Elliptic curve isogeny class with Cremona label 27456e (LMFDB label 27456.d)

• Label: 27456e
• Number of curves: $2$
• Conductor: $27456$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 27456e have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(11\)	\(1 + T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 27456e do not have complex multiplication.

Modular form 27456.2.a.e

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 27456e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
27456.d1	27456e1	\([0, -1, 0, -6655137, 6610430241]\)	\(-124352595912593543977/103332962304\)	\(-27088116070219776\)	\([]\)	\(599040\)	\(2.4565\)	\(\Gamma_0(N)\)-optimal
27456.d2	27456e2	\([0, -1, 0, -5166177, 9644645601]\)	\(-58169016237585194137/119573538788081664\)	\(-31345485752062879727616\)	\([]\)	\(1797120\)	\(3.0058\)