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
10.1-a4
10.1-a
$4$
$6$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( 2 \cdot 5 \)
$1.23088$
$(2,a+1), (5,a)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$4$
\( 1 \)
$1$
$22.35500709$
0.320668778
\( \frac{105678766089}{10} a + \frac{81859053049}{2} \)
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 2 a - 21\) , \( 30 a - 116\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a-21\right){x}+30a-116$
10.1-d4
10.1-d
$4$
$6$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( 2^{13} \cdot 5 \)
$1.23088$
$(2,a+1), (5,a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$4$
\( 1 \)
$1$
$22.35500709$
2.886019006
\( \frac{105678766089}{10} a + \frac{81859053049}{2} \)
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 1474 a - 5705\) , \( 61924 a - 239825\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(1474a-5705\right){x}+61924a-239825$
10.1-e4
10.1-e
$4$
$6$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( 2^{13} \cdot 5 \)
$1.23088$
$(2,a+1), (5,a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$4$
\( 1 \)
$1$
$11.26497123$
1.454301533
\( \frac{105678766089}{10} a + \frac{81859053049}{2} \)
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 1472 a - 5700\) , \( -57504 a + 222712\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(1472a-5700\right){x}-57504a+222712$
10.1-h4
10.1-h
$4$
$6$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( 2 \cdot 5 \)
$1.23088$
$(2,a+1), (5,a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$4$
\( 1 \)
$1$
$11.26497123$
1.454301533
\( \frac{105678766089}{10} a + \frac{81859053049}{2} \)
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 6 a - 21\) , \( -22 a + 74\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-21\right){x}-22a+74$
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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.