Elliptic curve isogeny class with Cremona label 72897a (LMFDB label 72897.a)

• Label: 72897a
• Number of curves: $4$
• Conductor: $72897$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 72897a have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 + T\)
\(11\)	\(1 + T\)
\(47\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 72897a do not have complex multiplication.

Modular form 72897.2.a.a

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 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 72897a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
72897.a3	72897a1	\([1, 1, 0, -14404, 653827]\)	\(30664297/297\)	\(3201426952713\)	\([2]\)	\(154560\)	\(1.2193\)	\(\Gamma_0(N)\)-optimal
72897.a2	72897a2	\([1, 1, 0, -25449, -501480]\)	\(169112377/88209\)	\(950823804955761\)	\([2, 2]\)	\(309120\)	\(1.5659\)
72897.a4	72897a3	\([1, 1, 0, 96046, -3781845]\)	\(9090072503/5845851\)	\(-63013686710249979\)	\([2]\)	\(618240\)	\(1.9124\)
72897.a1	72897a4	\([1, 1, 0, -323664, -70939863]\)	\(347873904937/395307\)	\(4261099274061003\)	\([2]\)	\(618240\)	\(1.9124\)