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-a2
49.1-a
$4$
$4$
5.5.36497.1
$5$
$[5, 0]$
49.1
\( 7^{2} \)
\( 7^{2} \)
$25.19340$
$(a^4-2a^3-4a^2+6a+2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$0.016471345$
$19054.75690$
2.05359085
\( \frac{827}{7} a^{4} + 5033 a^{3} - \frac{28282}{7} a^{2} - \frac{26855}{7} a + \frac{13946}{7} \)
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 2\) , \( 2 a^{4} - 3 a^{3} - 8 a^{2} + 9 a + 5\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 2\) , \( 10 a^{4} - 17 a^{3} - 35 a^{2} + 39 a + 24\) , \( 16 a^{4} - 27 a^{3} - 54 a^{2} + 56 a + 36\bigr] \)
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+6a+2\right){x}{y}+\left(2a^{4}-3a^{3}-6a^{2}+7a+2\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-8a^{2}+9a+5\right){x}^{2}+\left(10a^{4}-17a^{3}-35a^{2}+39a+24\right){x}+16a^{4}-27a^{3}-54a^{2}+56a+36$
49.1-b2
49.1-b
$4$
$4$
5.5.36497.1
$5$
$[5, 0]$
49.1
\( 7^{2} \)
\( 7^{2} \)
$25.19340$
$(a^4-2a^3-4a^2+6a+2)$
$0 \le r \le 2$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$3724.106794$
1.21835419
\( \frac{827}{7} a^{4} + 5033 a^{3} - \frac{28282}{7} a^{2} - \frac{26855}{7} a + \frac{13946}{7} \)
\( \bigl[2 a^{4} - 3 a^{3} - 6 a^{2} + 6 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( 2 a^{4} - 3 a^{3} - 5 a^{2} + 6 a + 1\) , \( 2 a^{4} - 2 a^{3} - 7 a^{2} + 4 a + 2\bigr] \)
${y}^2+\left(2a^{4}-3a^{3}-6a^{2}+6a+1\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+6a+1\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){x}^{2}+\left(2a^{4}-3a^{3}-5a^{2}+6a+1\right){x}+2a^{4}-2a^{3}-7a^{2}+4a+2$
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Pari/GP
SageMath
Magma
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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.