Elliptic curve isogeny class with LMFDB label 352872.z (Cremona label 352872z)

• Label: 352872.z
• Number of curves: $2$
• Conductor: $352872$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 352872.z have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(13\)	\(1\)
\(29\)	\(1 - T\)

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
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 352872.z do not have complex multiplication.

Modular form 352872.2.a.z

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 LMFDB numbering.

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

Isogeny graph

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

Elliptic curves in class 352872.z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
352872.z1	352872z2	\([0, 0, 0, -16731, 417430]\)	\(1940598/841\)	\(224465616820224\)	\([2]\)	\(1032192\)	\(1.4499\)
352872.z2	352872z1	\([0, 0, 0, 3549, 48334]\)	\(37044/29\)	\(-3870096841728\)	\([2]\)	\(516096\)	\(1.1033\)	\(\Gamma_0(N)\)-optimal