Elliptic curve isogeny class with Cremona label 2880p (LMFDB label 2880.ba)

• Label: 2880p
• Number of curves: $4$
• Conductor: $2880$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 2880p have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2880p do not have complex multiplication.

Modular form 2880.2.a.p

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 2880p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2880.ba4	2880p1	\([0, 0, 0, 33, 196]\)	\(85184/405\)	\(-18895680\)	\([2]\)	\(512\)	\(0.078535\)	\(\Gamma_0(N)\)-optimal
2880.ba3	2880p2	\([0, 0, 0, -372, 2464]\)	\(1906624/225\)	\(671846400\)	\([2, 2]\)	\(1024\)	\(0.42511\)
2880.ba2	2880p3	\([0, 0, 0, -1452, -18704]\)	\(14172488/1875\)	\(44789760000\)	\([2]\)	\(2048\)	\(0.77168\)
2880.ba1	2880p4	\([0, 0, 0, -5772, 168784]\)	\(890277128/15\)	\(358318080\)	\([4]\)	\(2048\)	\(0.77168\)