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
2401.3-CMd1
2401.3-CMd
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
2401.3
\( 7^{4} \)
\( 7^{14} \)
$1.08342$
$(-3a+1), (3a-2)$
0
$\mathsf{trivial}$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$7$
7Cs.1.2
$1$
\( 1 \)
$1$
$1.450642192$
1.675057320
\( 0 \)
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( a\) , \( -27 a + 50\bigr] \)
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}-27a+50$
2401.3-CMc1
2401.3-CMc
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
2401.3
\( 7^{4} \)
\( 7^{14} \)
$1.08342$
$(-3a+1), (3a-2)$
0
$\mathsf{trivial}$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$7$
7Cs.1.4
$1$
\( 1 \)
$1$
$1.450642192$
1.675057320
\( 0 \)
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( a\) , \( -10 a + 48\bigr] \)
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-10a+48$
2401.3-CMb1
2401.3-CMb
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
2401.3
\( 7^{4} \)
\( 7^{14} \)
$1.08342$
$(-3a+1), (3a-2)$
0
$\mathsf{trivial}$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$7$
7Cs.1.4
$1$
\( 1 \)
$1$
$1.450642192$
1.675057320
\( 0 \)
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( a\) , \( 9 a + 38\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}+9a+38$
2401.3-CMa1
2401.3-CMa
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
2401.3
\( 7^{4} \)
\( 7^{14} \)
$1.08342$
$(-3a+1), (3a-2)$
0
$\mathsf{trivial}$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$7$
7Cs.1.2
$1$
\( 1 \)
$1$
$1.450642192$
1.675057320
\( 0 \)
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( a\) , \( 27 a + 23\bigr] \)
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}+27a+23$
2401.3-a1
2401.3-a
$4$
$14$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
2401.3
\( 7^{4} \)
\( 7^{6} \)
$1.08342$
$(-3a+1), (3a-2)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
✓
$7$
7B.1.5
$1$
\( 2^{2} \)
$0.109590133$
$4.944504600$
1.251392664
\( -3375 \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -2\) , \( -1\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-2{x}-1$
2401.3-a2
2401.3-a
$4$
$14$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
2401.3
\( 7^{4} \)
\( 7^{18} \)
$1.08342$
$(-3a+1), (3a-2)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
✓
$7$
7B.1.2
$1$
\( 2^{2} \)
$0.767130934$
$0.706357800$
1.251392664
\( -3375 \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -107\) , \( 552\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-107{x}+552$
2401.3-a3
2401.3-a
$4$
$14$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
2401.3
\( 7^{4} \)
\( 7^{6} \)
$1.08342$
$(-3a+1), (3a-2)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-28$
$N(\mathrm{U}(1))$
✓
✓
✓
$7$
7B.1.5
$1$
\( 2^{2} \)
$0.219180266$
$2.472252300$
1.251392664
\( 16581375 \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -37\) , \( -78\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-37{x}-78$
2401.3-a4
2401.3-a
$4$
$14$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
2401.3
\( 7^{4} \)
\( 7^{18} \)
$1.08342$
$(-3a+1), (3a-2)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-28$
$N(\mathrm{U}(1))$
✓
✓
✓
$7$
7B.1.2
$1$
\( 2^{2} \)
$1.534261868$
$0.353178900$
1.251392664
\( 16581375 \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -1822\) , \( 30393\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-1822{x}+30393$
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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.