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
7.1-a1
7.1-a
$2$
$3$
3.3.733.1
$3$
$[3, 0]$
7.1
\( 7 \)
\( - 7^{9} \)
$3.34611$
$(a^2+2a-3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 3^{2} \)
$1$
$3.407152534$
1.132614452
\( -\frac{16146410084579303}{40353607} a^{2} - \frac{24513786018922996}{40353607} a + \frac{51294295430574624}{40353607} \)
\( \bigl[a^{2} + a - 4\) , \( a^{2} + a - 6\) , \( a + 1\) , \( 77 a^{2} + 9 a - 494\) , \( 499 a^{2} + 93 a - 3377\bigr] \)
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(77a^{2}+9a-494\right){x}+499a^{2}+93a-3377$
49.2-b1
49.2-b
$2$
$3$
3.3.733.1
$3$
$[3, 0]$
49.2
\( 7^{2} \)
\( - 7^{15} \)
$4.62796$
$(a^2+2a-3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$9$
\( 2 \)
$1$
$1.224374221$
0.814019287
\( -\frac{16146410084579303}{40353607} a^{2} - \frac{24513786018922996}{40353607} a + \frac{51294295430574624}{40353607} \)
\( \bigl[a^{2} - 4\) , \( -a^{2} + a + 4\) , \( a^{2} - 5\) , \( 41 a^{2} - 4 a - 258\) , \( 302 a^{2} + 68 a - 2098\bigr] \)
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(41a^{2}-4a-258\right){x}+302a^{2}+68a-2098$
112.3-e2
112.3-e
$2$
$3$
3.3.733.1
$3$
$[3, 0]$
112.3
\( 2^{4} \cdot 7 \)
\( - 2^{12} \cdot 7^{9} \)
$5.31162$
$(a^2-6), (a^2+2a-3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$9$
\( 1 \)
$1$
$1.619694851$
0.538423149
\( -\frac{16146410084579303}{40353607} a^{2} - \frac{24513786018922996}{40353607} a + \frac{51294295430574624}{40353607} \)
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 5\) , \( a\) , \( -244 a^{2} - 399 a + 707\) , \( -4901 a^{2} - 7610 a + 15107\bigr] \)
${y}^2+\left(a^{2}+a-4\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-244a^{2}-399a+707\right){x}-4901a^{2}-7610a+15107$
175.2-a1
175.2-a
$2$
$3$
3.3.733.1
$3$
$[3, 0]$
175.2
\( 5^{2} \cdot 7 \)
\( - 5^{6} \cdot 7^{9} \)
$5.72177$
$(-a+3), (a^2+2a-3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 3^{2} \)
$1$
$4.761309222$
1.582766718
\( -\frac{16146410084579303}{40353607} a^{2} - \frac{24513786018922996}{40353607} a + \frac{51294295430574624}{40353607} \)
\( \bigl[a\) , \( a^{2} + a - 5\) , \( a^{2} + a - 5\) , \( 33 a^{2} + a - 225\) , \( -218 a^{2} - 51 a + 1450\bigr] \)
${y}^2+a{x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(33a^{2}+a-225\right){x}-218a^{2}-51a+1450$
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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.