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
55.1-a1
55.1-a
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
55.1
\( 5 \cdot 11 \)
\( - 5 \cdot 11^{4} \)
$0.54414$
$(-2a+1), (-3a+1)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2 \)
$1$
$19.86707574$
0.493601465
\( -\frac{626283905886387}{73205} a + \frac{1013348626965991}{73205} \)
\( \bigl[1\) , \( -\phi + 1\) , \( 1\) , \( 9 \phi - 25\) , \( -6 \phi + 44\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(9\phi-25\right){x}-6\phi+44$
275.2-a1
275.2-a
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
275.2
\( 5^{2} \cdot 11 \)
\( - 5^{7} \cdot 11^{4} \)
$0.81369$
$(-2a+1), (-3a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$1$
$1.109734269$
0.992576504
\( -\frac{626283905886387}{73205} a + \frac{1013348626965991}{73205} \)
\( \bigl[\phi + 1\) , \( \phi + 1\) , \( \phi\) , \( -30 \phi - 78\) , \( -706 \phi - 622\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\left(\phi+1\right){x}^{2}+\left(-30\phi-78\right){x}-706\phi-622$
605.3-b1
605.3-b
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
605.3
\( 5 \cdot 11^{2} \)
\( - 5 \cdot 11^{10} \)
$0.99097$
$(-2a+1), (-3a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1$
$2.819090767$
1.260735718
\( -\frac{626283905886387}{73205} a + \frac{1013348626965991}{73205} \)
\( \bigl[\phi\) , \( \phi + 1\) , \( 0\) , \( 49 \phi - 224\) , \( -1605 \phi + 529\bigr] \)
${y}^2+\phi{x}{y}={x}^{3}+\left(\phi+1\right){x}^{2}+\left(49\phi-224\right){x}-1605\phi+529$
3025.3-e1
3025.3-e
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
3025.3
\( 5^{2} \cdot 11^{2} \)
\( - 5^{7} \cdot 11^{10} \)
$1.48185$
$(-2a+1), (-3a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$1.702687909$
$0.710969876$
2.165515227
\( -\frac{626283905886387}{73205} a + \frac{1013348626965991}{73205} \)
\( \bigl[1\) , \( \phi - 1\) , \( 1\) , \( -651 \phi - 888\) , \( 41894 \phi + 21992\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-651\phi-888\right){x}+41894\phi+21992$
4455.1-a1
4455.1-a
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
4455.1
\( 3^{4} \cdot 5 \cdot 11 \)
\( - 3^{12} \cdot 5 \cdot 11^{4} \)
$1.63243$
$(-2a+1), (-3a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.2
$1$
\( 2^{4} \)
$1$
$0.827147087$
1.479645692
\( -\frac{626283905886387}{73205} a + \frac{1013348626965991}{73205} \)
\( \bigl[1\) , \( -1\) , \( \phi\) , \( 85 \phi - 228\) , \( 387 \phi - 1504\bigr] \)
${y}^2+{x}{y}+\phi{y}={x}^{3}-{x}^{2}+\left(85\phi-228\right){x}+387\phi-1504$
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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.