Elliptic curve isogeny class with Cremona label 12054ba (LMFDB label 12054.bd)

• Label: 12054ba
• Number of curves: $4$
• Conductor: $12054$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 12054ba have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(7\)	\(1\)
\(41\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 - 5 T + 23 T^{2}\)	1.23.af
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 12054ba do not have complex multiplication.

Modular form 12054.2.a.ba

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 12054ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12054.bd3	12054ba1	\([1, 1, 1, -442, -3529]\)	\(81182737/5904\)	\(694599696\)	\([2]\)	\(6912\)	\(0.44295\)	\(\Gamma_0(N)\)-optimal
12054.bd2	12054ba2	\([1, 1, 1, -1422, 16071]\)	\(2703045457/544644\)	\(64076821956\)	\([2, 2]\)	\(13824\)	\(0.78952\)
12054.bd1	12054ba3	\([1, 1, 1, -21512, 1205399]\)	\(9357915116017/538002\)	\(63295397298\)	\([2]\)	\(27648\)	\(1.1361\)
12054.bd4	12054ba4	\([1, 1, 1, 2988, 100743]\)	\(25076571983/50863698\)	\(-5984063206002\)	\([2]\)	\(27648\)	\(1.1361\)