Elliptic curve isogeny class with Cremona label 35280be (LMFDB label 35280.bi)

• Label: 35280be
• Number of curves: $4$
• Conductor: $35280$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 35280be have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 3 T + 19 T^{2}\)	1.19.d
\(23\)	\( 1 - 7 T + 23 T^{2}\)	1.23.ah
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 35280be do not have complex multiplication.

Modular form 35280.2.a.be

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 35280be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
35280.bi3	35280be1	\([0, 0, 0, -12344178, 16690170427]\)	\(151591373397612544/32558203125\)	\(44678252620181250000\)	\([2]\)	\(1474560\)	\(2.7654\)	\(\Gamma_0(N)\)-optimal
35280.bi2	35280be2	\([0, 0, 0, -13722303, 12733022302]\)	\(13015144447800784/4341909875625\)	\(95331524547570867360000\)	\([2, 2]\)	\(2949120\)	\(3.1119\)
35280.bi4	35280be3	\([0, 0, 0, 39859197, 87822136402]\)	\(79743193254623804/84085819746075\)	\(-7384795740903483110476800\)	\([2]\)	\(5898240\)	\(3.4585\)
35280.bi1	35280be4	\([0, 0, 0, -89353803, -315613571798]\)	\(898353183174324196/29899176238575\)	\(2625880439887819077196800\)	\([2]\)	\(5898240\)	\(3.4585\)