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
40.3-a1
40.3-a
$1$
$1$
3.3.169.1
$3$
$[3, 0]$
40.3
\( 2^{3} \cdot 5 \)
\( - 2^{3} \cdot 5^{5} \)
$2.14829$
$(-a+1), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$14.96312317$
1.151009474
\( \frac{391592090541}{6250} a^{2} - \frac{99769067817}{1250} a - \frac{1429739883649}{6250} \)
\( \bigl[a^{2} - a - 2\) , \( -a^{2} + 3\) , \( a^{2} - 3\) , \( 4 a^{2} - 6 a - 15\) , \( 12 a^{2} - 16 a - 46\bigr] \)
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(4a^{2}-6a-15\right){x}+12a^{2}-16a-46$
40.3-b1
40.3-b
$2$
$3$
3.3.169.1
$3$
$[3, 0]$
40.3
\( 2^{3} \cdot 5 \)
\( - 2^{9} \cdot 5 \)
$2.14829$
$(-a+1), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$9$
\( 1 \)
$1$
$1.805263776$
1.249797999
\( -\frac{222655206023281}{40} a^{2} - 9190701307653 a - \frac{41995505984563}{20} \)
\( \bigl[1\) , \( a^{2} - 4\) , \( a + 1\) , \( 40 a^{2} - 87 a - 54\) , \( 107 a^{2} - 248 a - 107\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(40a^{2}-87a-54\right){x}+107a^{2}-248a-107$
40.3-b2
40.3-b
$2$
$3$
3.3.169.1
$3$
$[3, 0]$
40.3
\( 2^{3} \cdot 5 \)
\( - 2^{3} \cdot 5^{3} \)
$2.14829$
$(-a+1), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 3 \)
$1$
$48.74212197$
1.249797999
\( -\frac{5576389}{250} a^{2} + \frac{987684}{25} a + \frac{3110871}{250} \)
\( \bigl[1\) , \( a^{2} - 4\) , \( a + 1\) , \( -10 a^{2} + 23 a + 11\) , \( 29 a^{2} - 69 a - 23\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-10a^{2}+23a+11\right){x}+29a^{2}-69a-23$
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.