Elliptic curve isogeny class with Cremona label 54150ca (LMFDB label 54150.bm)

• Label: 54150ca
• Number of curves: $4$
• Conductor: $54150$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 54150ca have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 54150ca do not have complex multiplication.

Modular form 54150.2.a.ca

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 54150ca

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
54150.bm4	54150ca1	\([1, 1, 1, -17147688, -28572181719]\)	\(-758575480593601/40535043840\)	\(-29796982012912860000000\)	\([2]\)	\(8294400\)	\(3.0713\)	\(\Gamma_0(N)\)-optimal
54150.bm3	54150ca2	\([1, 1, 1, -277789688, -1782171557719]\)	\(3225005357698077121/8526675600\)	\(6267890087550056250000\)	\([2, 2]\)	\(16588800\)	\(3.4179\)
54150.bm2	54150ca3	\([1, 1, 1, -281219188, -1735914461719]\)	\(3345930611358906241/165622259047500\)	\(121747579532810286679687500\)	\([2]\)	\(33177600\)	\(3.7644\)
54150.bm1	54150ca4	\([1, 1, 1, -4444632188, -114053575877719]\)	\(13209596798923694545921/92340\)	\(67878385180312500\)	\([2]\)	\(33177600\)	\(3.7644\)