Elliptic curve isogeny class with Cremona label 331200ph (LMFDB label 331200.ph)

• Label: 331200ph
• Number of curves: $2$
• Conductor: $331200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 331200ph have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 331200ph do not have complex multiplication.

Modular form 331200.2.a.ph

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 331200ph

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
331200.ph1	331200ph1	\([0, 0, 0, -41700, -14699000]\)	\(-687518464/7604375\)	\(-88697430000000000\)	\([]\)	\(3317760\)	\(1.9340\)	\(\Gamma_0(N)\)-optimal
331200.ph2	331200ph2	\([0, 0, 0, 372300, 379429000]\)	\(489277573376/5615234375\)	\(-65496093750000000000\)	\([]\)	\(9953280\)	\(2.4833\)