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-a6
55.1-a
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
55.1
\( 5 \cdot 11 \)
\( 5^{2} \cdot 11^{2} \)
$0.54414$
$(-2a+1), (-3a+1)$
0
$\Z/2\Z\oplus\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2Cs , 3B.1.1
$1$
\( 2^{2} \)
$1$
$39.73415148$
0.493601465
\( \frac{132583563}{605} a + \frac{166070482}{605} \)
\( \bigl[\phi + 1\) , \( 0\) , \( \phi + 1\) , \( 4 \phi - 11\) , \( -9 \phi + 13\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(4\phi-11\right){x}-9\phi+13$
275.2-a6
275.2-a
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
275.2
\( 5^{2} \cdot 11 \)
\( 5^{8} \cdot 11^{2} \)
$0.81369$
$(-2a+1), (-3a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2Cs , 3B
$1$
\( 2^{3} \)
$1$
$4.438937076$
0.992576504
\( \frac{132583563}{605} a + \frac{166070482}{605} \)
\( \bigl[\phi\) , \( 1\) , \( \phi\) , \( -\phi - 26\) , \( -5 \phi - 62\bigr] \)
${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+{x}^{2}+\left(-\phi-26\right){x}-5\phi-62$
605.3-b6
605.3-b
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
605.3
\( 5 \cdot 11^{2} \)
\( 5^{2} \cdot 11^{8} \)
$0.99097$
$(-2a+1), (-3a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2Cs , 3B
$1$
\( 2^{3} \)
$1$
$5.638181535$
1.260735718
\( \frac{132583563}{605} a + \frac{166070482}{605} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( 35 \phi - 87\) , \( -210 \phi + 261\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(35\phi-87\right){x}-210\phi+261$
3025.3-e6
3025.3-e
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
3025.3
\( 5^{2} \cdot 11^{2} \)
\( 5^{8} \cdot 11^{8} \)
$1.48185$
$(-2a+1), (-3a+1)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2Cs , 3B
$1$
\( 2^{4} \)
$0.851343954$
$2.843879507$
2.165515227
\( \frac{132583563}{605} a + \frac{166070482}{605} \)
\( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( -87 \phi - 262\) , \( 1694 \phi - 64\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\phi{x}^{2}+\left(-87\phi-262\right){x}+1694\phi-64$
4455.1-a6
4455.1-a
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
4455.1
\( 3^{4} \cdot 5 \cdot 11 \)
\( 3^{12} \cdot 5^{2} \cdot 11^{2} \)
$1.63243$
$(-2a+1), (-3a+1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2Cs , 3B.1.2
$1$
\( 2^{4} \)
$1$
$3.308588349$
1.479645692
\( \frac{132583563}{605} a + \frac{166070482}{605} \)
\( \bigl[\phi + 1\) , \( 1\) , \( 1\) , \( 46 \phi - 92\) , \( 224 \phi - 410\bigr] \)
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(46\phi-92\right){x}+224\phi-410$
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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.