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
98.1-a5
98.1-a
$12$
$36$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
98.1
\( 2 \cdot 7^{2} \)
\( 2^{6} \cdot 7^{12} \)
$0.79523$
$(a), (-2a+1), (2a+1)$
0
$\Z/2\Z\oplus\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cs , 3Cs.1.1
$1$
\( 2^{3} \cdot 3^{2} \)
$1$
$3.925715946$
0.693975091
\( \frac{4956477625}{941192} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$
686.1-d5
686.1-d
$12$
$36$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
686.1
\( 2 \cdot 7^{3} \)
\( 2^{6} \cdot 7^{18} \)
$1.29349$
$(a), (-2a+1), (2a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2Cs , 3Cs
$1$
\( 2^{4} \cdot 3 \)
$1$
$1.985259457$
2.105685636
\( \frac{4956477625}{941192} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -143 a - 321\) , \( 1534 a + 1743\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-143a-321\right){x}+1534a+1743$
686.2-d5
686.2-d
$12$
$36$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
686.2
\( 2 \cdot 7^{3} \)
\( 2^{6} \cdot 7^{18} \)
$1.29349$
$(a), (-2a+1), (2a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2Cs , 3Cs
$1$
\( 2^{4} \cdot 3 \)
$1$
$1.985259457$
2.105685636
\( \frac{4956477625}{941192} \)
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 141 a - 321\) , \( -1535 a + 1743\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(141a-321\right){x}-1535a+1743$
784.1-a5
784.1-a
$12$
$36$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
784.1
\( 2^{4} \cdot 7^{2} \)
\( 2^{18} \cdot 7^{12} \)
$1.33740$
$(a), (-2a+1), (2a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2Cs , 3Cs
$1$
\( 2^{4} \)
$1$
$3.513854052$
1.242335014
\( \frac{4956477625}{941192} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( -142\) , \( 558\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-142{x}+558$
4802.1-z5
4802.1-z
$12$
$36$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
4802.1
\( 2 \cdot 7^{4} \)
\( 2^{6} \cdot 7^{24} \)
$2.10397$
$(a), (-2a+1), (2a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2Cs , 3Cs
$1$
\( 2^{5} \)
$1$
$1.003958300$
0.709905722
\( \frac{4956477625}{941192} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( -1740\) , \( 22184\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}-1740{x}+22184$
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Pari/GP
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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.