Elliptic curve isogeny class with Cremona label 47424by (LMFDB label 47424.cv)

• Label: 47424by
• Number of curves: $2$
• Conductor: $47424$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 47424by have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(13\)	\(1 + T\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(23\)	\( 1 - 7 T + 23 T^{2}\)	1.23.ah
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 47424by do not have complex multiplication.

Modular form 47424.2.a.by

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 47424by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
47424.cv1	47424by1	\([0, 1, 0, -5933, -176013]\)	\(22559008000000/277116957\)	\(283767763968\)	\([2]\)	\(71680\)	\(1.0079\)	\(\Gamma_0(N)\)-optimal
47424.cv2	47424by2	\([0, 1, 0, -1073, -451089]\)	\(-8346562000/5351892507\)	\(-87685406834688\)	\([2]\)	\(143360\)	\(1.3545\)