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-a2
15.1-a
$8$
$16$
\(\Q(\sqrt{105}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 2^{12} \cdot 3^{2} \cdot 5^{2} \)
$1.80201$
$(3,a+1), (2a-11)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$2.756712307$
$10.19195692$
1.370958724
\( -\frac{1}{15} \)
\( \bigl[a\) , \( 0\) , \( 0\) , \( -13023 a - 60202\) , \( -294878872 a - 1363365200\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-13023a-60202\right){x}-294878872a-1363365200$
15.1-b2
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
\( -\frac{1}{15} \)
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -13 a - 54\) , \( 9992 a + 46191\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-13a-54\right){x}+9992a+46191$
15.1-c2
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
\( -\frac{1}{15} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$
15.1-d2
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
$1$
\( 2^{2} \)
$1$
$10.19195692$
0.994633150
\( -\frac{1}{15} \)
\( \bigl[a\) , \( -a\) , \( 0\) , \( -5 a + 10\) , \( -540 a - 2460\bigr] \)
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-5a+10\right){x}-540a-2460$
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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.