Elliptic curves over \(\Q(\sqrt{-1}) \) of conductor 10530.4

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 100000 over imaginary quadratic fields with absolute discriminant 4

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
10530.4-a1	10530.4-a	$6$	$18$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	10530.4	\( 2 \cdot 3^{4} \cdot 5 \cdot 13 \)	\( 2^{18} \cdot 3^{12} \cdot 5^{9} \cdot 13 \)	$1.81040$	$(a+1), (2a+1), (2a+3), (3)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.1	$1$	\( 2^{2} \cdot 3^{4} \)	$1$	$0.320242129$	2.882179168	\( -\frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \)	\( \bigl[i\) , \( 1\) , \( 1\) , \( -806 i - 453\) , \( -11194 i - 21\bigr] \)	${y}^2+i{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-806i-453\right){x}-11194i-21$
10530.4-a2	10530.4-a	$6$	$18$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	10530.4	\( 2 \cdot 3^{4} \cdot 5 \cdot 13 \)	\( 2^{6} \cdot 3^{12} \cdot 5^{3} \cdot 13^{3} \)	$1.81040$	$(a+1), (2a+1), (2a+3), (3)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3Cs.1.1	$1$	\( 2^{2} \cdot 3^{3} \)	$1$	$0.960726389$	2.882179168	\( \frac{37525044319}{2197000} a - \frac{7169596274}{274625} \)	\( \bigl[i\) , \( 1\) , \( 1\) , \( -86 i + 42\) , \( 11 i - 354\bigr] \)	${y}^2+i{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-86i+42\right){x}+11i-354$
10530.4-a3	10530.4-a	$6$	$18$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	10530.4	\( 2 \cdot 3^{4} \cdot 5 \cdot 13 \)	\( 2^{3} \cdot 3^{12} \cdot 5^{6} \cdot 13^{6} \)	$1.81040$	$(a+1), (2a+1), (2a+3), (3)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3Cs.1.1	$1$	\( 2^{3} \cdot 3^{3} \)	$1$	$0.480363194$	2.882179168	\( \frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \)	\( \bigl[1\) , \( -1\) , \( i\) , \( 4 i + 132\) , \( -947 i + 678\bigr] \)	${y}^2+{x}{y}+i{y}={x}^{3}-{x}^{2}+\left(4i+132\right){x}-947i+678$
10530.4-a4	10530.4-a	$6$	$18$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	10530.4	\( 2 \cdot 3^{4} \cdot 5 \cdot 13 \)	\( 2^{9} \cdot 3^{12} \cdot 5^{18} \cdot 13^{2} \)	$1.81040$	$(a+1), (2a+1), (2a+3), (3)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.1	$1$	\( 2^{3} \cdot 3^{4} \)	$1$	$0.160121064$	2.882179168	\( -\frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \)	\( \bigl[1\) , \( -1\) , \( i\) , \( -86 i - 1173\) , \( 19834 i - 22731\bigr] \)	${y}^2+{x}{y}+i{y}={x}^{3}-{x}^{2}+\left(-86i-1173\right){x}+19834i-22731$
10530.4-a5	10530.4-a	$6$	$18$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	10530.4	\( 2 \cdot 3^{4} \cdot 5 \cdot 13 \)	\( 2^{2} \cdot 3^{12} \cdot 5 \cdot 13 \)	$1.81040$	$(a+1), (2a+1), (2a+3), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.2	$1$	\( 2^{2} \)	$1$	$2.882179168$	2.882179168	\( \frac{31409}{130} a + \frac{101344}{65} \)	\( \bigl[i\) , \( 1\) , \( 1\) , \( 4 i - 3\) , \( 2 i - 3\bigr] \)	${y}^2+i{x}{y}+{y}={x}^{3}+{x}^{2}+\left(4i-3\right){x}+2i-3$
10530.4-a6	10530.4-a	$6$	$18$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	10530.4	\( 2 \cdot 3^{4} \cdot 5 \cdot 13 \)	\( 2 \cdot 3^{12} \cdot 5^{2} \cdot 13^{2} \)	$1.81040$	$(a+1), (2a+1), (2a+3), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.2	$1$	\( 2^{3} \)	$1$	$1.441089584$	2.882179168	\( \frac{4406742137}{8450} a + \frac{1310300809}{8450} \)	\( \bigl[1\) , \( -1\) , \( i\) , \( 49 i - 48\) , \( -218 i + 93\bigr] \)	${y}^2+{x}{y}+i{y}={x}^{3}-{x}^{2}+\left(49i-48\right){x}-218i+93$

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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.