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
14.1-a5
14.1-a
$6$
$18$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
14.1
\( 2 \cdot 7 \)
\( 2^{2} \cdot 7^{4} \)
$1.29349$
$(-a+4), (-2a+7)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{3} \)
$0.701695037$
$35.33144352$
1.472425245
\( \frac{128787625}{98} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$
14.1-b5
14.1-b
$6$
$18$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
14.1
\( 2 \cdot 7 \)
\( 2^{2} \cdot 7^{4} \)
$1.29349$
$(-a+4), (-2a+7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1$
$7.027708105$
0.939116998
\( \frac{128787625}{98} \)
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 1262 a - 4719\) , \( 45312 a - 169541\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1262a-4719\right){x}+45312a-169541$
98.1-a5
98.1-a
$6$
$18$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
98.1
\( 2 \cdot 7^{2} \)
\( 2^{2} \cdot 7^{10} \)
$2.10397$
$(-a+4), (-2a+7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$0.817158102$
$5.955778371$
2.601420732
\( \frac{128787625}{98} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 293 a - 1096\) , \( -4680 a + 17508\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(293a-1096\right){x}-4680a+17508$
98.1-b5
98.1-b
$6$
$18$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
98.1
\( 2 \cdot 7^{2} \)
\( 2^{2} \cdot 7^{10} \)
$2.10397$
$(-a+4), (-2a+7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$0.817158102$
$5.955778371$
2.601420732
\( \frac{128787625}{98} \)
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -293 a - 1096\) , \( 4680 a + 17508\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-293a-1096\right){x}+4680a+17508$
112.1-a5
112.1-a
$6$
$18$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
112.1
\( 2^{4} \cdot 7 \)
\( 2^{14} \cdot 7^{4} \)
$2.17539$
$(-a+4), (-2a+7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{4} \)
$0.194844842$
$17.66572176$
3.679732717
\( \frac{128787625}{98} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -45\) , \( 54\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-45{x}+54$
112.1-f5
112.1-f
$6$
$18$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
112.1
\( 2^{4} \cdot 7 \)
\( 2^{14} \cdot 7^{4} \)
$2.17539$
$(-a+4), (-2a+7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$1$
$3.513854052$
0.939116998
\( \frac{128787625}{98} \)
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 5047 a - 18884\) , \( 391484 a - 1464799\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(5047a-18884\right){x}+391484a-1464799$
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Pari/GP
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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.