Elliptic curve isogeny class with Cremona label 47040hi (LMFDB label 47040.ft)

• Label: 47040hi
• Number of curves: $4$
• Conductor: $47040$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 47040hi have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 + 3 T + 13 T^{2}\)	1.13.d
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 47040hi do not have complex multiplication.

Modular form 47040.2.a.hi

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 47040hi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
47040.ft4	47040hi1	\([0, 1, 0, -78407660, 263920143150]\)	\(7079962908642659949376/100085966990454375\)	\(753600891549437872920000\)	\([2]\)	\(10321920\)	\(3.3864\)	\(\Gamma_0(N)\)-optimal
47040.ft2	47040hi2	\([0, 1, 0, -1250235065, 17014724166663]\)	\(448487713888272974160064/91549016015625\)	\(44116583158670400000000\)	\([2, 2]\)	\(20643840\)	\(3.7329\)
47040.ft3	47040hi3	\([0, 1, 0, -1245948545, 17137192614975]\)	\(-55486311952875723077768/801237030029296875\)	\(-3088866847815000000000000000\)	\([2]\)	\(41287680\)	\(4.0795\)
47040.ft1	47040hi4	\([0, 1, 0, -20003760065, 1088962462461663]\)	\(229625675762164624948320008/9568125\)	\(36886293319680000\)	\([2]\)	\(41287680\)	\(4.0795\)