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-a3
28.1-a
$6$
$18$
\(\Q(\sqrt{105}) \)
$2$
$[2, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( 2^{24} \cdot 7^{6} \)
$2.10631$
$(2,a), (2,a+1), (7,a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3Cs
$1$
\( 2^{3} \)
$1$
$7.027708105$
1.371668170
\( \frac{9938375}{21952} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( -48 a + 297\) , \( -819 a + 4634\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-48a+297\right){x}-819a+4634$
28.1-b3
28.1-b
$6$
$18$
\(\Q(\sqrt{105}) \)
$2$
$[2, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( 2^{24} \cdot 7^{6} \)
$2.10631$
$(2,a), (2,a+1), (7,a+3)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3Cs.1.1
$1$
\( 2^{3} \cdot 3^{3} \)
$0.625416265$
$7.027708105$
5.147181506
\( \frac{9938375}{21952} \)
\( \bigl[a\) , \( 0\) , \( 0\) , \( -331614 a + 1864844\) , \( -395481484 a + 2223980408\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-331614a+1864844\right){x}-395481484a+2223980408$
28.1-c3
28.1-c
$6$
$18$
\(\Q(\sqrt{105}) \)
$2$
$[2, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( 2^{12} \cdot 7^{6} \)
$2.10631$
$(2,a), (2,a+1), (7,a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3Cs
$1$
\( 2^{3} \cdot 3^{2} \)
$1$
$3.925715946$
6.895991662
\( \frac{9938375}{21952} \)
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -2939 a + 16532\) , \( 334628 a - 1881779\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2939a+16532\right){x}+334628a-1881779$
28.1-d3
28.1-d
$6$
$18$
\(\Q(\sqrt{105}) \)
$2$
$[2, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( 2^{12} \cdot 7^{6} \)
$2.10631$
$(2,a), (2,a+1), (7,a+3)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3Cs.1.1
$1$
\( 2^{3} \cdot 3 \)
$2.177164227$
$3.925715946$
1.112126396
\( \frac{9938375}{21952} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$
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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.