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-b4
16.1-b
$4$
$14$
4.4.2777.1
$4$
$[4, 0]$
16.1
\( 2^{4} \)
\( - 2^{43} \)
$6.65950$
$(-a), (a^3-a^2-4a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 7$
2B , 7B.1.3
$49$
\( 2 \cdot 7 \)
$1$
$0.460733588$
1.499429526
\( \frac{14221956074310291}{16384} a^{3} + \frac{19421003373675559}{16384} a^{2} - \frac{5542858545784381}{8192} a - \frac{1512226792940977}{2048} \)
\( \bigl[1\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( a^{2} - a - 1\) , \( 559 a^{3} - 1437 a^{2} - 22 a + 670\) , \( 15729 a^{3} - 39584 a^{2} - 3004 a + 20573\bigr] \)
${y}^2+{x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-3\right){x}^{2}+\left(559a^{3}-1437a^{2}-22a+670\right){x}+15729a^{3}-39584a^{2}-3004a+20573$
128.2-a3
128.2-a
$4$
$14$
4.4.2777.1
$4$
$[4, 0]$
128.2
\( 2^{7} \)
\( - 2^{55} \)
$8.63630$
$(-a), (a^3-a^2-4a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 7$
2B , 7B.6.3
$1$
\( 2^{3} \)
$0.383849493$
$41.62804950$
2.425766985
\( \frac{14221956074310291}{16384} a^{3} + \frac{19421003373675559}{16384} a^{2} - \frac{5542858545784381}{8192} a - \frac{1512226792940977}{2048} \)
\( \bigl[a^{3} - 3 a\) , \( -a^{2} + 2 a + 3\) , \( 0\) , \( -1341 a^{3} - 1930 a^{2} + 1043 a + 1163\) , \( 78103 a^{3} + 106898 a^{2} - 61425 a - 66588\bigr] \)
${y}^2+\left(a^{3}-3a\right){x}{y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-1341a^{3}-1930a^{2}+1043a+1163\right){x}+78103a^{3}+106898a^{2}-61425a-66588$
512.3-d3
512.3-d
$4$
$14$
4.4.2777.1
$4$
$[4, 0]$
512.3
\( 2^{9} \)
\( - 2^{61} \)
$10.27035$
$(-a), (a^3-a^2-4a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 7$
2B , 7B.6.3
$1$
\( 2^{2} \cdot 7 \)
$1$
$13.38771138$
1.778346732
\( \frac{14221956074310291}{16384} a^{3} + \frac{19421003373675559}{16384} a^{2} - \frac{5542858545784381}{8192} a - \frac{1512226792940977}{2048} \)
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + 4 a + 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 655 a^{3} - 155 a^{2} - 2717 a - 1670\) , \( -34267 a^{3} + 5951 a^{2} + 141230 a + 82772\bigr] \)
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{3}+4a+2\right){x}^{2}+\left(655a^{3}-155a^{2}-2717a-1670\right){x}-34267a^{3}+5951a^{2}+141230a+82772$
512.3-g2
512.3-g
$4$
$14$
4.4.2777.1
$4$
$[4, 0]$
512.3
\( 2^{9} \)
\( - 2^{61} \)
$10.27035$
$(-a), (a^3-a^2-4a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 7$
2B , 7B.6.3
$49$
\( 2^{2} \)
$1$
$1.732725826$
1.611157468
\( \frac{14221956074310291}{16384} a^{3} + \frac{19421003373675559}{16384} a^{2} - \frac{5542858545784381}{8192} a - \frac{1512226792940977}{2048} \)
\( \bigl[a^{3} - 4 a\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( 0\) , \( -756 a^{3} + 2036 a^{2} + 1496 a - 4993\) , \( -59611 a^{3} + 65161 a^{2} + 200305 a - 50787\bigr] \)
${y}^2+\left(a^{3}-4a\right){x}{y}={x}^{3}+\left(a^{3}-2a^{2}-3a+3\right){x}^{2}+\left(-756a^{3}+2036a^{2}+1496a-4993\right){x}-59611a^{3}+65161a^{2}+200305a-50787$
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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.