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
180.1-b5
180.1-b
$8$
$12$
\(\Q(\sqrt{85}) \)
$2$
$[2, 0]$
180.1
\( 2^{2} \cdot 3^{2} \cdot 5 \)
\( 2^{4} \cdot 3^{12} \cdot 5^{4} \)
$3.01763$
$(3,a), (3,a+2), (5,a+2), (2)$
$1$
$\Z/2\Z\oplus\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cs , 3B.1.1
$1$
\( 2^{4} \cdot 3^{2} \)
$2.102317712$
$11.23555713$
5.124051602
\( \frac{702595369}{72900} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -19\) , \( 26\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-19{x}+26$
180.1-r5
180.1-r
$8$
$12$
\(\Q(\sqrt{85}) \)
$2$
$[2, 0]$
180.1
\( 2^{2} \cdot 3^{2} \cdot 5 \)
\( 2^{4} \cdot 3^{24} \cdot 5^{4} \)
$3.01763$
$(3,a), (3,a+2), (5,a+2), (2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cs , 3B
$1$
\( 2^{5} \)
$1$
$11.23555713$
2.437334552
\( \frac{702595369}{72900} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 202 a - 1059\) , \( -2737 a + 13984\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(202a-1059\right){x}-2737a+13984$
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Pari/GP
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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.