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
18225.1-a1
18225.1-a
$2$
$3$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
18225.1
\( 3^{6} \cdot 5^{2} \)
\( 3^{8} \cdot 5^{6} \)
$1.79832$
$(-2a+1), (5)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1[2]
$1$
\( 3^{2} \)
$0.355512380$
$2.583827223$
2.121375572
\( \frac{2359296}{125} \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( 12 a\) , \( 15\bigr] \)
${y}^2+{y}={x}^{3}+12a{x}+15$
18225.1-a2
18225.1-a
$2$
$3$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
18225.1
\( 3^{6} \cdot 5^{2} \)
\( 3^{12} \cdot 5^{2} \)
$1.79832$
$(-2a+1), (5)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1[2]
$1$
\( 3 \)
$1.066537142$
$2.583827223$
2.121375572
\( \frac{884736}{5} \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( 18 a\) , \( 29\bigr] \)
${y}^2+{y}={x}^{3}+18a{x}+29$
18225.1-b1
18225.1-b
$2$
$7$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
18225.1
\( 3^{6} \cdot 5^{2} \)
\( 3^{8} \cdot 5^{14} \)
$1.79832$
$(-2a+1), (5)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$7$
7B.2.3
$1$
\( 3 \cdot 7 \)
$0.035785774$
$0.737322105$
2.559271316
\( -\frac{15590912409}{78125} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -225\) , \( -1250\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-225{x}-1250$
18225.1-b2
18225.1-b
$2$
$7$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
18225.1
\( 3^{6} \cdot 5^{2} \)
\( 3^{8} \cdot 5^{2} \)
$1.79832$
$(-2a+1), (5)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$7$
7B.2.1
$1$
\( 3 \)
$0.035785774$
$5.161254739$
2.559271316
\( -\frac{9}{5} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 0\) , \( 1\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+1$
18225.1-c1
18225.1-c
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
18225.1
\( 3^{6} \cdot 5^{2} \)
\( 3^{8} \cdot 5^{2} \)
$1.79832$
$(-2a+1), (5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$1$
\( 1 \)
$0.272277013$
$4.687945914$
2.947765521
\( \frac{36864}{5} \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( -3 a + 3\) , \( -2\bigr] \)
${y}^2+{y}={x}^{3}+\left(-3a+3\right){x}-2$
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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.