Elliptic curve isogeny class with Cremona label 43120bi (LMFDB label 43120.cm)

• Label: 43120bi
• Number of curves: $2$
• Conductor: $43120$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 43120bi have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 43120bi do not have complex multiplication.

Modular form 43120.2.a.bi

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 43120bi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
43120.cm2	43120bi1	\([0, -1, 0, -261, 176]\)	\(1048576/605\)	\(1138842320\)	\([2]\)	\(18432\)	\(0.42731\)	\(\Gamma_0(N)\)-optimal
43120.cm1	43120bi2	\([0, -1, 0, -2956, 62700]\)	\(94875856/275\)	\(8282489600\)	\([2]\)	\(36864\)	\(0.77388\)