Elliptic curve isogeny class with LMFDB label 4416.f (Cremona label 4416c)

• Label: 4416.f
• Number of curves: $2$
• Conductor: $4416$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 4416.f have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 4416.f do not have complex multiplication.

Modular form 4416.2.a.f

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 4416.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4416.f1	4416c2	\([0, -1, 0, -993, -11679]\)	\(413493625/1587\)	\(416022528\)	\([2]\)	\(2048\)	\(0.51233\)
4416.f2	4416c1	\([0, -1, 0, -33, -351]\)	\(-15625/207\)	\(-54263808\)	\([2]\)	\(1024\)	\(0.16575\)	\(\Gamma_0(N)\)-optimal