Elliptic curve isogeny class with LMFDB label 77616.dw (Cremona label 77616bk)

• Label: 77616.dw
• Number of curves: $2$
• Conductor: $77616$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 77616.dw have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 4 T + 23 T^{2}\)	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 77616.dw do not have complex multiplication.

Modular form 77616.2.a.dw

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 77616.dw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
77616.dw1	77616bk2	\([0, 0, 0, -156555, -6501222]\)	\(2415899250/1294139\)	\(227314241668749312\)	\([2]\)	\(589824\)	\(2.0217\)
77616.dw2	77616bk1	\([0, 0, 0, 37485, -796446]\)	\(66325500/41503\)	\(-3644980551539712\)	\([2]\)	\(294912\)	\(1.6751\)	\(\Gamma_0(N)\)-optimal