Elliptic curve isogeny class with Cremona label 322752ec (LMFDB label 322752.ec)

• Label: 322752ec
• Number of curves: $2$
• Conductor: $322752$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 322752ec have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(41\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 322752ec do not have complex multiplication.

Modular form 322752.2.a.ec

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 322752ec

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
322752.ec1	322752ec1	\([0, 1, 0, -7156577, -7329657825]\)	\(32553430057/212544\)	\(264662196105800318976\)	\([2]\)	\(15482880\)	\(2.7546\)	\(\Gamma_0(N)\)-optimal
322752.ec2	322752ec2	\([0, 1, 0, -2853217, -16056011233]\)	\(-2062933417/88232328\)	\(-109867894158420357414912\)	\([2]\)	\(30965760\)	\(3.1012\)