Elliptic curve isogeny class with LMFDB label 284961.g (Cremona label 284961g)

• Label: 284961.g
• Number of curves: $4$
• Conductor: $284961$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 284961.g have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(43\)	\(1 - T\)
\(47\)	\(1\)

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.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 284961.g do not have complex multiplication.

Modular form 284961.2.a.g

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 284961.g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
284961.g1	284961g4	\([1, 0, 1, -540147, -150964841]\)	\(1616855892553/22851963\)	\(246326229867340827\)	\([2]\)	\(3157440\)	\(2.1419\)
284961.g2	284961g2	\([1, 0, 1, -65212, 2724125]\)	\(2845178713/1347921\)	\(14529530705481009\)	\([2, 2]\)	\(1578720\)	\(1.7953\)
284961.g3	284961g1	\([1, 0, 1, -54167, 4844765]\)	\(1630532233/1161\)	\(12514668996969\)	\([2]\)	\(789360\)	\(1.4488\)	\(\Gamma_0(N)\)-optimal
284961.g4	284961g3	\([1, 0, 1, 233003, 20736311]\)	\(129784785047/92307627\)	\(-995003787942014283\)	\([2]\)	\(3157440\)	\(2.1419\)