Elliptic curves over \(\Q(\sqrt{-30}) \) of conductor 300.1

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 1000 over imaginary quadratic fields with absolute discriminant 120

Note: The completeness Only modular elliptic curves are included

Results (16 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
300.1-a1	300.1-a	$2$	$3$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	300.1	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( 2^{4} \cdot 3^{2} \cdot 5^{16} \)	$4.07389$	$(2,a), (3,a), (5,a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3$	3B	$1$	\( 2 \cdot 3 \)	$0.342467425$	$1.200470374$	0.900723170	\( -\frac{30866268160}{3} \)	\( \bigl[0\) , \( -1\) , \( a\) , \( -7583\) , \( -251643\bigr] \)	${y}^2+a{y}={x}^3-{x}^2-7583{x}-251643$
300.1-a2	300.1-a	$2$	$3$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	300.1	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( 2^{4} \cdot 3^{6} \cdot 5^{16} \)	$4.07389$	$(2,a), (3,a), (5,a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3$	3B	$1$	\( 2 \cdot 3 \)	$0.114155808$	$3.601411123$	0.900723170	\( -\frac{40960}{27} \)	\( \bigl[0\) , \( -1\) , \( a\) , \( -83\) , \( -393\bigr] \)	${y}^2+a{y}={x}^3-{x}^2-83{x}-393$
300.1-b1	300.1-b	$2$	$2$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	300.1	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( 2^{16} \cdot 3^{8} \cdot 5^{6} \)	$4.07389$	$(2,a), (3,a), (5,a)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{3} \cdot 3 \)	$0.689619051$	$2.388115705$	7.216310809	\( \frac{5488}{81} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( 12\) , \( 72\bigr] \)	${y}^2={x}^3-{x}^2+12{x}+72$
300.1-b2	300.1-b	$2$	$2$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	300.1	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( 2^{8} \cdot 3^{4} \cdot 5^{6} \)	$4.07389$	$(2,a), (3,a), (5,a)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{3} \cdot 3 \)	$0.689619051$	$2.388115705$	7.216310809	\( \frac{131072}{9} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -13\) , \( 22\bigr] \)	${y}^2={x}^3-{x}^2-13{x}+22$
300.1-c1	300.1-c	$2$	$2$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	300.1	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( 2^{4} \cdot 3^{8} \cdot 5^{18} \)	$4.07389$	$(2,a), (3,a), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$4$	\( 2^{3} \)	$1$	$2.388115705$	3.488066244	\( \frac{5488}{81} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( 97\) , \( 957\bigr] \)	${y}^2+a{x}{y}={x}^3-{x}^2+97{x}+957$
300.1-c2	300.1-c	$2$	$2$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	300.1	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( 2^{8} \cdot 3^{16} \cdot 5^{6} \)	$4.07389$	$(2,a), (3,a), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$4$	\( 2^{3} \)	$1$	$2.388115705$	3.488066244	\( \frac{131072}{9} \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -120\) , \( -475\bigr] \)	${y}^2={x}^3-120{x}-475$
300.1-d1	300.1-d	$2$	$3$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	300.1	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( 2^{16} \cdot 3^{2} \cdot 5^{4} \)	$4.07389$	$(2,a), (3,a), (5,a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3$	3B	$1$	\( 2 \cdot 3 \)	$2.276601350$	$1.200470374$	5.987686514	\( -\frac{30866268160}{3} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -1213\) , \( -15863\bigr] \)	${y}^2={x}^3-{x}^2-1213{x}-15863$
300.1-d2	300.1-d	$2$	$3$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	300.1	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( 2^{16} \cdot 3^{6} \cdot 5^{4} \)	$4.07389$	$(2,a), (3,a), (5,a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3$	3B	$1$	\( 2 \cdot 3 \)	$0.758867116$	$3.601411123$	5.987686514	\( -\frac{40960}{27} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -13\) , \( -23\bigr] \)	${y}^2={x}^3-{x}^2-13{x}-23$
