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
49.1-a1
49.1-a
$2$
$3$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
49.1
\( 7^{2} \)
\( 7^{8} \)
$1.08342$
$(a+3)$
0
$\mathsf{trivial}$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
$7$
7Cs.1.2
$1$
\( 1 \)
$1$
$7.676076964$
1.675057320
\( 0 \)
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( a + 2\) , \( 5 a - 16\bigr] \)
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}+5a-16$
49.1-a2
49.1-a
$2$
$3$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
49.1
\( 7^{2} \)
\( 7^{8} \)
$1.08342$
$(a+3)$
0
$\mathsf{trivial}$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
$7$
7Cs.1.2
$1$
\( 1 \)
$1$
$7.676076964$
1.675057320
\( 0 \)
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( a + 2\) , \( -5 a - 9\bigr] \)
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}-5a-9$
49.1-b1
49.1-b
$4$
$14$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
49.1
\( 7^{2} \)
\( 7^{6} \)
$1.08342$
$(a+3)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
✓
$7$
7B.1.2
$1$
\( 2^{2} \)
$0.109590133$
$26.16385905$
1.251392664
\( -3375 \)
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 10 a - 28\) , \( -24 a + 67\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(10a-28\right){x}-24a+67$
49.1-b2
49.1-b
$4$
$14$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
49.1
\( 7^{2} \)
\( 7^{6} \)
$1.08342$
$(a+3)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
✓
$7$
7B.1.5
$1$
\( 2^{2} \)
$0.767130934$
$3.737694151$
1.251392664
\( -3375 \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -2\) , \( -1\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-2{x}-1$
49.1-b3
49.1-b
$4$
$14$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
49.1
\( 7^{2} \)
\( 7^{6} \)
$1.08342$
$(a+3)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-28$
$N(\mathrm{U}(1))$
✓
✓
✓
$7$
7B.1.2
$1$
\( 2 \)
$0.219180266$
$26.16385905$
1.251392664
\( 16581375 \)
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 185 a - 518\) , \( -1872 a + 5226\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(185a-518\right){x}-1872a+5226$
49.1-b4
49.1-b
$4$
$14$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
49.1
\( 7^{2} \)
\( 7^{6} \)
$1.08342$
$(a+3)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-28$
$N(\mathrm{U}(1))$
✓
✓
✓
$7$
7B.1.5
$1$
\( 2 \)
$1.534261868$
$3.737694151$
1.251392664
\( 16581375 \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -37\) , \( -78\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-37{x}-78$
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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.