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-b1
10.1-b
$2$
$5$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( - 2^{10} \cdot 5^{5} \)
$1.18914$
$(-a+4), (-a+3)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.1
$1$
\( 2 \cdot 5^{2} \)
$1$
$8.284026412$
2.213999186
\( \frac{73603923}{100000} a + \frac{358833109}{100000} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -27 a - 102\) , \( -216 a - 811\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-27a-102\right){x}-216a-811$
10.1-c1
10.1-c
$2$
$5$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( - 2^{10} \cdot 5^{5} \)
$1.18914$
$(-a+4), (-a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.1
$1$
\( 2 \cdot 5 \)
$0.054400494$
$14.16313473$
2.059198521
\( \frac{73603923}{100000} a + \frac{358833109}{100000} \)
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -5 a + 29\) , \( -20 a + 81\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-5a+29\right){x}-20a+81$
80.1-a1
80.1-a
$2$
$5$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
80.1
\( 2^{4} \cdot 5 \)
\( - 2^{22} \cdot 5^{5} \)
$1.99989$
$(-a+4), (-a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B.4.1
$1$
\( 2 \cdot 5 \)
$0.166708413$
$7.081567369$
3.155170927
\( \frac{73603923}{100000} a + \frac{358833109}{100000} \)
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -22 a + 97\) , \( -139 a + 535\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-22a+97\right){x}-139a+535$
80.1-f1
80.1-f
$2$
$5$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
80.1
\( 2^{4} \cdot 5 \)
\( - 2^{22} \cdot 5^{5} \)
$1.99989$
$(-a+4), (-a+3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B.4.1
$1$
\( 2 \)
$1$
$4.142013206$
1.106999593
\( \frac{73603923}{100000} a + \frac{358833109}{100000} \)
\( \bigl[a\) , \( -1\) , \( a\) , \( -115 a - 435\) , \( -1203 a - 4504\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-115a-435\right){x}-1203a-4504$
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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.