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
56.1-a1
56.1-a
$4$
$4$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
56.1
\( 2^{3} \cdot 7 \)
\( 2^{4} \cdot 7^{2} \)
$1.29349$
$(a+3), (a)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$24.47471212$
1.156321458
\( \frac{432}{7} \)
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 14 a + 36\) , \( 221 a + 584\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(14a+36\right){x}+221a+584$
56.1-d1
56.1-d
$4$
$4$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
56.1
\( 2^{3} \cdot 7 \)
\( 2^{4} \cdot 7^{2} \)
$1.29349$
$(a+3), (a)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1.891959002$
$10.54517411$
1.885195806
\( \frac{432}{7} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 15 a + 40\) , \( -161 a - 426\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(15a+40\right){x}-161a-426$
392.1-b1
392.1-b
$4$
$4$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
392.1
\( 2^{3} \cdot 7^{2} \)
\( 2^{4} \cdot 7^{8} \)
$2.10397$
$(a+3), (a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$6.072068378$
1.147513062
\( \frac{432}{7} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 3 a + 10\) , \( 5 a + 8\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a+10\right){x}+5a+8$
392.1-k1
392.1-k
$4$
$4$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
392.1
\( 2^{3} \cdot 7^{2} \)
\( 2^{4} \cdot 7^{8} \)
$2.10397$
$(a+3), (a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$6.072068378$
1.147513062
\( \frac{432}{7} \)
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 2 a + 6\) , \( a + 6\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+6\right){x}+a+6$
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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.