Elliptic curve isogeny class with Cremona label 15600q (LMFDB label 15600.bp)

• Label: 15600q
• Number of curves: $4$
• Conductor: $15600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 15600q have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 15600q do not have complex multiplication.

Modular form 15600.2.a.q

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 15600q

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
15600.bp3	15600q1	\([0, 1, 0, -2783, -57312]\)	\(9538484224/26325\)	\(6581250000\)	\([2]\)	\(18432\)	\(0.75689\)	\(\Gamma_0(N)\)-optimal
15600.bp2	15600q2	\([0, 1, 0, -3908, -7812]\)	\(1650587344/950625\)	\(3802500000000\)	\([2, 2]\)	\(36864\)	\(1.1035\)
15600.bp1	15600q3	\([0, 1, 0, -41408, 3217188]\)	\(490757540836/2142075\)	\(34273200000000\)	\([2]\)	\(73728\)	\(1.4500\)
15600.bp4	15600q4	\([0, 1, 0, 15592, -46812]\)	\(26198797244/15234375\)	\(-243750000000000\)	\([2]\)	\(73728\)	\(1.4500\)