Elliptic curve isogeny class with Cremona label 278080cm (LMFDB label 278080.cm)

• Label: 278080cm
• Number of curves: $2$
• Conductor: $278080$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 278080cm have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(11\)	\(1 + T\)
\(79\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 278080cm do not have complex multiplication.

Modular form 278080.2.a.cm

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 278080cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
278080.cm2	278080cm1	\([0, -1, 0, -481, 7425]\)	\(-188183524/238975\)	\(-15661465600\)	\([2]\)	\(225280\)	\(0.64944\)	\(\Gamma_0(N)\)-optimal
278080.cm1	278080cm2	\([0, -1, 0, -9281, 347105]\)	\(674597763362/343255\)	\(44991119360\)	\([2]\)	\(450560\)	\(0.99602\)