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-a7
15.1-a
$8$
$16$
\(\Q(\sqrt{105}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \)
$1.80201$
$(3,a+1), (2a-11)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$2.756712307$
$2.547989231$
1.370958724
\( \frac{56667352321}{15} \)
\( \bigl[a\) , \( 0\) , \( 0\) , \( -50025583 a - 231292042\) , \( -436078729470 a - 2016199270740\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-50025583a-231292042\right){x}-436078729470a-2016199270740$
15.1-b7
15.1-b
$8$
$16$
\(\Q(\sqrt{105}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 3^{2} \cdot 5^{2} \)
$1.80201$
$(3,a+1), (2a-11)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$31.38702211$
3.063059717
\( \frac{56667352321}{15} \)
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -52493 a - 242694\) , \( 14698280 a + 67957129\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-52493a-242694\right){x}+14698280a+67957129$
15.1-c7
15.1-c
$8$
$16$
\(\Q(\sqrt{105}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 3^{2} \cdot 5^{2} \)
$1.80201$
$(3,a+1), (2a-11)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$0.654479105$
$31.38702211$
1.002354292
\( \frac{56667352321}{15} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$
15.1-d7
15.1-d
$8$
$16$
\(\Q(\sqrt{105}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \)
$1.80201$
$(3,a+1), (2a-11)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$4$
\( 2^{2} \)
$1$
$2.547989231$
0.994633150
\( \frac{56667352321}{15} \)
\( \bigl[a\) , \( -a\) , \( 0\) , \( -7445 a - 34390\) , \( -796682 a - 3683408\bigr] \)
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-7445a-34390\right){x}-796682a-3683408$
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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.