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
25.2-a1
25.2-a
$2$
$5$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
25.2
\( 5^{2} \)
\( 5^{2} \)
$0.97888$
$(-a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.1
$1$
\( 1 \)
$1$
$10.14732862$
2.071314782
\( -118784 a - 290816 \)
\( \bigl[0\) , \( -1\) , \( a + 1\) , \( -a - 2\) , \( -a - 3\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-a-2\right){x}-a-3$
25.2-c1
25.2-c
$2$
$5$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
25.2
\( 5^{2} \)
\( 5^{2} \)
$0.97888$
$(-a+1)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.1
$1$
\( 1 \)
$1$
$29.38675386$
0.239941840
\( -118784 a - 290816 \)
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -3 a + 8\) , \( 13 a - 32\bigr] \)
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a+8\right){x}+13a-32$
225.2-c1
225.2-c
$2$
$5$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
225.2
\( 3^{2} \cdot 5^{2} \)
\( 3^{6} \cdot 5^{8} \)
$1.69547$
$(a+3), (-a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.1
$1$
\( 3 \)
$1$
$1.795632472$
1.099595830
\( -118784 a - 290816 \)
\( \bigl[0\) , \( a\) , \( 1\) , \( -61 a - 147\) , \( -455 a - 1116\bigr] \)
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-61a-147\right){x}-455a-1116$
225.2-h1
225.2-h
$2$
$5$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
225.2
\( 3^{2} \cdot 5^{2} \)
\( 3^{6} \cdot 5^{8} \)
$1.69547$
$(a+3), (-a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.1
$1$
\( 1 \)
$1$
$11.07119833$
2.259898897
\( -118784 a - 290816 \)
\( \bigl[0\) , \( a\) , \( a + 1\) , \( -9 a + 21\) , \( -62 a + 149\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-9a+21\right){x}-62a+149$
400.2-d1
400.2-d
$2$
$5$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
400.2
\( 2^{4} \cdot 5^{2} \)
\( 2^{12} \cdot 5^{2} \)
$1.95776$
$(-a+2), (-a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.1
$1$
\( 1 \)
$1$
$14.69337693$
2.999273006
\( -118784 a - 290816 \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -10 a + 25\) , \( 69 a - 169\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a+25\right){x}+69a-169$
400.2-j1
400.2-j
$2$
$5$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
400.2
\( 2^{4} \cdot 5^{2} \)
\( 2^{12} \cdot 5^{2} \)
$1.95776$
$(-a+2), (-a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.1
$1$
\( 1 \)
$1$
$5.073664312$
1.035657391
\( -118784 a - 290816 \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -4 a - 9\) , \( -8 a - 19\bigr] \)
${y}^2={x}^{3}+{x}^{2}+\left(-4a-9\right){x}-8a-19$
625.1-c1
625.1-c
$2$
$5$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
625.1
\( 5^{4} \)
\( 5^{14} \)
$2.18884$
$(-a-1), (-a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.1
$1$
\( 2 \)
$1.220999155$
$2.029465725$
2.023258879
\( -118784 a - 290816 \)
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( -25 a - 58\) , \( -113 a - 270\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-25a-58\right){x}-113a-270$
625.1-f1
625.1-f
$2$
$5$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
625.1
\( 5^{4} \)
\( 5^{14} \)
$2.18884$
$(-a-1), (-a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.4
$1$
\( 2 \cdot 3 \)
$0.511080379$
$5.877350772$
7.357774015
\( -118784 a - 290816 \)
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -59 a + 144\) , \( 1183 a - 2897\bigr] \)
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-59a+144\right){x}+1183a-2897$
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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.