Elliptic curve isogeny class with Cremona label 54978br (LMFDB label 54978.bo)

• Label: 54978br
• Number of curves: $4$
• Conductor: $54978$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 54978br have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(7\)	\(1\)
\(11\)	\(1 + T\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 54978br do not have complex multiplication.

Modular form 54978.2.a.br

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 54978br

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
54978.bo3	54978br1	\([1, 1, 1, -10066953, 12165719607]\)	\(959024269496848362625/11151660319506432\)	\(1311981684929612218368\)	\([2]\)	\(4147200\)	\(2.8646\)	\(\Gamma_0(N)\)-optimal
54978.bo4	54978br2	\([1, 1, 1, -2038793, 31044740663]\)	\(-7966267523043306625/3534510366354604032\)	\(-415831610091252809760768\)	\([2]\)	\(8294400\)	\(3.2112\)
54978.bo1	54978br3	\([1, 1, 1, -813133833, 8924310531639]\)	\(505384091400037554067434625/815656731648\)	\(95961198821655552\)	\([2]\)	\(12441600\)	\(3.4139\)
54978.bo2	54978br4	\([1, 1, 1, -813125993, 8924491237367]\)	\(-505369473241574671219626625/20303219722982711328\)	\(-2388653497189193005027872\)	\([2]\)	\(24883200\)	\(3.7605\)