Elliptic curve isogeny class with LMFDB label 91728.dj (Cremona label 91728ct)

• Label: 91728.dj
• Number of curves: $2$
• Conductor: $91728$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 91728.dj have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 91728.dj do not have complex multiplication.

Modular form 91728.2.a.dj

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 91728.dj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
91728.dj1	91728ct1	\([0, 0, 0, -3675, 67914]\)	\(421875/91\)	\(1184004476928\)	\([2]\)	\(98304\)	\(1.0307\)	\(\Gamma_0(N)\)-optimal
91728.dj2	91728ct2	\([0, 0, 0, 8085, 413658]\)	\(4492125/8281\)	\(-107744407400448\)	\([2]\)	\(196608\)	\(1.3773\)