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
1.1-a7
1.1-a
$18$
$72$
\(\Q(\sqrt{2}, \sqrt{3})\)
$4$
$[4, 0]$
1.1
\( 1 \)
\( 1 \)
$4.28923$
$\textsf{none}$
0
$\Z/2\Z\oplus\Z/6\Z$
$\textsf{potential}$
$-72$
$N(\mathrm{U}(1))$
✓
✓
✓
✓
$2, 3$
2Cs , 3B.1.1
$1$
\( 1 \)
$1$
$2576.572294$
0.372767982
\( 77092288000 a^{3} - 385461440000 a + 188837384000 \)
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 5 a - 1\) , \( 1\) , \( 15 a^{3} - 76 a - 40\) , \( -73 a^{3} + 365 a + 179\bigr] \)
${y}^2+\left(a^{3}-3a\right){x}{y}+{y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}+\left(15a^{3}-76a-40\right){x}-73a^{3}+365a+179$
1.1-a11
1.1-a
$18$
$72$
\(\Q(\sqrt{2}, \sqrt{3})\)
$4$
$[4, 0]$
1.1
\( 1 \)
\( 1 \)
$4.28923$
$\textsf{none}$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{potential}$
$-72$
$N(\mathrm{U}(1))$
✓
✓
✓
✓
$2, 3$
2Cs , 3B.1.2
$9$
\( 1 \)
$1$
$31.80953449$
0.372767982
\( 77092288000 a^{3} - 385461440000 a + 188837384000 \)
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 5 a\) , \( a^{2} - 2\) , \( 16 a^{3} - 80 a - 40\) , \( 73 a^{3} - 365 a - 180\bigr] \)
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(16a^{3}-80a-40\right){x}+73a^{3}-365a-180$
256.1-j11
256.1-j
$18$
$72$
\(\Q(\sqrt{2}, \sqrt{3})\)
$4$
$[4, 0]$
256.1
\( 2^{8} \)
\( 2^{12} \)
$8.57847$
$(a^3-4a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{potential}$
$-72$
$N(\mathrm{U}(1))$
✓
✓
$2$
2Cs
$9$
\( 2 \)
$1$
$71.57145261$
1.677455920
\( 77092288000 a^{3} - 385461440000 a + 188837384000 \)
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( 0\) , \( 75 a^{3} + a^{2} - 269 a - 124\) , \( -355 a^{3} - 297 a^{2} + 1601 a + 857\bigr] \)
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(75a^{3}+a^{2}-269a-124\right){x}-355a^{3}-297a^{2}+1601a+857$
256.1-j12
256.1-j
$18$
$72$
\(\Q(\sqrt{2}, \sqrt{3})\)
$4$
$[4, 0]$
256.1
\( 2^{8} \)
\( 2^{12} \)
$8.57847$
$(a^3-4a+1)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{potential}$
$-72$
$N(\mathrm{U}(1))$
✓
✓
$2$
2Cs
$9$
\( 2 \)
$1$
$286.2858104$
1.677455920
\( 77092288000 a^{3} - 385461440000 a + 188837384000 \)
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - 4 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 980 a^{3} + 505 a^{2} - 3658 a - 1897\) , \( 21780 a^{3} + 11274 a^{2} - 81292 a - 42078\bigr] \)
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}-4a-1\right){x}^{2}+\left(980a^{3}+505a^{2}-3658a-1897\right){x}+21780a^{3}+11274a^{2}-81292a-42078$
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Pari/GP
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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.