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
1156.1-a1
1156.1-a
$1$
$1$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
1156.1
\( 2^{2} \cdot 17^{2} \)
\( 2^{14} \cdot 17^{2} \)
$1.16510$
$(2), (17)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$1$
\( 1 \)
$1$
$2.881796594$
1.288778616
\( -\frac{5177717}{2176} \)
\( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -4 \phi - 4\) , \( -5 \phi - 4\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-4\phi-4\right){x}-5\phi-4$
1156.1-b1
1156.1-b
$4$
$6$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
1156.1
\( 2^{2} \cdot 17^{2} \)
\( 2^{12} \cdot 17^{2} \)
$1.16510$
$(2), (17)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2 \cdot 3 \)
$1$
$20.21098874$
1.506438157
\( \frac{3048625}{1088} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -3\) , \( 1\bigr] \)
${y}^2+{x}{y}={x}^{3}-3{x}+1$
1156.1-b2
1156.1-b
$4$
$6$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
1156.1
\( 2^{2} \cdot 17^{2} \)
\( 2^{2} \cdot 17^{12} \)
$1.16510$
$(2), (17)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2 \cdot 3 \)
$1$
$2.245665415$
1.506438157
\( \frac{159661140625}{48275138} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -113\) , \( -329\bigr] \)
${y}^2+{x}{y}={x}^{3}-113{x}-329$
1156.1-b3
1156.1-b
$4$
$6$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
1156.1
\( 2^{2} \cdot 17^{2} \)
\( 2^{6} \cdot 17^{4} \)
$1.16510$
$(2), (17)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2 \cdot 3 \)
$1$
$20.21098874$
1.506438157
\( \frac{8805624625}{2312} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -43\) , \( 105\bigr] \)
${y}^2+{x}{y}={x}^{3}-43{x}+105$
1156.1-b4
1156.1-b
$4$
$6$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
1156.1
\( 2^{2} \cdot 17^{2} \)
\( 2^{4} \cdot 17^{6} \)
$1.16510$
$(2), (17)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2 \cdot 3 \)
$1$
$2.245665415$
1.506438157
\( \frac{120920208625}{19652} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -103\) , \( -411\bigr] \)
${y}^2+{x}{y}={x}^{3}-103{x}-411$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.