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
127.1-a1
127.1-a
$4$
$6$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
127.1
\( 127 \)
\( - 127^{6} \)
$1.40240$
$(-2a^2+5a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2 \cdot 3 \)
$1$
$3.388700109$
0.726150023
\( -\frac{4759697343611292353825}{4195872914689} a^{2} + \frac{2641742776592019153693}{4195872914689} a + \frac{10694400410777785068038}{4195872914689} \)
\( \bigl[a^{2} - 1\) , \( a^{2} - a - 2\) , \( a^{2} + a - 2\) , \( 13 a^{2} - 11 a - 78\) , \( 96 a^{2} + 20 a - 254\bigr] \)
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(13a^{2}-11a-78\right){x}+96a^{2}+20a-254$
127.1-a2
127.1-a
$4$
$6$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
127.1
\( 127 \)
\( - 127^{3} \)
$1.40240$
$(-2a^2+5a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 3 \)
$1$
$6.777400218$
0.726150023
\( \frac{19597282882830890}{2048383} a^{2} - \frac{44034589527863449}{2048383} a + \frac{15715650738463747}{2048383} \)
\( \bigl[a^{2} - 1\) , \( a^{2} - a - 2\) , \( a^{2} + a - 2\) , \( -12 a^{2} + 14 a - 8\) , \( -33 a^{2} + 49 a - 17\bigr] \)
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-12a^{2}+14a-8\right){x}-33a^{2}+49a-17$
127.1-a3
127.1-a
$4$
$6$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
127.1
\( 127 \)
\( -127 \)
$1.40240$
$(-2a^2+5a+2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 1 \)
$1$
$182.9898059$
0.726150023
\( \frac{5240495}{127} a^{2} + \frac{3964622}{127} a - \frac{2637585}{127} \)
\( \bigl[a^{2} - 1\) , \( a^{2} - a - 2\) , \( a^{2} + a - 2\) , \( -2 a^{2} - a + 2\) , \( -1\bigr] \)
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-2a^{2}-a+2\right){x}-1$
127.1-a4
127.1-a
$4$
$6$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
127.1
\( 127 \)
\( - 127^{2} \)
$1.40240$
$(-2a^2+5a+2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2 \)
$1$
$91.49490295$
0.726150023
\( \frac{110982184499208}{16129} a^{2} + \frac{89000817993497}{16129} a - \frac{61590436345415}{16129} \)
\( \bigl[a^{2} - 1\) , \( a^{2} - a - 2\) , \( a^{2} + a - 2\) , \( -12 a^{2} - 11 a + 7\) , \( 28 a^{2} + 23 a - 16\bigr] \)
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-12a^{2}-11a+7\right){x}+28a^{2}+23a-16$
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Pari/GP
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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.