Elliptic curves over \(\Q(\sqrt{-19}) \) of conductor 3025.9

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 15000 over imaginary quadratic fields with absolute discriminant 19

Note: The completeness Only modular elliptic curves are included

Results (3 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
3025.9-CMa1	3025.9-CMa	$1$	$1$	\(\Q(\sqrt{-19}) \)	$2$	$[0, 1]$	3025.9	\( 5^{2} \cdot 11^{2} \)	\( 5^{6} \cdot 11^{6} \)	$2.88866$	$(a-1), (a-3)$	0	$\mathsf{trivial}$	$\textsf{yes}$	$-19$	$\mathrm{U}(1)$	✓			✓			$1$	\( 1 \)	$1$	$1.183942790$	0.543230208	\( -884736 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( 42 a - 82\) , \( -203 a + 144\bigr] \)	${y}^2+{y}={x}^3+\left(42a-82\right){x}-203a+144$
3025.9-a1	3025.9-a	$2$	$11$	\(\Q(\sqrt{-19}) \)	$2$	$[0, 1]$	3025.9	\( 5^{2} \cdot 11^{2} \)	\( 5^{17} \cdot 11^{4} \)	$2.88866$	$(a-1), (a-3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$11$	11B	$1$	\( 2^{2} \cdot 3 \)	$1$	$0.603203564$	3.321225324	\( -\frac{31584309676}{48828125} a + \frac{44048857481}{9765625} \)	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -50 a - 94\) , \( 291 a + 257\bigr] \)	${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(-50a-94\right){x}+291a+257$
3025.9-a2	3025.9-a	$2$	$11$	\(\Q(\sqrt{-19}) \)	$2$	$[0, 1]$	3025.9	\( 5^{2} \cdot 11^{2} \)	\( 5^{7} \cdot 11^{8} \)	$2.88866$	$(a-1), (a-3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$11$	11B	$1$	\( 2^{2} \cdot 3 \)	$1$	$0.603203564$	3.321225324	\( -\frac{8119316}{5} a + 2077473 \)	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -229 a + 268\) , \( -501 a + 4904\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3+\left(a-1\right){x}^2+\left(-229a+268\right){x}-501a+4904$

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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.