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
75.1-a2
75.1-a
$8$
$16$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
75.1
\( 3 \cdot 5^{2} \)
\( 3^{2} \cdot 5^{2} \)
$1.20507$
$(-a+2), (-a), (-a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2 \)
$1$
$31.38702211$
0.856151218
\( -\frac{1}{15} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$
75.1-b2
75.1-b
$8$
$16$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
75.1
\( 3 \cdot 5^{2} \)
\( 3^{2} \cdot 5^{2} \)
$1.20507$
$(-a+2), (-a), (-a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2 \)
$0.689178076$
$10.19195692$
1.532778450
\( -\frac{1}{15} \)
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 2 a + 4\) , \( 6 a - 10\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+4\right){x}+6a-10$
225.1-a2
225.1-a
$8$
$16$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
225.1
\( 3^{2} \cdot 5^{2} \)
\( 3^{8} \cdot 5^{2} \)
$1.58597$
$(-a+2), (-a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$10.32626388$
2.253375518
\( -\frac{1}{15} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 4 a + 7\) , \( a + 12\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4a+7\right){x}+a+12$
225.1-b2
225.1-b
$8$
$16$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
225.1
\( 3^{2} \cdot 5^{2} \)
\( 3^{8} \cdot 5^{2} \)
$1.58597$
$(-a+2), (-a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$10.32626388$
2.253375518
\( -\frac{1}{15} \)
\( \bigl[a\) , \( a\) , \( 1\) , \( a + 3\) , \( 3 a + 5\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(a+3\right){x}+3a+5$
1875.1-u2
1875.1-u
$8$
$16$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1875.1
\( 3 \cdot 5^{4} \)
\( 3^{2} \cdot 5^{14} \)
$2.69463$
$(-a+2), (-a), (-a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{5} \)
$1$
$2.038391385$
0.889626935
\( -\frac{1}{15} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -4 a - 5\) , \( -561 a - 1005\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a-5\right){x}-561a-1005$
1875.1-x2
1875.1-x
$8$
$16$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1875.1
\( 3 \cdot 5^{4} \)
\( 3^{2} \cdot 5^{14} \)
$2.69463$
$(-a+2), (-a), (-a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$0.654479105$
$6.277404423$
3.586131735
\( -\frac{1}{15} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 23\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}+23$
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Pari/GP
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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.