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
484.1-a1
484.1-a
$2$
$3$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
484.1
\( 2^{2} \cdot 11^{2} \)
\( 2^{4} \cdot 11^{6} \)
$1.45191$
$(a+1), (-2a+1), (2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.2
$1$
\( 1 \)
$3.281855644$
$1.294911296$
2.453572336
\( -\frac{199794688}{1331} \)
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -78 a - 134\) , \( -475 a - 824\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-78a-134\right){x}-475a-824$
484.1-a2
484.1-a
$2$
$3$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
484.1
\( 2^{2} \cdot 11^{2} \)
\( 2^{4} \cdot 11^{2} \)
$1.45191$
$(a+1), (-2a+1), (2a+1)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1
$1$
\( 3 \)
$1.093951881$
$11.65420166$
2.453572336
\( \frac{8192}{11} \)
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( 2 a + 6\) , \( -5 a - 8\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a+6\right){x}-5a-8$
484.1-b1
484.1-b
$2$
$3$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
484.1
\( 2^{2} \cdot 11^{2} \)
\( 2^{4} \cdot 11^{6} \)
$1.45191$
$(a+1), (-2a+1), (2a+1)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1
$1$
\( 3^{3} \)
$0.058354610$
$18.65468372$
1.885487636
\( -\frac{199794688}{1331} \)
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( -78 a - 134\) , \( 474 a + 822\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-78a-134\right){x}+474a+822$
484.1-b2
484.1-b
$2$
$3$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
484.1
\( 2^{2} \cdot 11^{2} \)
\( 2^{4} \cdot 11^{2} \)
$1.45191$
$(a+1), (-2a+1), (2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.2
$1$
\( 1 \)
$0.175063830$
$18.65468372$
1.885487636
\( \frac{8192}{11} \)
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 2 a + 6\) , \( 4 a + 6\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a+6\right){x}+4a+6$
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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.