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
49.1-a1
49.1-a
$4$
$14$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
49.1
\( 7^{2} \)
\( 7^{3} \)
$1.19656$
$(-a^2-a+2)$
0
$\Z/14\Z$
$\textsf{potential}$
$-28$
$N(\mathrm{U}(1))$
✓
✓
✓
$7$
7B.1.1[3]
$1$
\( 2 \)
$1$
$354.0802648$
0.516151989
\( 16581375 \)
\( \bigl[a^{2} - 2\) , \( a^{2} - a - 3\) , \( a + 1\) , \( 62 a^{2} - 26 a - 156\) , \( -380 a^{2} + 192 a + 886\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(62a^{2}-26a-156\right){x}-380a^{2}+192a+886$
49.1-a3
49.1-a
$4$
$14$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
49.1
\( 7^{2} \)
\( 7^{9} \)
$1.19656$
$(-a^2-a+2)$
0
$\Z/2\Z$
$\textsf{potential}$
$-28$
$N(\mathrm{U}(1))$
✓
✓
✓
$7$
7B.1.6[3]
$1$
\( 2 \)
$1$
$7.226127854$
0.516151989
\( 16581375 \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -37\) , \( -78\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-37{x}-78$
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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.