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
80.1-a4
80.1-a
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
80.1
\( 2^{4} \cdot 5 \)
\( 2^{8} \cdot 5^{2} \)
$0.59758$
$(-2a+1), (2)$
0
$\Z/2\Z\oplus\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2Cs , 3B.1.1
$1$
\( 2 \cdot 3 \)
$1$
$31.90837977$
0.594577551
\( \frac{16384}{5} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \)
${y}^2={x}^{3}+{x}^{2}-{x}$
400.1-a4
400.1-a
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
400.1
\( 2^{4} \cdot 5^{2} \)
\( 2^{8} \cdot 5^{8} \)
$0.89359$
$(-2a+1), (2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2Cs , 3B
$1$
\( 2^{2} \)
$1$
$9.251646022$
1.034365470
\( \frac{16384}{5} \)
\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( -7 \phi - 6\) , \( -6 \phi - 6\bigr] \)
${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-7\phi-6\right){x}-6\phi-6$
1280.1-d4
1280.1-d
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
1280.1
\( 2^{8} \cdot 5 \)
\( 2^{8} \cdot 5^{2} \)
$1.19516$
$(-2a+1), (2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2Cs , 3B
$1$
\( 2 \)
$1$
$25.69238262$
1.436247851
\( \frac{16384}{5} \)
\( \bigl[0\) , \( \phi\) , \( 0\) , \( -\phi - 1\) , \( 0\bigr] \)
${y}^2={x}^{3}+\phi{x}^{2}+\left(-\phi-1\right){x}$
1280.1-f4
1280.1-f
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
1280.1
\( 2^{8} \cdot 5 \)
\( 2^{8} \cdot 5^{2} \)
$1.19516$
$(-2a+1), (2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2Cs , 3B
$1$
\( 2 \)
$1$
$20.68730941$
1.156455752
\( \frac{16384}{5} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( 0\bigr] \)
${y}^2={x}^{3}-{x}^{2}-{x}$
1280.1-k4
1280.1-k
$8$
$12$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
1280.1
\( 2^{8} \cdot 5 \)
\( 2^{8} \cdot 5^{2} \)
$1.19516$
$(-2a+1), (2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2Cs , 3B
$1$
\( 2 \)
$1$
$25.69238262$
1.436247851
\( \frac{16384}{5} \)
\( \bigl[0\) , \( -\phi\) , \( 0\) , \( -\phi - 1\) , \( 0\bigr] \)
${y}^2={x}^{3}-\phi{x}^{2}+\left(-\phi-1\right){x}$
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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.