Elliptic curve isogeny class with Cremona label 282240hm (LMFDB label 282240.hm)

• Label: 282240hm
• Number of curves: $2$
• Conductor: $282240$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 282240hm have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 282240hm do not have complex multiplication.

Modular form 282240.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 282240hm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
282240.hm2	282240hm1	\([0, 0, 0, -1617, -6174]\)	\(1149984/625\)	\(254121840000\)	\([2]\)	\(184320\)	\(0.87932\)	\(\Gamma_0(N)\)-optimal
282240.hm1	282240hm2	\([0, 0, 0, -19992, -1086624]\)	\(16979328/25\)	\(1301103820800\)	\([2]\)	\(368640\)	\(1.2259\)