Elliptic curve isogeny class with Cremona label 286650ph (LMFDB label 286650.ph)

• Label: 286650ph
• Number of curves: $2$
• Conductor: $286650$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 286650ph have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 286650ph do not have complex multiplication.

Modular form 286650.2.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 286650ph

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
286650.ph1	286650ph1	\([1, -1, 1, -11995430, -16114177803]\)	\(-11167382937025/102503232\)	\(-1752093550423125000000\)	\([]\)	\(21150720\)	\(2.8987\)	\(\Gamma_0(N)\)-optimal
286650.ph2	286650ph2	\([1, -1, 1, 37617070, -84976327803]\)	\(344396625134975/381761977428\)	\(-6525479103413806757812500\)	\([]\)	\(63452160\)	\(3.4480\)