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 $1$
$1$
3.3.985.1 $3$
$[3, 0]$
49.2
\( 7^{2} \)
\( - 7^{10} \)
$5.36483$
$(-a+2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$4$
\( 1 \)
$1$
$18.96052639$
2.41653042
\( 12124909 a^{2} + 23419146 a - 4119521 \)
\( \bigl[a + 1\) , \( -a^{2} + 4\) , \( 0\) , \( -6 a^{2} - 11 a + 7\) , \( -19 a^{2} - 29 a + 7\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-6a^{2}-11a+7\right){x}-19a^{2}-29a+7$
49.2-b1 49.2-b $1$
$1$
3.3.985.1 $3$
$[3, 0]$
49.2
\( 7^{2} \)
\( - 7^{4} \)
$5.36483$
$(-a+2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$1$
\( 1 \)
$0.885035674$
$32.14211800$
2.71918282
\( 12124909 a^{2} + 23419146 a - 4119521 \)
\( \bigl[a^{2} - a - 3\) , \( a^{2} - 2 a - 4\) , \( a^{2} - 4\) , \( 4 a^{2} - 14 a - 3\) , \( -17 a^{2} + 51 a - 12\bigr] \) ${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(4a^{2}-14a-3\right){x}-17a^{2}+51a-12$
49.2-c1 49.2-c $1$
$1$
3.3.985.1 $3$
$[3, 0]$
49.2
\( 7^{2} \)
\( - 7^{10} \)
$5.36483$
$(-a+2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$1$
\( 1 \)
$1$
$36.62722921$
1.16704056
\( 12124909 a^{2} + 23419146 a - 4119521 \)
\( \bigl[a\) , \( 1\) , \( a\) , \( 37 a^{2} - 116 a + 18\) , \( -1629 a^{2} + 5039 a - 778\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(37a^{2}-116a+18\right){x}-1629a^{2}+5039a-778$
49.2-d1 49.2-d $1$
$1$
3.3.985.1 $3$
$[3, 0]$
49.2
\( 7^{2} \)
\( - 7^{4} \)
$5.36483$
$(-a+2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$1$
\( 3 \)
$0.058315779$
$151.2439479$
2.52923094
\( 12124909 a^{2} + 23419146 a - 4119521 \)
\( \bigl[a\) , \( -a^{2} + 4\) , \( 1\) , \( -7 a^{2} - 12 a + 7\) , \( 28 a^{2} + 55 a - 8\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-7a^{2}-12a+7\right){x}+28a^{2}+55a-8$
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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.
