Elliptic curve isogeny class with Cremona label 252648k (LMFDB label 252648.k)

• Label: 252648k
• Number of curves: $2$
• Conductor: $252648$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 252648k have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1\)
\(29\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 252648k do not have complex multiplication.

Modular form 252648.2.a.k

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.

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

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 252648k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
252648.k2	252648k1	\([0, 0, 0, 22869, 790614]\)	\(37044/29\)	\(-1035488685800448\)	\([2]\)	\(967680\)	\(1.5691\)	\(\Gamma_0(N)\)-optimal
252648.k1	252648k2	\([0, 0, 0, -107811, 6828030]\)	\(1940598/841\)	\(60058343776425984\)	\([2]\)	\(1935360\)	\(1.9157\)