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
11.2-a1
11.2-a
$2$
$5$
5.5.38569.1
$5$
$[5, 0]$
11.2
\( 11 \)
\( 11 \)
$22.30473$
$(a^3-3a)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.1
$1$
\( 1 \)
$1$
$5802.035803$
1.18173802
\( -\frac{47085}{11} a^{4} - \frac{72108}{11} a^{3} + \frac{99835}{11} a^{2} + \frac{108037}{11} a - \frac{35124}{11} \)
\( \bigl[a^{2} - 2\) , \( 2 a^{4} + a^{3} - 9 a^{2} - 4 a + 3\) , \( a^{3} - 4 a + 1\) , \( -a^{4} + 3 a^{2} + a + 2\) , \( a^{4} - 4 a^{2} - 1\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(2a^{4}+a^{3}-9a^{2}-4a+3\right){x}^{2}+\left(-a^{4}+3a^{2}+a+2\right){x}+a^{4}-4a^{2}-1$
11.2-a2
11.2-a
$2$
$5$
5.5.38569.1
$5$
$[5, 0]$
11.2
\( 11 \)
\( 11^{5} \)
$22.30473$
$(a^3-3a)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.2
$25$
\( 5 \)
$1$
$1.856651456$
1.18173802
\( -\frac{189055389402903109375}{161051} a^{4} + \frac{369423059874161169972}{161051} a^{3} + \frac{223392156144464926449}{161051} a^{2} - \frac{436496489695753499092}{161051} a + \frac{96739883027171908222}{161051} \)
\( \bigl[-a^{4} + 5 a^{2} + a - 2\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 1\) , \( a^{4} + a^{3} - 4 a^{2} - 4 a + 2\) , \( -6 a^{4} - 90 a^{3} + 108 a^{2} + 359 a - 308\) , \( 40 a^{4} - 663 a^{3} + 389 a^{2} + 2588 a - 1988\bigr] \)
${y}^2+\left(-a^{4}+5a^{2}+a-2\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-4a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+3a+1\right){x}^{2}+\left(-6a^{4}-90a^{3}+108a^{2}+359a-308\right){x}+40a^{4}-663a^{3}+389a^{2}+2588a-1988$
11.2-b1
11.2-b
$2$
$5$
5.5.38569.1
$5$
$[5, 0]$
11.2
\( 11 \)
\( 11 \)
$22.30473$
$(a^3-3a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.1
$1$
\( 1 \)
$0.005433471$
$9903.445669$
1.36998089
\( -\frac{47085}{11} a^{4} - \frac{72108}{11} a^{3} + \frac{99835}{11} a^{2} + \frac{108037}{11} a - \frac{35124}{11} \)
\( \bigl[a^{4} - 4 a^{2} + 2\) , \( -a^{4} - a^{3} + 5 a^{2} + 5 a - 4\) , \( -a^{4} + 5 a^{2} - 3\) , \( a^{3} - a^{2} - 3 a + 4\) , \( -a^{3} + a^{2} + 4 a - 3\bigr] \)
${y}^2+\left(a^{4}-4a^{2}+2\right){x}{y}+\left(-a^{4}+5a^{2}-3\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+5a-4\right){x}^{2}+\left(a^{3}-a^{2}-3a+4\right){x}-a^{3}+a^{2}+4a-3$
11.2-b2
11.2-b
$2$
$5$
5.5.38569.1
$5$
$[5, 0]$
11.2
\( 11 \)
\( 11^{5} \)
$22.30473$
$(a^3-3a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.2
$1$
\( 1 \)
$0.027167356$
$1980.689133$
1.36998089
\( -\frac{189055389402903109375}{161051} a^{4} + \frac{369423059874161169972}{161051} a^{3} + \frac{223392156144464926449}{161051} a^{2} - \frac{436496489695753499092}{161051} a + \frac{96739883027171908222}{161051} \)
\( \bigl[a^{4} - 4 a^{2} + 1\) , \( a^{4} - 5 a^{2} - a + 4\) , \( a^{4} + a^{3} - 4 a^{2} - 4 a + 2\) , \( -788 a^{4} - 219 a^{3} + 3884 a^{2} + 1089 a - 2876\) , \( 13707 a^{4} + 3782 a^{3} - 67511 a^{2} - 18659 a + 49736\bigr] \)
${y}^2+\left(a^{4}-4a^{2}+1\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-4a+2\right){y}={x}^{3}+\left(a^{4}-5a^{2}-a+4\right){x}^{2}+\left(-788a^{4}-219a^{3}+3884a^{2}+1089a-2876\right){x}+13707a^{4}+3782a^{3}-67511a^{2}-18659a+49736$
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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.