Elliptic curve isogeny class with Cremona label 110400hm (LMFDB label 110400.hd)

• Label: 110400hm
• Number of curves: $4$
• Conductor: $110400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 110400hm have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 110400hm do not have complex multiplication.

Modular form 110400.2.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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 110400hm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
110400.hd4	110400hm1	\([0, 1, 0, 4767, -122337]\)	\(2924207/3312\)	\(-13565952000000\)	\([2]\)	\(196608\)	\(1.2063\)	\(\Gamma_0(N)\)-optimal
110400.hd3	110400hm2	\([0, 1, 0, -27233, -1178337]\)	\(545338513/171396\)	\(702038016000000\)	\([2, 2]\)	\(393216\)	\(1.5529\)
110400.hd2	110400hm3	\([0, 1, 0, -171233, 26325663]\)	\(135559106353/5037138\)	\(20632117248000000\)	\([2]\)	\(786432\)	\(1.8995\)
110400.hd1	110400hm4	\([0, 1, 0, -395233, -95754337]\)	\(1666957239793/301806\)	\(1236197376000000\)	\([2]\)	\(786432\)	\(1.8995\)