Elliptic curve isogeny class with Cremona label 216384in (LMFDB label 216384.dk)

• Label: 216384in
• Number of curves: $4$
• Conductor: $216384$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 216384in have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(7\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 216384in do not have complex multiplication.

Modular form 216384.2.a.in

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 216384in

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
216384.dk4	216384in1	\([0, -1, 0, 9343, -343167]\)	\(2924207/3312\)	\(-102145323958272\)	\([2]\)	\(589824\)	\(1.3745\)	\(\Gamma_0(N)\)-optimal
216384.dk3	216384in2	\([0, -1, 0, -53377, -3190655]\)	\(545338513/171396\)	\(5286020514840576\)	\([2, 2]\)	\(1179648\)	\(1.7211\)
216384.dk2	216384in3	\([0, -1, 0, -335617, 72506113]\)	\(135559106353/5037138\)	\(155350269575036928\)	\([2]\)	\(2359296\)	\(2.0677\)
216384.dk1	216384in4	\([0, -1, 0, -774657, -262130175]\)	\(1666957239793/301806\)	\(9307992645697536\)	\([2]\)	\(2359296\)	\(2.0677\)