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
28.1-a1
28.1-a
$1$
$1$
4.4.18736.1
$4$
$[4, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( - 2^{10} \cdot 7^{8} \)
$18.55119$
$(a^2-a-2), (-a^2+a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$1$
$118.5765875$
1.732568861
\( \frac{738092002225}{23059204} a^{3} - \frac{607944512351}{6588344} a^{2} - \frac{3532776509883}{46118408} a + \frac{8686252915607}{46118408} \)
\( \bigl[a^{3} - 2 a^{2} - 3 a + 3\) , \( -a^{3} + a^{2} + 4 a + 2\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( -8 a^{3} + 19 a^{2} + 28 a - 32\) , \( -24 a^{3} + 59 a^{2} + 70 a - 125\bigr] \)
${y}^2+\left(a^{3}-2a^{2}-3a+3\right){x}{y}+\left(a^{3}-2a^{2}-2a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+2\right){x}^{2}+\left(-8a^{3}+19a^{2}+28a-32\right){x}-24a^{3}+59a^{2}+70a-125$
28.1-b1
28.1-b
$1$
$1$
4.4.18736.1
$4$
$[4, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( - 2^{10} \cdot 7^{8} \)
$18.55119$
$(a^2-a-2), (-a^2+a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \cdot 5 \)
$0.030411820$
$367.4328612$
3.265441906
\( \frac{738092002225}{23059204} a^{3} - \frac{607944512351}{6588344} a^{2} - \frac{3532776509883}{46118408} a + \frac{8686252915607}{46118408} \)
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( -a^{3} + 3 a^{2} + 2 a - 6\) , \( a^{2} - 3\) , \( -4 a^{3} + 9 a^{2} + 13 a - 10\) , \( -17 a^{3} - 9 a^{2} + 131 a + 165\bigr] \)
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-6\right){x}^{2}+\left(-4a^{3}+9a^{2}+13a-10\right){x}-17a^{3}-9a^{2}+131a+165$
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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.