Elliptic curve isogeny class with LMFDB label 19536.bc (Cremona label 19536n)

• Label: 19536.bc
• Number of curves: $4$
• Conductor: $19536$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 19536.bc have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(11\)	\(1 - T\)
\(37\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 19536.bc do not have complex multiplication.

Modular form 19536.2.a.bc

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 19536.bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
19536.bc1	19536n3	\([0, 1, 0, -1152, 10692]\)	\(165256339972/43879077\)	\(44932174848\)	\([4]\)	\(14336\)	\(0.75252\)
19536.bc2	19536n2	\([0, 1, 0, -412, -3220]\)	\(30285104848/1490841\)	\(381655296\)	\([2, 2]\)	\(7168\)	\(0.40595\)
19536.bc3	19536n1	\([0, 1, 0, -407, -3300]\)	\(467147020288/1221\)	\(19536\)	\([2]\)	\(3584\)	\(0.059377\)	\(\Gamma_0(N)\)-optimal
19536.bc4	19536n4	\([0, 1, 0, 248, -11932]\)	\(1640689628/61847313\)	\(-63331648512\)	\([2]\)	\(14336\)	\(0.75252\)