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-b5
7.1-b
$6$
$8$
3.3.733.1
$3$
$[3, 0]$
7.1
\( 7 \)
\( 7^{4} \)
$3.34611$
$(a^2+2a-3)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$4$
\( 2^{2} \)
$1$
$91.75838097$
0.847293282
\( -\frac{225573007}{2401} a^{2} - \frac{58067834}{2401} a + \frac{1583231073}{2401} \)
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 248 a^{2} + 46 a - 1678\) , \( 3590 a^{2} + 641 a - 24373\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(248a^{2}+46a-1678\right){x}+3590a^{2}+641a-24373$
49.2-a2
49.2-a
$6$
$8$
3.3.733.1
$3$
$[3, 0]$
49.2
\( 7^{2} \)
\( 7^{10} \)
$4.62796$
$(a^2+2a-3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$4$
\( 2^{2} \)
$1$
$58.60028647$
2.164450966
\( -\frac{225573007}{2401} a^{2} - \frac{58067834}{2401} a + \frac{1583231073}{2401} \)
\( \bigl[a^{2} - 5\) , \( a^{2} + a - 5\) , \( a^{2} - 4\) , \( 138 a^{2} + 26 a - 937\) , \( 1439 a^{2} + 257 a - 9772\bigr] \)
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(138a^{2}+26a-937\right){x}+1439a^{2}+257a-9772$
112.3-d2
112.3-d
$6$
$8$
3.3.733.1
$3$
$[3, 0]$
112.3
\( 2^{4} \cdot 7 \)
\( 2^{12} \cdot 7^{4} \)
$5.31162$
$(a^2-6), (a^2+2a-3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$77.52089237$
1.431649745
\( -\frac{225573007}{2401} a^{2} - \frac{58067834}{2401} a + \frac{1583231073}{2401} \)
\( \bigl[a^{2} - 4\) , \( -a^{2} + a + 5\) , \( a^{2} + a - 4\) , \( 3542 a^{2} + 632 a - 24056\) , \( 192487 a^{2} + 34296 a - 1306992\bigr] \)
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(3542a^{2}+632a-24056\right){x}+192487a^{2}+34296a-1306992$
175.2-c3
175.2-c
$6$
$8$
3.3.733.1
$3$
$[3, 0]$
175.2
\( 5^{2} \cdot 7 \)
\( 5^{6} \cdot 7^{4} \)
$5.72177$
$(-a+3), (a^2+2a-3)$
$2$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{4} \)
$0.074458170$
$144.8036275$
3.584118192
\( -\frac{225573007}{2401} a^{2} - \frac{58067834}{2401} a + \frac{1583231073}{2401} \)
\( \bigl[1\) , \( -a^{2} + a + 6\) , \( a\) , \( 115 a^{2} + 19 a - 779\) , \( -877 a^{2} - 156 a + 5952\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(115a^{2}+19a-779\right){x}-877a^{2}-156a+5952$
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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.