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-a1
10.1-a
$2$
$3$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( - 2^{4} \cdot 5 \)
$1.18914$
$(-a+4), (-a+3)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 2 \)
$1$
$36.43104508$
1.081845150
\( \frac{5689}{20} a + \frac{21627}{20} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2 a + 7\) , \( -30 a + 112\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-2a+7\right){x}-30a+112$
10.1-d1
10.1-d
$2$
$3$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( - 2^{4} \cdot 5 \)
$1.18914$
$(-a+4), (-a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 2 \)
$0.115049867$
$20.19548844$
1.241956719
\( \frac{5689}{20} a + \frac{21627}{20} \)
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 3\) , \( 1\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+3{x}+1$
80.1-d1
80.1-d
$2$
$3$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
80.1
\( 2^{4} \cdot 5 \)
\( - 2^{16} \cdot 5 \)
$1.99989$
$(-a+4), (-a+3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2 \)
$1$
$10.09774422$
2.698735661
\( \frac{5689}{20} a + \frac{21627}{20} \)
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( a + 4\) , \( -4 a - 15\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+4\right){x}-4a-15$
80.1-e1
80.1-e
$2$
$3$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
80.1
\( 2^{4} \cdot 5 \)
\( - 2^{16} \cdot 5 \)
$1.99989$
$(-a+4), (-a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2 \)
$0.281972863$
$18.21552254$
2.745458774
\( \frac{5689}{20} a + \frac{21627}{20} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -8 a + 27\) , \( -248 a + 926\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-8a+27\right){x}-248a+926$
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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.