Elliptic curves over \(\Q(\sqrt{-67}) \) of conductor 196.1

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 10000 over imaginary quadratic fields with absolute discriminant 67

Note: The completeness Only modular elliptic curves are included

Results (6 matches)

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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
196.1-a1	196.1-a	$6$	$18$	\(\Q(\sqrt{-67}) \)	$2$	$[0, 1]$	196.1	\( 2^{2} \cdot 7^{2} \)	\( 2^{36} \cdot 7^{2} \)	$2.73678$	$(2), (7)$	$0 \le r \le 1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.2		\( 2 \cdot 3^{2} \)	$1$	$0.875417135$	4.861651226	\( -\frac{548347731625}{1835008} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-171{x}-874$
196.1-a2	196.1-a	$6$	$18$	\(\Q(\sqrt{-67}) \)	$2$	$[0, 1]$	196.1	\( 2^{2} \cdot 7^{2} \)	\( 2^{4} \cdot 7^{2} \)	$2.73678$	$(2), (7)$	$0 \le r \le 1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.1		\( 2 \)	$1$	$7.878754216$	4.861651226	\( -\frac{15625}{28} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-{x}$
196.1-a3	196.1-a	$6$	$18$	\(\Q(\sqrt{-67}) \)	$2$	$[0, 1]$	196.1	\( 2^{2} \cdot 7^{2} \)	\( 2^{12} \cdot 7^{6} \)	$2.73678$	$(2), (7)$	$0 \le r \le 1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs.1.1		\( 2 \cdot 3^{2} \)	$1$	$2.626251405$	4.861651226	\( \frac{9938375}{21952} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \)	${y}^2+{x}{y}+{y}={x}^3+4{x}-6$
196.1-a4	196.1-a	$6$	$18$	\(\Q(\sqrt{-67}) \)	$2$	$[0, 1]$	196.1	\( 2^{2} \cdot 7^{2} \)	\( 2^{6} \cdot 7^{12} \)	$2.73678$	$(2), (7)$	$0 \le r \le 1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs.1.1		\( 2 \cdot 3^{2} \)	$1$	$1.313125702$	4.861651226	\( \frac{4956477625}{941192} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-36{x}-70$
196.1-a5	196.1-a	$6$	$18$	\(\Q(\sqrt{-67}) \)	$2$	$[0, 1]$	196.1	\( 2^{2} \cdot 7^{2} \)	\( 2^{2} \cdot 7^{4} \)	$2.73678$	$(2), (7)$	$0 \le r \le 1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.1		\( 2 \)	$1$	$3.939377108$	4.861651226	\( \frac{128787625}{98} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-11{x}+12$
196.1-a6	196.1-a	$6$	$18$	\(\Q(\sqrt{-67}) \)	$2$	$[0, 1]$	196.1	\( 2^{2} \cdot 7^{2} \)	\( 2^{18} \cdot 7^{4} \)	$2.73678$	$(2), (7)$	$0 \le r \le 1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.2		\( 2 \cdot 3^{2} \)	$1$	$0.437708567$	4.861651226	\( \frac{2251439055699625}{25088} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-2731{x}-55146$

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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.