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
504.1-v4
504.1-v
$6$
$8$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
504.1
\( 2^{3} \cdot 3^{2} \cdot 7 \)
\( 2^{4} \cdot 3^{12} \cdot 7^{4} \)
$2.24040$
$(a+3), (-a+2), (-a-2), (a)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{4} \cdot 3^{2} \)
$0.498256261$
$2.871513647$
4.866952851
\( \frac{6940769488}{35721} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 3028 a - 8010\) , \( 143877 a - 380662\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3028a-8010\right){x}+143877a-380662$
504.1-w4
504.1-w
$6$
$8$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
504.1
\( 2^{3} \cdot 3^{2} \cdot 7 \)
\( 2^{4} \cdot 3^{12} \cdot 7^{4} \)
$2.24040$
$(a+3), (-a+2), (-a-2), (a)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{5} \)
$1$
$10.77881089$
1.018501895
\( \frac{6940769488}{35721} \)
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 3029 a - 8009\) , \( -148859 a + 393848\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(3029a-8009\right){x}-148859a+393848$
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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.