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-a5
24.1-a
$6$
$8$
\(\Q(\sqrt{51}) \)
$2$
$[2, 0]$
24.1
\( 2^{3} \cdot 3 \)
\( 2^{8} \cdot 3^{14} \)
$2.82492$
$(a-7), (3,a)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$5.080054440$
$37.20447790$
6.616350463
\( \frac{28756228}{3} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -101313 a - 723519\) , \( 46145736 a + 329546471\bigr] \)
${y}^2+\left(w+1\right){x}{y}={x}^3+\left(w-1\right){x}^2+\left(-101313w-723519\right){x}+46145736w+329546471$
24.1-b5
24.1-b
$6$
$8$
\(\Q(\sqrt{51}) \)
$2$
$[2, 0]$
24.1
\( 2^{3} \cdot 3 \)
\( 2^{8} \cdot 3^{2} \)
$2.82492$
$(a-7), (3,a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$5.683508517$
0.795850378
\( \frac{28756228}{3} \)
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -11254 a - 80340\) , \( -1799688 a - 12852312\bigr] \)
${y}^2+\left(w+1\right){x}{y}={x}^3+\left(-11254w-80340\right){x}-1799688w-12852312$
24.1-c5
24.1-c
$6$
$8$
\(\Q(\sqrt{51}) \)
$2$
$[2, 0]$
24.1
\( 2^{3} \cdot 3 \)
\( 2^{8} \cdot 3^{14} \)
$2.82492$
$(a-7), (3,a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$2.984607485$
$5.683508517$
4.750601994
\( \frac{28756228}{3} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -101314 a - 723545\) , \( -47679881 a - 340502467\bigr] \)
${y}^2+\left(w+1\right){x}{y}+\left(w+1\right){y}={x}^3+\left(w-1\right){x}^2+\left(-101314w-723545\right){x}-47679881w-340502467$
24.1-d5
24.1-d
$6$
$8$
\(\Q(\sqrt{51}) \)
$2$
$[2, 0]$
24.1
\( 2^{3} \cdot 3 \)
\( 2^{8} \cdot 3^{2} \)
$2.82492$
$(a-7), (3,a)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$37.20447790$
0.651208618
\( \frac{28756228}{3} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -11264 a - 80357\) , \( 1698361 a + 12128915\bigr] \)
${y}^2+\left(w+1\right){x}{y}+\left(w+1\right){y}={x}^3+\left(-w+1\right){x}^2+\left(-11264w-80357\right){x}+1698361w+12128915$
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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.