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
45.1-a10
45.1-a
$10$
$32$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( - 3^{4} \cdot 5 \)
$0.51752$
$(-2a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$16$
\( 2 \)
$1$
$0.122605555$
0.438646969
\( \frac{152409672113485069453847362}{45} a + \frac{94194357580360793912853799}{45} \)
\( \bigl[\phi + 1\) , \( \phi - 1\) , \( \phi + 1\) , \( 4364 \phi - 12105\) , \( 243301 \phi - 535402\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(4364\phi-12105\right){x}+243301\phi-535402$
225.1-b10
225.1-b
$10$
$32$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
225.1
\( 3^{2} \cdot 5^{2} \)
\( - 3^{4} \cdot 5^{7} \)
$0.77387$
$(-2a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$2.278990851$
1.019195692
\( \frac{152409672113485069453847362}{45} a + \frac{94194357580360793912853799}{45} \)
\( \bigl[\phi\) , \( \phi - 1\) , \( \phi + 1\) , \( -16876 \phi - 38700\) , \( 2081328 \phi + 3131243\bigr] \)
${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-16876\phi-38700\right){x}+2081328\phi+3131243$
405.1-a10
405.1-a
$10$
$32$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
405.1
\( 3^{4} \cdot 5 \)
\( - 3^{16} \cdot 5 \)
$0.89637$
$(-2a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$1.698659487$
0.759663617
\( \frac{152409672113485069453847362}{45} a + \frac{94194357580360793912853799}{45} \)
\( \bigl[\phi + 1\) , \( 1\) , \( \phi + 1\) , \( 39285 \phi - 108946\) , \( -6708461 \phi + 14534412\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(39285\phi-108946\right){x}-6708461\phi+14534412$
2025.1-b10
2025.1-b
$10$
$32$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
2025.1
\( 3^{4} \cdot 5^{2} \)
\( - 3^{16} \cdot 5^{7} \)
$1.34039$
$(-2a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$64$
\( 2^{4} \)
$1$
$0.018276957$
2.092468141
\( \frac{152409672113485069453847362}{45} a + \frac{94194357580360793912853799}{45} \)
\( \bigl[\phi\) , \( -\phi - 1\) , \( \phi\) , \( -151874 \phi - 348302\) , \( -56544176 \phi - 84347149\bigr] \)
${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-151874\phi-348302\right){x}-56544176\phi-84347149$
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.