300.1-e1	300.1-e	$2$	$3$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	300.1	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( 2^{4} \cdot 3^{2} \cdot 5^{4} \)	$4.07389$	$(2,a), (3,a), (5,a)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3$	3B.1.2	$9$	\( 2 \cdot 3^{2} \)	$1$	$1.200470374$	3.945148222	\( -\frac{30866268160}{3} \)	\( \bigl[0\) , \( 1\) , \( a\) , \( -303\) , \( -2127\bigr] \)	${y}^2+a{y}={x}^3+{x}^2-303{x}-2127$
300.1-e2	300.1-e	$2$	$3$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	300.1	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( 2^{4} \cdot 3^{6} \cdot 5^{4} \)	$4.07389$	$(2,a), (3,a), (5,a)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3$	3B.1.2	$1$	\( 2 \cdot 3 \)	$1$	$3.601411123$	3.945148222	\( -\frac{40960}{27} \)	\( \bigl[0\) , \( 1\) , \( a\) , \( -3\) , \( 3\bigr] \)	${y}^2+a{y}={x}^3+{x}^2-3{x}+3$
300.1-f1	300.1-f	$2$	$2$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	300.1	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( 2^{4} \cdot 3^{20} \cdot 5^{6} \)	$4.07389$	$(2,a), (3,a), (5,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{5} \)	$0.929138799$	$2.388115705$	6.481795364	\( \frac{5488}{81} \)	\( \bigl[a\) , \( 0\) , \( a\) , \( 60\) , \( -330\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3+60{x}-330$
300.1-f2	300.1-f	$2$	$2$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	300.1	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( 2^{8} \cdot 3^{4} \cdot 5^{18} \)	$4.07389$	$(2,a), (3,a), (5,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{4} \)	$1.858277598$	$2.388115705$	6.481795364	\( \frac{131072}{9} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -333\) , \( 2088\bigr] \)	${y}^2={x}^3+{x}^2-333{x}+2088$
300.1-g1	300.1-g	$2$	$2$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	300.1	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( 2^{4} \cdot 3^{8} \cdot 5^{6} \)	$4.07389$	$(2,a), (3,a), (5,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{5} \cdot 3 \)	$0.385518528$	$2.388115705$	8.068284988	\( \frac{5488}{81} \)	\( \bigl[a\) , \( 1\) , \( 0\) , \( 17\) , \( -7\bigr] \)	${y}^2+a{x}{y}={x}^3+{x}^2+17{x}-7$
300.1-g2	300.1-g	$2$	$2$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	300.1	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( 2^{20} \cdot 3^{4} \cdot 5^{6} \)	$4.07389$	$(2,a), (3,a), (5,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{4} \cdot 3 \)	$0.771037056$	$2.388115705$	8.068284988	\( \frac{131072}{9} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -53\) , \( 123\bigr] \)	${y}^2={x}^3+{x}^2-53{x}+123$
300.1-h1	300.1-h	$2$	$3$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	300.1	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( 2^{4} \cdot 3^{14} \cdot 5^{4} \)	$4.07389$	$(2,a), (3,a), (5,a)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3$	3B.1.1	$9$	\( 2 \)	$1$	$1.200470374$	3.945148222	\( -\frac{30866268160}{3} \)	\( \bigl[0\) , \( 0\) , \( a\) , \( -2730\) , \( 54910\bigr] \)	${y}^2+a{y}={x}^3-2730{x}+54910$
300.1-h2	300.1-h	$2$	$3$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	300.1	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( 2^{4} \cdot 3^{18} \cdot 5^{4} \)	$4.07389$	$(2,a), (3,a), (5,a)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3$	3B.1.1	$1$	\( 2 \cdot 3^{3} \)	$1$	$3.601411123$	3.945148222	\( -\frac{40960}{27} \)	\( \bigl[0\) , \( 0\) , \( a\) , \( -30\) , \( 100\bigr] \)	${y}^2+a{y}={x}^3-30{x}+100$

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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.