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
49.2-a1
49.2-a
$4$
$10$
4.4.725.1
$4$
$[4, 0]$
49.2
\( 7^{2} \)
\( - 7^{20} \)
$3.91365$
$(a^2+a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.4[2]
$25$
\( 2 \)
$1$
$1.529162171$
0.709895716
\( -\frac{1193439842515136061069547}{282475249} a^{3} + \frac{313110512005426696931835}{282475249} a^{2} + \frac{3811282462382714725362911}{282475249} a + \frac{1617915718191536947748889}{282475249} \)
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - 4 a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( 427 a^{3} - 605 a^{2} - 535 a - 162\) , \( 6328 a^{3} - 10800 a^{2} - 5249 a + 192\bigr] \)
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(a^{3}-4a+1\right){x}^{2}+\left(427a^{3}-605a^{2}-535a-162\right){x}+6328a^{3}-10800a^{2}-5249a+192$
49.2-a2
49.2-a
$4$
$10$
4.4.725.1
$4$
$[4, 0]$
49.2
\( 7^{2} \)
\( - 7^{4} \)
$3.91365$
$(a^2+a-3)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.1[2]
$1$
\( 2 \)
$1$
$955.7263573$
0.709895716
\( \frac{161387418421454}{49} a^{3} + \frac{176766655197752}{49} a^{2} - \frac{113784125852197}{49} a - \frac{77023745174588}{49} \)
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - 4 a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( -3 a^{3} + 5 a^{2} - 2\) , \( -18 a^{3} + 42 a^{2} - 2 a - 14\bigr] \)
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(a^{3}-4a+1\right){x}^{2}+\left(-3a^{3}+5a^{2}-2\right){x}-18a^{3}+42a^{2}-2a-14$
49.2-a3
49.2-a
$4$
$10$
4.4.725.1
$4$
$[4, 0]$
49.2
\( 7^{2} \)
\( 7^{2} \)
$3.91365$
$(a^2+a-3)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.1[2]
$1$
\( 1 \)
$1$
$1911.452714$
0.709895716
\( -\frac{3680716}{7} a^{3} - \frac{3956693}{7} a^{2} + \frac{2572128}{7} a + 248684 \)
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - 4 a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( 2 a^{3} - 5 a^{2} + 3\) , \( -a^{3} + 2 a^{2} - 1\bigr] \)
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(a^{3}-4a+1\right){x}^{2}+\left(2a^{3}-5a^{2}+3\right){x}-a^{3}+2a^{2}-1$
49.2-a4
49.2-a
$4$
$10$
4.4.725.1
$4$
$[4, 0]$
49.2
\( 7^{2} \)
\( 7^{10} \)
$3.91365$
$(a^2+a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.4[2]
$25$
\( 1 \)
$1$
$3.058324343$
0.709895716
\( \frac{252950065091819511}{16807} a^{3} - \frac{373671346411971114}{16807} a^{2} - \frac{82930605545918026}{2401} a + \frac{530004191810724000}{16807} \)
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - 4 a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( 237 a^{3} - 560 a^{2} + 85 a + 103\) , \( 4228 a^{3} - 10047 a^{2} + 1135 a + 2839\bigr] \)
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(a^{3}-4a+1\right){x}^{2}+\left(237a^{3}-560a^{2}+85a+103\right){x}+4228a^{3}-10047a^{2}+1135a+2839$
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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.