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
1875.1-a2
1875.1-a
$2$
$5$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
1875.1
\( 3 \cdot 5^{4} \)
\( 3^{10} \cdot 5^{16} \)
$2.03695$
$(a), (5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.1.4
$1$
\( 2 \cdot 3 \)
$1$
$1.967118283$
3.407148812
\( \frac{20480}{243} \)
\( \bigl[0\) , \( a - 1\) , \( a\) , \( -2334 a + 4043\) , \( -354472 a + 613963\bigr] \)
${y}^2+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2334a+4043\right){x}-354472a+613963$
1875.1-b2
1875.1-b
$2$
$5$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
1875.1
\( 3 \cdot 5^{4} \)
\( 3^{10} \cdot 5^{4} \)
$2.03695$
$(a), (5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.4.1
$1$
\( 2 \)
$1$
$4.360907218$
2.517770956
\( \frac{20480}{243} \)
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -94 a + 163\) , \( 2938 a - 5089\bigr] \)
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-94a+163\right){x}+2938a-5089$
1875.1-e2
1875.1-e
$2$
$5$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
1875.1
\( 3 \cdot 5^{4} \)
\( 3^{10} \cdot 5^{4} \)
$2.03695$
$(a), (5)$
$1$
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.1.1
$1$
\( 2 \cdot 5 \)
$0.918330811$
$9.835591419$
2.085926488
\( \frac{20480}{243} \)
\( \bigl[0\) , \( -a + 1\) , \( a\) , \( -94 a + 163\) , \( -2938 a + 5088\bigr] \)
${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-94a+163\right){x}-2938a+5088$
1875.1-f2
1875.1-f
$2$
$5$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
1875.1
\( 3 \cdot 5^{4} \)
\( 3^{10} \cdot 5^{16} \)
$2.03695$
$(a), (5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.4.1
$1$
\( 2 \cdot 3 \cdot 5 \)
$0.127940452$
$0.872181443$
1.932748529
\( \frac{20480}{243} \)
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -2334 a + 4043\) , \( 354472 a - 613964\bigr] \)
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2334a+4043\right){x}+354472a-613964$
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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.