Elliptic curve isogeny class with LMFDB label 49725.k (Cremona label 49725f)

• Label: 49725.k
• Number of curves: $4$
• Conductor: $49725$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 49725.k have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(13\)	\(1 + T\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 49725.k do not have complex multiplication.

Modular form 49725.2.a.k

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 49725.k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
49725.k1	49725f4	\([1, -1, 1, -235355, 44001272]\)	\(126574061279329/16286595\)	\(185514496171875\)	\([2]\)	\(344064\)	\(1.7590\)
49725.k2	49725f2	\([1, -1, 1, -15980, 565022]\)	\(39616946929/10989225\)	\(125174141015625\)	\([2, 2]\)	\(172032\)	\(1.4124\)
49725.k3	49725f1	\([1, -1, 1, -5855, -163978]\)	\(1948441249/89505\)	\(1019517890625\)	\([2]\)	\(86016\)	\(1.0658\)	\(\Gamma_0(N)\)-optimal
49725.k4	49725f3	\([1, -1, 1, 41395, 3663272]\)	\(688699320191/910381875\)	\(-10369818544921875\)	\([2]\)	\(344064\)	\(1.7590\)