Elliptic curve isogeny class with Cremona label 158400dk (LMFDB label 158400.fs)

• Label: 158400dk
• Number of curves: $2$
• Conductor: $158400$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 158400dk have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 158400dk do not have complex multiplication.

Modular form 158400.2.a.dk

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 158400dk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
158400.fs1	158400dk1	\([0, 0, 0, -198300, 33988880]\)	\(-2888047810000/35937\)	\(-10730730700800\)	\([]\)	\(663552\)	\(1.6475\)	\(\Gamma_0(N)\)-optimal
158400.fs2	158400dk2	\([0, 0, 0, -90300, 70700240]\)	\(-272709010000/7073843073\)	\(-2112238223448883200\)	\([]\)	\(1990656\)	\(2.1968\)