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
3.1-a1
3.1-a
$2$
$5$
5.5.65657.1
$5$
$[5, 0]$
3.1
\( 3 \)
\( - 3^{10} \)
$25.55590$
$(-a^4+a^3+4a^2-2a-2)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.1
$1$
\( 2 \cdot 5 \)
$1$
$813.6852207$
1.27021109
\( \frac{747179612}{59049} a^{4} - \frac{4155930605}{19683} a^{3} - \frac{9128857582}{59049} a^{2} + \frac{3220249090}{6561} a + \frac{7149149617}{59049} \)
\( \bigl[a^{2} - a - 2\) , \( 3 a^{4} - 4 a^{3} - 13 a^{2} + 12 a + 8\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 7 a - 4\) , \( 2 a^{3} - 2 a^{2} - 8 a + 8\) , \( 4 a^{4} - 5 a^{3} - 19 a^{2} + 16 a + 11\bigr] \)
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(-a^{4}+2a^{3}+5a^{2}-7a-4\right){y}={x}^{3}+\left(3a^{4}-4a^{3}-13a^{2}+12a+8\right){x}^{2}+\left(2a^{3}-2a^{2}-8a+8\right){x}+4a^{4}-5a^{3}-19a^{2}+16a+11$
9.1-b1
9.1-b
$2$
$5$
5.5.65657.1
$5$
$[5, 0]$
9.1
\( 3^{2} \)
\( - 3^{16} \)
$28.52353$
$(-a^4+a^3+4a^2-2a-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B.4.1
$1$
\( 2 \)
$1$
$134.1493644$
1.04707574
\( \frac{747179612}{59049} a^{4} - \frac{4155930605}{19683} a^{3} - \frac{9128857582}{59049} a^{2} + \frac{3220249090}{6561} a + \frac{7149149617}{59049} \)
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 6 a - 2\) , \( a^{3} - 3 a\) , \( -a^{3} - a^{2} + 2 a + 4\) , \( 2 a^{4} - 3 a^{3} - 10 a^{2} + 7 a + 8\bigr] \)
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+3\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-6a-2\right){x}^{2}+\left(-a^{3}-a^{2}+2a+4\right){x}+2a^{4}-3a^{3}-10a^{2}+7a+8$
75.1-d1
75.1-d
$2$
$5$
5.5.65657.1
$5$
$[5, 0]$
75.1
\( 3 \cdot 5^{2} \)
\( - 3^{10} \cdot 5^{6} \)
$35.26023$
$(-a^4+a^3+4a^2-2a-2), (-a^2+a+2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B.4.1
$1$
\( 2 \)
$0.025081541$
$2778.826129$
2.72003869
\( \frac{747179612}{59049} a^{4} - \frac{4155930605}{19683} a^{3} - \frac{9128857582}{59049} a^{2} + \frac{3220249090}{6561} a + \frac{7149149617}{59049} \)
\( \bigl[-2 a^{4} + 3 a^{3} + 9 a^{2} - 9 a - 6\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 4 a - 7\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 6 a - 5\) , \( 393 a^{4} - 485 a^{3} - 1852 a^{2} + 1219 a + 1683\) , \( 8052 a^{4} - 9936 a^{3} - 37936 a^{2} + 24979 a + 34418\bigr] \)
${y}^2+\left(-2a^{4}+3a^{3}+9a^{2}-9a-6\right){x}{y}+\left(-a^{4}+2a^{3}+5a^{2}-6a-5\right){y}={x}^{3}+\left(-2a^{4}+2a^{3}+9a^{2}-4a-7\right){x}^{2}+\left(393a^{4}-485a^{3}-1852a^{2}+1219a+1683\right){x}+8052a^{4}-9936a^{3}-37936a^{2}+24979a+34418$
225.1-f1
225.1-f
$2$
$5$
5.5.65657.1
$5$
$[5, 0]$
225.1
\( 3^{2} \cdot 5^{2} \)
\( - 3^{16} \cdot 5^{6} \)
$39.35476$
$(-a^4+a^3+4a^2-2a-2), (-a^2+a+2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B.4.1
$1$
\( 2 \)
$1$
$264.7816814$
2.06669988
\( \frac{747179612}{59049} a^{4} - \frac{4155930605}{19683} a^{3} - \frac{9128857582}{59049} a^{2} + \frac{3220249090}{6561} a + \frac{7149149617}{59049} \)
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 4 a + 7\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 6 a - 5\) , \( 14 a^{4} - 21 a^{3} - 55 a^{2} + 46 a + 47\) , \( -3 a^{4} + 4 a^{3} + 17 a^{2} - 15 a - 13\bigr] \)
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){x}{y}+\left(-a^{4}+2a^{3}+5a^{2}-6a-5\right){y}={x}^{3}+\left(2a^{4}-2a^{3}-9a^{2}+4a+7\right){x}^{2}+\left(14a^{4}-21a^{3}-55a^{2}+46a+47\right){x}-3a^{4}+4a^{3}+17a^{2}-15a-13$
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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.