Elliptic curve isogeny class with LMFDB label 1872.p (Cremona label 1872j)

• Label: 1872.p
• Number of curves: $2$
• Conductor: $1872$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 1872.p have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1872.p do not have complex multiplication.

Modular form 1872.2.a.p

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 1872.p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1872.p1	1872j2	\([0, 0, 0, -9099, 333882]\)	\(1033364331/676\)	\(54500179968\)	\([2]\)	\(2304\)	\(0.99980\)
1872.p2	1872j1	\([0, 0, 0, -459, 7290]\)	\(-132651/208\)	\(-16769286144\)	\([2]\)	\(1152\)	\(0.65322\)	\(\Gamma_0(N)\)-optimal