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
218.3-a2
218.3-a
$3$
$9$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
218.3
\( 2 \cdot 109 \)
\( 2^{3} \cdot 109 \)
$0.90845$
$(-a+1), (-4a-7)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 1 \)
$1$
$7.614619944$
0.639567958
\( -\frac{657631}{872} a - \frac{483123}{436} \)
\( \bigl[a\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}$
6976.13-b2
6976.13-b
$3$
$9$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
6976.13
\( 2^{6} \cdot 109 \)
\( 2^{21} \cdot 109 \)
$2.16067$
$(-a+1), (-4a-7)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2^{2} \)
$0.163521751$
$2.692174699$
2.662255488
\( -\frac{657631}{872} a - \frac{483123}{436} \)
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( a + 5\) , \( -5 a + 3\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a+5\right){x}-5a+3$
13952.3-h2
13952.3-h
$3$
$9$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
13952.3
\( 2^{7} \cdot 109 \)
\( 2^{9} \cdot 109 \)
$2.56949$
$(a), (-a+1), (-4a-7)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 3 \)
$0.239315180$
$5.384349399$
5.844343151
\( -\frac{657631}{872} a - \frac{483123}{436} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( -a\) , \( 1\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-a{x}+1$
17658.3-a2
17658.3-a
$3$
$9$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
17658.3
\( 2 \cdot 3^{4} \cdot 109 \)
\( 2^{3} \cdot 3^{12} \cdot 109 \)
$2.72535$
$(-a+1), (-4a-7), (3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.2
$1$
\( 2 \cdot 3 \)
$0.221029326$
$2.538206648$
5.089077913
\( -\frac{657631}{872} a - \frac{483123}{436} \)
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 5 a + 1\) , \( -6 a - 6\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a+1\right){x}-6a-6$
23762.4-a2
23762.4-a
$3$
$9$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
23762.4
\( 2 \cdot 109^{2} \)
\( 2^{3} \cdot 109^{7} \)
$2.93534$
$(-a+1), (-4a-7)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2 \cdot 3 \)
$1$
$0.729348313$
3.308013011
\( -\frac{657631}{872} a - \frac{483123}{436} \)
\( \bigl[a\) , \( -a\) , \( 1\) , \( 47 a - 82\) , \( -307 a + 272\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(47a-82\right){x}-307a+272$
27904.9-b2
27904.9-b
$3$
$9$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
27904.9
\( 2^{8} \cdot 109 \)
\( 2^{27} \cdot 109 \)
$3.05565$
$(a), (-a+1), (-4a-7)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2 \)
$1$
$1.903654986$
2.878055814
\( -\frac{657631}{872} a - \frac{483123}{436} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 10 a - 1\) , \( -9 a - 15\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(10a-1\right){x}-9a-15$
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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.