Elliptic curve isogeny class with Cremona label 285090ce (LMFDB label 285090.ce)

• Label: 285090ce
• Number of curves: $2$
• Conductor: $285090$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 285090ce have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(13\)	\(1 + T\)
\(17\)	\(1 - T\)
\(43\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 285090ce do not have complex multiplication.

Modular form 285090.2.a.ce

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 285090ce

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
285090.ce1	285090ce1	\([1, 0, 0, -186364200, 979307640000]\)	\(-715832117907767882405148124801/65214833959432170000000\)	\(-65214833959432170000000\)	\([7]\)	\(78675968\)	\(3.4168\)	\(\Gamma_0(N)\)-optimal
285090.ce2	285090ce2	\([1, 0, 0, 1244830950, -31268332431570]\)	\(213331430131166950008878809576799/545828612088802939198075490730\)	\(-545828612088802939198075490730\)	\([]\)	\(550731776\)	\(4.3898\)