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
16.1-a6
16.1-a
$8$
$12$
4.4.2777.1
$4$
$[4, 0]$
16.1
\( 2^{4} \)
\( - 2^{15} \)
$6.65950$
$(-a), (a^3-a^2-4a+1)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2 \)
$1$
$658.7206488$
0.694449760
\( -\frac{14270157697541427}{4096} a^{3} + \frac{35796422109839569}{4096} a^{2} + \frac{1541200524057185}{2048} a - \frac{18919901006348423}{4096} \)
\( \bigl[a + 1\) , \( a^{2} - a - 1\) , \( 0\) , \( 42 a^{3} - 3 a^{2} - 178 a - 115\) , \( 260 a^{3} - 47 a^{2} - 1076 a - 623\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(42a^{3}-3a^{2}-178a-115\right){x}+260a^{3}-47a^{2}-1076a-623$
128.2-c3
128.2-c
$8$
$12$
4.4.2777.1
$4$
$[4, 0]$
128.2
\( 2^{7} \)
\( - 2^{27} \)
$8.63630$
$(-a), (a^3-a^2-4a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$4$
\( 2^{2} \)
$1$
$18.48825450$
1.403356344
\( -\frac{14270157697541427}{4096} a^{3} + \frac{35796422109839569}{4096} a^{2} + \frac{1541200524057185}{2048} a - \frac{18919901006348423}{4096} \)
\( \bigl[a^{3} - 4 a\) , \( a - 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( 15 a^{3} - 36 a^{2} - 7 a + 10\) , \( 61 a^{3} - 148 a^{2} - 29 a + 65\bigr] \)
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(15a^{3}-36a^{2}-7a+10\right){x}+61a^{3}-148a^{2}-29a+65$
512.3-l8
512.3-l
$8$
$12$
4.4.2777.1
$4$
$[4, 0]$
512.3
\( 2^{9} \)
\( - 2^{33} \)
$10.27035$
$(-a), (a^3-a^2-4a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$0.625108786$
$73.43182789$
3.484271543
\( -\frac{14270157697541427}{4096} a^{3} + \frac{35796422109839569}{4096} a^{2} + \frac{1541200524057185}{2048} a - \frac{18919901006348423}{4096} \)
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{3} + 2 a^{2} + a - 4\) , \( a^{2} - a - 2\) , \( 33 a^{3} - 90 a^{2} - 11 a + 45\) , \( 247 a^{3} - 606 a^{2} - 45 a + 327\bigr] \)
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+a-4\right){x}^{2}+\left(33a^{3}-90a^{2}-11a+45\right){x}+247a^{3}-606a^{2}-45a+327$
512.3-n8
512.3-n
$8$
$12$
4.4.2777.1
$4$
$[4, 0]$
512.3
\( 2^{9} \)
\( - 2^{33} \)
$10.27035$
$(-a), (a^3-a^2-4a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$0.344388037$
$138.4595911$
3.619454774
\( -\frac{14270157697541427}{4096} a^{3} + \frac{35796422109839569}{4096} a^{2} + \frac{1541200524057185}{2048} a - \frac{18919901006348423}{4096} \)
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{2} - 2\) , \( a^{2} - a - 2\) , \( -15 a^{3} + 23 a^{2} + 53 a - 58\) , \( 21 a^{3} - 34 a^{2} - 85 a + 90\bigr] \)
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-15a^{3}+23a^{2}+53a-58\right){x}+21a^{3}-34a^{2}-85a+90$
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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.