Elliptic curve isogeny class with Cremona label 284400ff (LMFDB label 284400.ff)

• Label: 284400ff
• Number of curves: $2$
• Conductor: $284400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 284400ff have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(79\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 284400ff do not have complex multiplication.

Modular form 284400.2.a.ff

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 284400ff

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
284400.ff2	284400ff1	\([0, 0, 0, 4425, -22250]\)	\(3286064/1975\)	\(-5759100000000\)	\([2]\)	\(368640\)	\(1.1378\)	\(\Gamma_0(N)\)-optimal
284400.ff1	284400ff2	\([0, 0, 0, -18075, -179750]\)	\(55990084/31205\)	\(363975120000000\)	\([2]\)	\(737280\)	\(1.4843\)