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
225.1-a1
225.1-a
$2$
$5$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
225.1
\( 3^{2} \cdot 5^{2} \)
\( 3^{2} \cdot 5^{2} \)
$0.77387$
$(-2a+1), (3)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.1[2]
$1$
\( 1 \)
$1$
$48.75642491$
0.872181443
\( -\frac{102400}{3} \)
\( \bigl[0\) , \( -\phi + 1\) , \( 1\) , \( -2 \phi - 1\) , \( 2 \phi + 1\bigr] \)
${y}^2+{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-2\phi-1\right){x}+2\phi+1$
225.1-c1
225.1-c
$2$
$5$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
225.1
\( 3^{2} \cdot 5^{2} \)
\( 3^{2} \cdot 5^{8} \)
$0.77387$
$(-2a+1), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.1.4[2]
$1$
\( 1 \)
$1$
$1.967118283$
0.879722040
\( -\frac{102400}{3} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -8\) , \( -7\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-8{x}-7$
2025.1-a1
2025.1-a
$2$
$5$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
2025.1
\( 3^{4} \cdot 5^{2} \)
\( 3^{14} \cdot 5^{8} \)
$1.34039$
$(-2a+1), (3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.4.1[2]
$1$
\( 2^{2} \cdot 3 \)
$0.025588090$
$7.268178697$
1.996134097
\( -\frac{102400}{3} \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( -75\) , \( 256\bigr] \)
${y}^2+{y}={x}^{3}-75{x}+256$
2025.1-f1
2025.1-f
$2$
$5$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
2025.1
\( 3^{4} \cdot 5^{2} \)
\( 3^{14} \cdot 5^{2} \)
$1.34039$
$(-2a+1), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.1[2]
$1$
\( 2 \)
$1$
$1.466203400$
1.311412189
\( -\frac{102400}{3} \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( -15 \phi - 15\) , \( -41 \phi - 31\bigr] \)
${y}^2+{y}={x}^{3}+\left(-15\phi-15\right){x}-41\phi-31$
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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.