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
41.1-c2
41.1-c
$2$
$7$
4.4.5125.1
$4$
$[4, 0]$
41.1
\( 41 \)
\( 41^{14} \)
$10.17615$
$(a^3-a^2-4a-3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$7$
7B.1.3
$49$
\( 2 \)
$1$
$0.891323980$
1.220154235
\( -\frac{7215644871110656}{194754273881} a^{2} + \frac{7215644871110656}{194754273881} a + \frac{16969651353047040}{194754273881} \)
\( \bigl[0\) , \( a^{2} - a - 4\) , \( a^{2} - a - 4\) , \( -10 a^{2} + 10 a\) , \( -31 a^{2} + 31 a + 11\bigr] \)
${y}^2+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-10a^{2}+10a\right){x}-31a^{2}+31a+11$
41.1-d1
41.1-d
$2$
$7$
4.4.5125.1
$4$
$[4, 0]$
41.1
\( 41 \)
\( 41^{14} \)
$10.17615$
$(a^3-a^2-4a-3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$7$
7B.6.3
$1$
\( 2 \)
$1$
$65.76400479$
1.837262932
\( -\frac{7215644871110656}{194754273881} a^{2} + \frac{7215644871110656}{194754273881} a + \frac{16969651353047040}{194754273881} \)
\( \bigl[0\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( a^{3} - 4 a - 3\) , \( 144 a^{3} - 153 a^{2} - 559 a - 225\) , \( -1890 a^{3} + 1126 a^{2} + 8698 a + 5670\bigr] \)
${y}^2+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-4\right){x}^{2}+\left(144a^{3}-153a^{2}-559a-225\right){x}-1890a^{3}+1126a^{2}+8698a+5670$
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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.