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
10.1-a2
10.1-a
$4$
$6$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( 2^{6} \cdot 5^{6} \)
$1.23088$
$(2,a+1), (5,a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{2} \)
$1$
$2.483889677$
0.320668778
\( \frac{22896613727}{1000} a - \frac{22169433439}{250} \)
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 27 a - 111\) , \( 260 a - 1010\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(27a-111\right){x}+260a-1010$
10.1-d2
10.1-d
$4$
$6$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( 2^{18} \cdot 5^{6} \)
$1.23088$
$(2,a+1), (5,a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \cdot 3^{2} \)
$1$
$2.483889677$
2.886019006
\( \frac{22896613727}{1000} a - \frac{22169433439}{250} \)
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 7454 a - 28865\) , \( 696920 a - 2699153\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(7454a-28865\right){x}+696920a-2699153$
10.1-e2
10.1-e
$4$
$6$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( 2^{18} \cdot 5^{6} \)
$1.23088$
$(2,a+1), (5,a)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \cdot 3^{2} \)
$1$
$11.26497123$
1.454301533
\( \frac{22896613727}{1000} a - \frac{22169433439}{250} \)
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 7452 a - 28860\) , \( -674560 a + 2612560\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(7452a-28860\right){x}-674560a+2612560$
10.1-h2
10.1-h
$4$
$6$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( 2^{6} \cdot 5^{6} \)
$1.23088$
$(2,a+1), (5,a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1$
$11.26497123$
1.454301533
\( \frac{22896613727}{1000} a - \frac{22169433439}{250} \)
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 31 a - 111\) , \( -202 a + 788\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(31a-111\right){x}-202a+788$
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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.