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
23.2-a2
23.2-a
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
23.2
\( 23 \)
\( -23 \)
$0.95869$
$(2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 1 \)
$1$
$10.38577982$
2.119988428
\( \frac{66417408}{23} a + \frac{162689472}{23} \)
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -2 a - 1\) , \( -a - 1\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-2a-1\right){x}-a-1$
23.2-b2
23.2-b
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
23.2
\( 23 \)
\( -23 \)
$0.95869$
$(2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$0.156973252$
$42.58064027$
0.682185096
\( \frac{66417408}{23} a + \frac{162689472}{23} \)
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -11 a + 23\) , \( -198 a + 482\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-11a+23\right){x}-198a+482$
368.2-d2
368.2-d
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
368.2
\( 2^{4} \cdot 23 \)
\( - 2^{12} \cdot 23 \)
$1.91737$
$(-a+2), (2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 1 \)
$1.522842897$
$21.29032013$
3.309037413
\( \frac{66417408}{23} a + \frac{162689472}{23} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -38 a + 95\) , \( -1445 a + 3540\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(-38a+95\right){x}-1445a+3540$
368.2-f2
368.2-f
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
368.2
\( 2^{4} \cdot 23 \)
\( - 2^{12} \cdot 23 \)
$1.91737$
$(-a+2), (2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 1 \)
$1$
$5.192889910$
1.059994214
\( \frac{66417408}{23} a + \frac{162689472}{23} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -2 a - 1\) , \( -a - 12\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(-2a-1\right){x}-a-12$
529.3-b2
529.3-b
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
529.3
\( 23^{2} \)
\( - 23^{7} \)
$2.09946$
$(2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$5.715641223$
$5.674868404$
6.620871118
\( \frac{66417408}{23} a + \frac{162689472}{23} \)
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -15 a - 31\) , \( 38 a + 35\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-15a-31\right){x}+38a+35$
529.3-f2
529.3-f
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
529.3
\( 23^{2} \)
\( - 23^{7} \)
$2.09946$
$(2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.902686763$
$3.388189308$
1.248616635
\( \frac{66417408}{23} a + \frac{162689472}{23} \)
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -144 a + 353\) , \( -10892 a + 26678\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-144a+353\right){x}-10892a+26678$
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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.