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
14.1-a1
14.1-a
$3$
$9$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
14.1
\( 2 \cdot 7 \)
\( - 2^{3} \cdot 7 \)
$1.33889$
$(2,a+1), (7,a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$9$
\( 3 \)
$1$
$0.760182873$
2.649758048
\( -\frac{632235090508565}{28} a - \frac{2448631469962925}{28} \)
\( \bigl[a\) , \( 1\) , \( 1\) , \( 5060 a - 19593\) , \( 393664 a - 1524653\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(5060a-19593\right){x}+393664a-1524653$
14.1-b1
14.1-b
$3$
$9$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
14.1
\( 2 \cdot 7 \)
\( - 2^{15} \cdot 7 \)
$1.33889$
$(2,a+1), (7,a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$9$
\( 1 \)
$1$
$0.760182873$
0.883252682
\( -\frac{632235090508565}{28} a - \frac{2448631469962925}{28} \)
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 287 a - 1415\) , \( 6278 a - 27239\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(287a-1415\right){x}+6278a-27239$
14.1-c1
14.1-c
$3$
$9$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
14.1
\( 2 \cdot 7 \)
\( - 2^{15} \cdot 7 \)
$1.33889$
$(2,a+1), (7,a+1)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 1 \)
$2.462835309$
$23.86614358$
1.686279194
\( -\frac{632235090508565}{28} a - \frac{2448631469962925}{28} \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 283 a - 1426\) , \( -5422 a + 22972\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(283a-1426\right){x}-5422a+22972$
14.1-d1
14.1-d
$3$
$9$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
14.1
\( 2 \cdot 7 \)
\( - 2^{3} \cdot 7 \)
$1.33889$
$(2,a+1), (7,a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 3 \)
$0.127739386$
$23.86614358$
2.361471463
\( -\frac{632235090508565}{28} a - \frac{2448631469962925}{28} \)
\( \bigl[1\) , \( 1\) , \( a\) , \( 5060 a - 19600\) , \( -383543 a + 1485452\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(5060a-19600\right){x}-383543a+1485452$
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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.