Elliptic curve isogeny class with Cremona label 48400dd (LMFDB label 48400.cv)

• Label: 48400dd
• Number of curves: $2$
• Conductor: $48400$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 48400dd have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 48400dd do not have complex multiplication.

Modular form 48400.2.a.dd

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 48400dd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
48400.cv2	48400dd1	\([0, -1, 0, 95792, 3726912]\)	\(34295/22\)	\(-62358947200000000\)	\([]\)	\(518400\)	\(1.9116\)	\(\Gamma_0(N)\)-optimal
48400.cv1	48400dd2	\([0, -1, 0, -1114208, -523833088]\)	\(-53969305/10648\)	\(-30181730444800000000\)	\([]\)	\(1555200\)	\(2.4609\)