Elliptic curve isogeny class with Cremona label 365904hm (LMFDB label 365904.hm)

• Label: 365904hm
• Number of curves: $2$
• Conductor: $365904$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 365904hm have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1 - T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 365904hm do not have complex multiplication.

Modular form 365904.2.a.hm

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 365904hm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
365904.hm2	365904hm1	\([0, 0, 0, 1089, -2662]\)	\(11664/7\)	\(-85715207424\)	\([]\)	\(388800\)	\(0.78714\)	\(\Gamma_0(N)\)-optimal
365904.hm1	365904hm2	\([0, 0, 0, -13431, 668162]\)	\(-2431344/343\)	\(-37800406473984\)	\([]\)	\(1166400\)	\(1.3364\)