Elliptic curve isogeny class with Cremona label 1920b (LMFDB label 1920.c)

• Label: 1920b
• Number of curves: $2$
• Conductor: $1920$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 1920b have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 1920b do not have complex multiplication.

Modular form 1920.2.a.b

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 1920b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1920.c1	1920b1	\([0, -1, 0, -306, 2106]\)	\(24836849888/820125\)	\(104976000\)	\([2]\)	\(768\)	\(0.31226\)	\(\Gamma_0(N)\)-optimal
1920.c2	1920b2	\([0, -1, 0, 99, 6885]\)	\(6483584/1265625\)	\(-20736000000\)	\([2]\)	\(1536\)	\(0.65883\)