Elliptic curve isogeny class with Cremona label 94080cy (LMFDB label 94080.g)

• Label: 94080cy
• Number of curves: $2$
• Conductor: $94080$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 94080cy have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 94080cy do not have complex multiplication.

Modular form 94080.2.a.cy

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 94080cy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
94080.g1	94080cy1	\([0, -1, 0, -214391, 1071855]\)	\(36184050630016/20925489375\)	\(630236902266720000\)	\([2]\)	\(1032192\)	\(2.1049\)	\(\Gamma_0(N)\)-optimal
94080.g2	94080cy2	\([0, -1, 0, 857239, 7715961]\)	\(72285432657952/41860546875\)	\(-40344383318400000000\)	\([2]\)	\(2064384\)	\(2.4515\)