Elliptic curve isogeny class with Cremona label 4900m (LMFDB label 4900.f)

• Label: 4900m
• Number of curves: $2$
• Conductor: $4900$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 4900m have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 4900m do not have complex multiplication.

Modular form 4900.2.a.m

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 4900m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4900.f2	4900m1	\([0, 1, 0, 82, 853]\)	\(1280/7\)	\(-329417200\)	\([]\)	\(1728\)	\(0.31647\)	\(\Gamma_0(N)\)-optimal
4900.f1	4900m2	\([0, 1, 0, -4818, 127273]\)	\(-262885120/343\)	\(-16141442800\)	\([]\)	\(5184\)	\(0.86578\)