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
15.1-a5
15.1-a
$8$
$16$
\(\Q(\sqrt{105}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 2^{12} \cdot 3^{4} \cdot 5^{4} \)
$1.80201$
$(3,a+1), (2a-11)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1.378356153$
$10.19195692$
1.370958724
\( \frac{13997521}{225} \)
\( \bigl[a\) , \( 0\) , \( 0\) , \( -3138808 a - 14512192\) , \( -6764057685 a - 31273454190\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-3138808a-14512192\right){x}-6764057685a-31273454190$
15.1-b5
15.1-b
$8$
$16$
\(\Q(\sqrt{105}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 3^{4} \cdot 5^{4} \)
$1.80201$
$(3,a+1), (2a-11)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$31.38702211$
3.063059717
\( \frac{13997521}{225} \)
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -3293 a - 15219\) , \( 222095 a + 1026844\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-3293a-15219\right){x}+222095a+1026844$
15.1-c5
15.1-c
$8$
$16$
\(\Q(\sqrt{105}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 3^{4} \cdot 5^{4} \)
$1.80201$
$(3,a+1), (2a-11)$
$1$
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1.308958211$
$31.38702211$
1.002354292
\( \frac{13997521}{225} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$
15.1-d5
15.1-d
$8$
$16$
\(\Q(\sqrt{105}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 2^{12} \cdot 3^{4} \cdot 5^{4} \)
$1.80201$
$(3,a+1), (2a-11)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$4$
\( 2^{2} \)
$1$
$10.19195692$
0.994633150
\( \frac{13997521}{225} \)
\( \bigl[a\) , \( -a\) , \( 0\) , \( -470 a - 2140\) , \( -12617 a - 58298\bigr] \)
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-470a-2140\right){x}-12617a-58298$
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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.