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
268.3-a1
268.3-a
$3$
$9$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
268.3
\( 2^{2} \cdot 67 \)
\( 2^{12} \cdot 67^{3} \)
$0.95658$
$(a), (-a+1), (-6a+1)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Cs.1.1
$1$
\( 3 \)
$1$
$2.266555825$
0.571118385
\( -\frac{294246215725}{153990656} a + \frac{877818327743}{153990656} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( -9 a + 4\) , \( 5 a - 10\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-9a+4\right){x}+5a-10$
268.3-a2
268.3-a
$3$
$9$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
268.3
\( 2^{2} \cdot 67 \)
\( 2^{4} \cdot 67 \)
$0.95658$
$(a), (-a+1), (-6a+1)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 1 \)
$1$
$6.799667476$
0.571118385
\( -\frac{1270577}{536} a + \frac{8913079}{536} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( a - 1\) , \( a - 1\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(a-1\right){x}+a-1$
268.3-a3
268.3-a
$3$
$9$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
268.3
\( 2^{2} \cdot 67 \)
\( 2^{36} \cdot 67 \)
$0.95658$
$(a), (-a+1), (-6a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 1 \)
$1$
$0.755518608$
0.571118385
\( \frac{6214903750470547}{8992587776} a + \frac{2878157116760767}{8992587776} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( -209 a + 149\) , \( -797 a + 1955\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-209a+149\right){x}-797a+1955$
268.3-b1
268.3-b
$2$
$11$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
268.3
\( 2^{2} \cdot 67 \)
\( 2^{22} \cdot 67 \)
$0.95658$
$(a), (-a+1), (-6a+1)$
0
$\Z/11\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$11$
11B.1.1
$1$
\( 11^{2} \)
$1$
$2.762336240$
2.088129922
\( \frac{4432109}{68608} a + \frac{1557205}{137216} \)
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -2 a - 2\) , \( -5 a + 7\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a-2\right){x}-5a+7$
268.3-b2
268.3-b
$2$
$11$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
268.3
\( 2^{2} \cdot 67 \)
\( 2^{2} \cdot 67^{11} \)
$0.95658$
$(a), (-a+1), (-6a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$11$
11B.1.2
$1$
\( 11 \)
$1$
$0.251121476$
2.088129922
\( -\frac{124766492512337161813063}{122130132904968017083} a + \frac{862831973730147670057381}{244260265809936034166} \)
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 658 a - 332\) , \( 3097 a + 4231\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(658a-332\right){x}+3097a+4231$
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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.