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-a1
24.1-a
$6$
$8$
\(\Q(\sqrt{51}) \)
$2$
$[2, 0]$
24.1
\( 2^{3} \cdot 3 \)
\( 2^{10} \cdot 3^{28} \)
$2.82492$
$(a-7), (3,a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{5} \)
$2.540027220$
$2.325279868$
6.616350463
\( \frac{207646}{6561} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 24687 a + 176301\) , \( -41091534 a - 293452249\bigr] \)
${y}^2+\left(w+1\right){x}{y}={x}^3+\left(w-1\right){x}^2+\left(24687w+176301\right){x}-41091534w-293452249$
24.1-b1
24.1-b
$6$
$8$
\(\Q(\sqrt{51}) \)
$2$
$[2, 0]$
24.1
\( 2^{3} \cdot 3 \)
\( 2^{10} \cdot 3^{16} \)
$2.82492$
$(a-7), (3,a)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 2^{5} \)
$1$
$5.683508517$
0.795850378
\( \frac{207646}{6561} \)
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -2746 a + 19640\) , \( -1543982 a + 11026268\bigr] \)
${y}^2+\left(w+1\right){x}{y}={x}^3-w{x}^2+\left(-2746w+19640\right){x}-1543982w+11026268$
24.1-c1
24.1-c
$6$
$8$
\(\Q(\sqrt{51}) \)
$2$
$[2, 0]$
24.1
\( 2^{3} \cdot 3 \)
\( 2^{10} \cdot 3^{28} \)
$2.82492$
$(a-7), (3,a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 2^{2} \)
$1.492303742$
$5.683508517$
4.750601994
\( \frac{207646}{6561} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 24686 a + 176275\) , \( 41465209 a + 296120813\bigr] \)
${y}^2+\left(w+1\right){x}{y}+\left(w+1\right){y}={x}^3+\left(w-1\right){x}^2+\left(24686w+176275\right){x}+41465209w+296120813$
24.1-d1
24.1-d
$6$
$8$
\(\Q(\sqrt{51}) \)
$2$
$[2, 0]$
24.1
\( 2^{3} \cdot 3 \)
\( 2^{10} \cdot 3^{16} \)
$2.82492$
$(a-7), (3,a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 2^{2} \)
$1$
$2.325279868$
0.651208618
\( \frac{207646}{6561} \)
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -2738 a + 19623\) , \( 1519308 a - 10849845\bigr] \)
${y}^2+\left(w+1\right){x}{y}+\left(w+1\right){y}={x}^3+{x}^2+\left(-2738w+19623\right){x}+1519308w-10849845$
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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.