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
1.1-a1
1.1-a
$4$
$14$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 1 \)
$0.66870$
$\textsf{none}$
0
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 1 \)
$1$
$26.16385905$
0.874073183
\( -3375 \)
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 2 a + 10\) , \( 2 a + 7\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(2a+10\right){x}+2a+7$
1.1-a2
1.1-a
$4$
$14$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 1 \)
$0.66870$
$\textsf{none}$
0
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 1 \)
$1$
$26.16385905$
0.874073183
\( -3375 \)
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 4 a + 3\) , \( a + 21\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(4a+3\right){x}+a+21$
16.1-a1
16.1-a
$4$
$14$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
16.1
\( 2^{4} \)
\( 2^{12} \)
$1.33740$
$(-a+4)$
0
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2^{2} \)
$1$
$13.08192952$
1.748146366
\( -3375 \)
\( \bigl[a\) , \( 1\) , \( a\) , \( -5 a - 19\) , \( 7 a + 26\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-5a-19\right){x}+7a+26$
16.1-a2
16.1-a
$4$
$14$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
16.1
\( 2^{4} \)
\( 2^{12} \)
$1.33740$
$(-a+4)$
0
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2^{2} \)
$1$
$13.08192952$
1.748146366
\( -3375 \)
\( \bigl[a\) , \( 1\) , \( a\) , \( 5 a - 19\) , \( -7 a + 26\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(5a-19\right){x}-7a+26$
49.1-a1
49.1-a
$4$
$14$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
49.1
\( 7^{2} \)
\( 7^{6} \)
$1.76922$
$(-2a+7)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
✓
$7$
7B.1.5
$1$
\( 2 \)
$6.543119480$
$3.737694151$
3.268094441
\( -3375 \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -2\) , \( -1\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-2{x}-1$
49.1-a2
49.1-a
$4$
$14$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
49.1
\( 7^{2} \)
\( 7^{6} \)
$1.76922$
$(-2a+7)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
✓
$7$
7B.1.2
$1$
\( 2 \)
$0.934731354$
$26.16385905$
3.268094441
\( -3375 \)
\( \bigl[1\) , \( -1\) , \( a\) , \( 262 a - 982\) , \( -5572 a + 20845\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(262a-982\right){x}-5572a+20845$
81.1-a1
81.1-a
$4$
$14$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
81.1
\( 3^{4} \)
\( 3^{12} \)
$2.00611$
$(3)$
0
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2^{2} \)
$1$
$8.721286352$
1.165430910
\( -3375 \)
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 15 a - 27\) , \( 46 a - 142\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(15a-27\right){x}+46a-142$
81.1-a2
81.1-a
$4$
$14$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
81.1
\( 3^{4} \)
\( 3^{12} \)
$2.00611$
$(3)$
0
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2^{2} \)
$1$
$8.721286352$
1.165430910
\( -3375 \)
\( \bigl[a + 1\) , \( a\) , \( a\) , \( -8 a - 34\) , \( -80 a - 303\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-8a-34\right){x}-80a-303$
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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.