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
35.1-a1
35.1-a
$3$
$9$
\(\Q(\sqrt{105}) \)
$2$
$[2, 0]$
35.1
\( 5 \cdot 7 \)
\( 5^{18} \cdot 7^{2} \)
$2.22715$
$(2a-11), (7,a+3)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B
$1$
\( 2^{2} \)
$3.380268306$
$0.494084210$
2.607819218
\( -\frac{250523582464}{13671875} \)
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -86155 a - 398325\) , \( -32460825 a - 150081819\bigr] \)
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-86155a-398325\right){x}-32460825a-150081819$
35.1-b1
35.1-b
$3$
$9$
\(\Q(\sqrt{105}) \)
$2$
$[2, 0]$
35.1
\( 5 \cdot 7 \)
\( 2^{12} \cdot 5^{18} \cdot 7^{2} \)
$2.22715$
$(2a-11), (7,a+3)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.1
$1$
\( 2^{2} \cdot 3^{2} \)
$1$
$4.862220259$
1.898016442
\( -\frac{250523582464}{13671875} \)
\( \bigl[0\) , \( 1\) , \( a\) , \( -12214 a - 56473\) , \( 1735781 a + 8025336\bigr] \)
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(-12214a-56473\right){x}+1735781a+8025336$
35.1-c1
35.1-c
$3$
$9$
\(\Q(\sqrt{105}) \)
$2$
$[2, 0]$
35.1
\( 5 \cdot 7 \)
\( 2^{12} \cdot 5^{18} \cdot 7^{2} \)
$2.22715$
$(2a-11), (7,a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B
$1$
\( 2^{2} \cdot 3^{2} \)
$0.040819755$
$4.862220259$
1.394578218
\( -\frac{250523582464}{13671875} \)
\( \bigl[0\) , \( a\) , \( a\) , \( 1445 a - 8134\) , \( -73135 a + 411269\bigr] \)
${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(1445a-8134\right){x}-73135a+411269$
35.1-d1
35.1-d
$3$
$9$
\(\Q(\sqrt{105}) \)
$2$
$[2, 0]$
35.1
\( 5 \cdot 7 \)
\( 5^{18} \cdot 7^{2} \)
$2.22715$
$(2a-11), (7,a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.2
$1$
\( 2^{2} \)
$7.121947793$
$0.494084210$
2.747230492
\( -\frac{250523582464}{13671875} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -131\) , \( -650\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}-131{x}-650$
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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.