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-b3
7.1-b
$6$
$8$
3.3.733.1
$3$
$[3, 0]$
7.1
\( 7 \)
\( 7^{2} \)
$3.34611$
$(a^2+2a-3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$16$
\( 2 \)
$1$
$11.46979762$
0.847293282
\( -\frac{2353024794450}{49} a^{2} - \frac{434940018425}{49} a + \frac{16016561377497}{49} \)
\( \bigl[a^{2} - 5\) , \( a^{2} - a - 5\) , \( 1\) , \( -32 a^{2} + 131 a - 128\) , \( -442 a^{2} + 1653 a - 1360\bigr] \)
${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-32a^{2}+131a-128\right){x}-442a^{2}+1653a-1360$
49.2-a5
49.2-a
$6$
$8$
3.3.733.1
$3$
$[3, 0]$
49.2
\( 7^{2} \)
\( 7^{8} \)
$4.62796$
$(a^2+2a-3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$16$
\( 2^{2} \)
$1$
$14.65007161$
2.164450966
\( -\frac{2353024794450}{49} a^{2} - \frac{434940018425}{49} a + \frac{16016561377497}{49} \)
\( \bigl[1\) , \( -a^{2} + 6\) , \( 1\) , \( -50 a^{2} + 159 a - 122\) , \( 535 a^{2} - 2021 a + 1609\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-50a^{2}+159a-122\right){x}+535a^{2}-2021a+1609$
112.3-d5
112.3-d
$6$
$8$
3.3.733.1
$3$
$[3, 0]$
112.3
\( 2^{4} \cdot 7 \)
\( 2^{12} \cdot 7^{2} \)
$5.31162$
$(a^2-6), (a^2+2a-3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$4$
\( 2^{3} \)
$1$
$19.38022309$
1.431649745
\( -\frac{2353024794450}{49} a^{2} - \frac{434940018425}{49} a + \frac{16016561377497}{49} \)
\( \bigl[a\) , \( a^{2} - 5\) , \( a^{2} - 4\) , \( -1387 a^{2} - 2108 a + 4408\) , \( -52665 a^{2} - 79956 a + 167308\bigr] \)
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-1387a^{2}-2108a+4408\right){x}-52665a^{2}-79956a+167308$
175.2-c5
175.2-c
$6$
$8$
3.3.733.1
$3$
$[3, 0]$
175.2
\( 5^{2} \cdot 7 \)
\( 5^{6} \cdot 7^{2} \)
$5.72177$
$(-a+3), (a^2+2a-3)$
$2$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$0.297832680$
$72.40181375$
3.584118192
\( -\frac{2353024794450}{49} a^{2} - \frac{434940018425}{49} a + \frac{16016561377497}{49} \)
\( \bigl[a + 1\) , \( a^{2} + a - 4\) , \( a^{2} + a - 4\) , \( -21 a^{2} + 22 a - 5\) , \( -30 a^{2} - 338 a + 452\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-21a^{2}+22a-5\right){x}-30a^{2}-338a+452$
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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.