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
98.2-a2
98.2-a
$4$
$21$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
98.2
\( 2 \cdot 7^{2} \)
\( 2 \cdot 7^{2} \)
$0.79523$
$(a), (-2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3, 7$
3B , 7B.1.3
$1$
\( 1 \)
$1$
$3.477455094$
1.229466039
\( \frac{753047}{2} a - 574009 \)
\( \bigl[1\) , \( a\) , \( 0\) , \( -2\) , \( -a - 2\bigr] \)
${y}^2+{x}{y}={x}^{3}+a{x}^{2}-2{x}-a-2$
98.2-b2
98.2-b
$4$
$21$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
98.2
\( 2 \cdot 7^{2} \)
\( 2 \cdot 7^{8} \)
$0.79523$
$(a), (-2a+1)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$3, 7$
3B.1.1 , 7B.6.3
$1$
\( 3 \)
$1$
$5.822641917$
0.686204930
\( \frac{753047}{2} a - 574009 \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 8 a - 24\) , \( -28 a + 26\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(8a-24\right){x}-28a+26$
784.2-b2
784.2-b
$4$
$21$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
784.2
\( 2^{4} \cdot 7^{2} \)
\( 2^{13} \cdot 7^{8} \)
$1.33740$
$(a), (-2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3, 7$
3B , 7B.6.3
$1$
\( 2 \)
$1$
$2.228183338$
1.575563548
\( \frac{753047}{2} a - 574009 \)
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 38 a - 91\) , \( 257 a - 305\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(38a-91\right){x}+257a-305$
784.2-g2
784.2-g
$4$
$21$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
784.2
\( 2^{4} \cdot 7^{2} \)
\( 2^{13} \cdot 7^{2} \)
$1.33740$
$(a), (-2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3, 7$
3B , 7B.6.3
$1$
\( 2^{2} \)
$0.026132930$
$26.11605138$
1.930370301
\( \frac{753047}{2} a - 574009 \)
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -a - 10\) , \( -2 a + 15\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-10\right){x}-2a+15$
4802.1-f2
4802.1-f
$4$
$21$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
4802.1
\( 2 \cdot 7^{4} \)
\( 2 \cdot 7^{14} \)
$2.10397$
$(a), (-2a+1), (2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3, 7$
3B , 7B.1.4
$1$
\( 1 \)
$1$
$7.461728967$
2.638119576
\( \frac{753047}{2} a - 574009 \)
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -9 a - 131\) , \( 99 a + 541\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-9a-131\right){x}+99a+541$
4802.1-o2
4802.1-o
$4$
$21$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
4802.1
\( 2 \cdot 7^{4} \)
\( 2 \cdot 7^{8} \)
$2.10397$
$(a), (-2a+1), (2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3, 7$
3B , 7B.6.3
$1$
\( 1 \)
$1$
$4.456366676$
1.575563548
\( \frac{753047}{2} a - 574009 \)
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -11 a - 24\) , \( 23 a + 24\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-11a-24\right){x}+23a+24$
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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.