{2}-174a-89\right){x}+49a^{3}-134a^{2}-66a+221$
4.1-d5
4.1-d
$6$
$45$
4.4.10512.1
$4$
$[4, 0]$
4.1
\( 2^{2} \)
\( 2^{2} \)
$10.89529$
$(a^3-a^2-5a)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3, 5$
3B , 5B.1.1
$9$
\( 1 \)
$1$
$361.3852036$
1.268908164
\( -34209743891669426 a^{3} + \frac{85596887776772763}{2} a^{2} + \frac{371849567703010955}{2} a - \frac{54689211566783959}{2} \)
\( \bigl[a\) , \( a^{2} - 2 a - 5\) , \( 1\) , \( 39 a^{3} - 35 a^{2} - 200 a - 120\) , \( -8 a^{3} + 142 a^{2} - 187 a - 471\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(39a^{3}-35a^{2}-200a-120\right){x}-8a^{3}+142a^{2}-187a-471$
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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.