Elliptic curve isogeny class with Cremona label 397488hp (LMFDB label 397488.hp)

• Label: 397488hp
• Number of curves: $2$
• Conductor: $397488$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 397488hp have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(7\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 397488hp do not have complex multiplication.

Modular form 397488.2.a.hp

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 397488hp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
397488.hp2	397488hp1	\([0, 1, 0, -69008, -740076]\)	\(2640625/1512\)	\(20810062686486528\)	\([]\)	\(2322432\)	\(1.8209\)	\(\Gamma_0(N)\)-optimal
397488.hp1	397488hp2	\([0, 1, 0, -4043888, -3131355564]\)	\(531373116625/2058\)	\(28324807545495552\)	\([]\)	\(6967296\)	\(2.3702\)