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
$2$
$5$
6.6.300125.1
$6$
$[6, 0]$
49.1
\( 7^{2} \)
\( 7^{30} \)
$67.70790$
$(a^5-a^4-6a^3+a^2+2a-1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.4[2]
$625$
\( 1 \)
$1$
$1.142635068$
1.30358
\( -\frac{2887553024}{16807} \)
\( \bigl[0\) , \( 4 a^{5} - a^{4} - 29 a^{3} - 13 a^{2} + 19 a + 5\) , \( 1\) , \( 120 a^{5} - 30 a^{4} - 870 a^{3} - 390 a^{2} + 570 a + 91\) , \( 408 a^{5} - 102 a^{4} - 2958 a^{3} - 1326 a^{2} + 1938 a + 324\bigr] \)
${y}^2+{y}={x}^{3}+\left(4a^{5}-a^{4}-29a^{3}-13a^{2}+19a+5\right){x}^{2}+\left(120a^{5}-30a^{4}-870a^{3}-390a^{2}+570a+91\right){x}+408a^{5}-102a^{4}-2958a^{3}-1326a^{2}+1938a+324$
49.1-a2
49.1-a
$2$
$5$
6.6.300125.1
$6$
$[6, 0]$
49.1
\( 7^{2} \)
\( 7^{6} \)
$67.70790$
$(a^5-a^4-6a^3+a^2+2a-1)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.1[2]
$1$
\( 1 \)
$1$
$17853.67294$
1.30358
\( \frac{4096}{7} \)
\( \bigl[0\) , \( 4 a^{5} - a^{4} - 29 a^{3} - 13 a^{2} + 19 a + 5\) , \( 1\) , \( 1\) , \( 0\bigr] \)
${y}^2+{y}={x}^{3}+\left(4a^{5}-a^{4}-29a^{3}-13a^{2}+19a+5\right){x}^{2}+{x}$
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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.