Elliptic curve isogeny class with LMFDB label 15840.d (Cremona label 15840o)

• Label: 15840.d
• Number of curves: $2$
• Conductor: $15840$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 15840.d have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 15840.d do not have complex multiplication.

Modular form 15840.2.a.d

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 15840.d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
15840.d1	15840o2	\([0, 0, 0, -588, -4192]\)	\(7529536/1815\)	\(5419560960\)	\([2]\)	\(8192\)	\(0.57882\)
15840.d2	15840o1	\([0, 0, 0, 87, -412]\)	\(1560896/2475\)	\(-115473600\)	\([2]\)	\(4096\)	\(0.23225\)	\(\Gamma_0(N)\)-optimal