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
3025.2-a1
3025.2-a
$1$
$1$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
3025.2
\( 5^{2} \cdot 11^{2} \)
\( 5^{2} \cdot 11^{6} \)
$1.87441$
$(a+3), (a-3), (5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$3.163441049$
2.236890618
\( -\frac{314878832}{805255} a + \frac{1086200609}{805255} \)
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -3 a - 1\) , \( 2 a\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-3a-1\right){x}+2a$
3025.2-b1
3025.2-b
$1$
$1$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
3025.2
\( 5^{2} \cdot 11^{2} \)
\( 5^{2} \cdot 11^{6} \)
$1.87441$
$(a+3), (a-3), (5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$3.163441049$
2.236890618
\( \frac{314878832}{805255} a + \frac{1086200609}{805255} \)
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 3 a - 1\) , \( -2 a\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(3a-1\right){x}-2a$
3025.2-c1
3025.2-c
$4$
$4$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
3025.2
\( 5^{2} \cdot 11^{2} \)
\( 5^{2} \cdot 11^{2} \)
$1.87441$
$(a+3), (a-3), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 1 \)
$1$
$7.082488443$
1.252018901
\( \frac{59319}{55} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+{x}$
3025.2-c2
3025.2-c
$4$
$4$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
3025.2
\( 5^{2} \cdot 11^{2} \)
\( 5^{4} \cdot 11^{4} \)
$1.87441$
$(a+3), (a-3), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$3.541244221$
1.252018901
\( \frac{8120601}{3025} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -4\) , \( 3\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-4{x}+3$
3025.2-c3
3025.2-c
$4$
$4$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
3025.2
\( 5^{2} \cdot 11^{2} \)
\( 5^{2} \cdot 11^{8} \)
$1.87441$
$(a+3), (a-3), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$1.770622110$
1.252018901
\( \frac{2749884201}{73205} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -29\) , \( -52\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-29{x}-52$
3025.2-c4
3025.2-c
$4$
$4$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
3025.2
\( 5^{2} \cdot 11^{2} \)
\( 5^{8} \cdot 11^{2} \)
$1.87441$
$(a+3), (a-3), (5)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$4$
\( 2^{2} \)
$1$
$1.770622110$
1.252018901
\( \frac{22930509321}{6875} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -59\) , \( 190\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-59{x}+190$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.