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-a2
10.1-a
$2$
$3$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( - 2^{12} \cdot 5^{3} \)
$1.18914$
$(-a+4), (-a+3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 2 \)
$1$
$4.047893897$
1.081845150
\( \frac{18258829169}{8000} a + \frac{68318145777}{8000} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( 18 a - 68\) , \( 814 a - 3046\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(18a-68\right){x}+814a-3046$
10.1-d2
10.1-d
$2$
$3$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( - 2^{12} \cdot 5^{3} \)
$1.18914$
$(-a+4), (-a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 2 \cdot 3 \)
$0.038349955$
$20.19548844$
1.241956719
\( \frac{18258829169}{8000} a + \frac{68318145777}{8000} \)
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -20 a - 72\) , \( 128 a + 480\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-20a-72\right){x}+128a+480$
80.1-d2
80.1-d
$2$
$3$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
80.1
\( 2^{4} \cdot 5 \)
\( - 2^{24} \cdot 5^{3} \)
$1.99989$
$(-a+4), (-a+3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2 \)
$1$
$10.09774422$
2.698735661
\( \frac{18258829169}{8000} a + \frac{68318145777}{8000} \)
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -79 a - 296\) , \( 560 a + 2097\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-79a-296\right){x}+560a+2097$
80.1-e2
80.1-e
$2$
$3$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
80.1
\( 2^{4} \cdot 5 \)
\( - 2^{24} \cdot 5^{3} \)
$1.99989$
$(-a+4), (-a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2 \cdot 3 \)
$0.845918590$
$2.023946948$
2.745458774
\( \frac{18258829169}{8000} a + \frac{68318145777}{8000} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( 72 a - 273\) , \( 6584 a - 24638\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(72a-273\right){x}+6584a-24638$
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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.