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
24.1-a4
24.1-a
$6$
$8$
\(\Q(\sqrt{51}) \)
$2$
$[2, 0]$
24.1
\( 2^{3} \cdot 3 \)
\( 2^{8} \cdot 3^{20} \)
$2.82492$
$(a-7), (3,a)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{4} \)
$5.080054440$
$9.301119475$
6.616350463
\( \frac{1556068}{81} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 38336 a - 273635\) , \( 10427941 a - 74469977\bigr] \)
${y}^2+\left(w+1\right){x}{y}+\left(w+1\right){y}={x}^3+\left(w-1\right){x}^2+\left(38336w-273635\right){x}+10427941w-74469977$
24.1-b4
24.1-b
$6$
$8$
\(\Q(\sqrt{51}) \)
$2$
$[2, 0]$
24.1
\( 2^{3} \cdot 3 \)
\( 2^{8} \cdot 3^{8} \)
$2.82492$
$(a-7), (3,a)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{5} \)
$1$
$22.73403407$
0.795850378
\( \frac{1556068}{81} \)
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 4254 a - 30350\) , \( -362098 a + 2585928\bigr] \)
${y}^2+\left(w+1\right){x}{y}={x}^3-w{x}^2+\left(4254w-30350\right){x}-362098w+2585928$
24.1-c4
24.1-c
$6$
$8$
\(\Q(\sqrt{51}) \)
$2$
$[2, 0]$
24.1
\( 2^{3} \cdot 3 \)
\( 2^{8} \cdot 3^{20} \)
$2.82492$
$(a-7), (3,a)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$2.984607485$
$22.73403407$
4.750601994
\( \frac{1556068}{81} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 38337 a - 273609\) , \( -10394976 a + 74235411\bigr] \)
${y}^2+\left(w+1\right){x}{y}={x}^3+\left(w-1\right){x}^2+\left(38337w-273609\right){x}-10394976w+74235411$
24.1-d4
24.1-d
$6$
$8$
\(\Q(\sqrt{51}) \)
$2$
$[2, 0]$
24.1
\( 2^{3} \cdot 3 \)
\( 2^{8} \cdot 3^{8} \)
$2.82492$
$(a-7), (3,a)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$4$
\( 2^{2} \)
$1$
$9.301119475$
0.651208618
\( \frac{1556068}{81} \)
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 4262 a - 30367\) , \( 400424 a - 2859415\bigr] \)
${y}^2+\left(w+1\right){x}{y}+\left(w+1\right){y}={x}^3+{x}^2+\left(4262w-30367\right){x}+400424w-2859415$
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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.