Elliptic curve isogeny class with LMFDB label 155526.dd (Cremona label 155526v)

• Label: 155526.dd
• Number of curves: $4$
• Conductor: $155526$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 155526.dd have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(7\)	\(1\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 155526.dd do not have complex multiplication.

Modular form 155526.2.a.dd

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 155526.dd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
155526.dd1	155526v3	\([1, 0, 0, -6403027, 6234778115]\)	\(1666957239793/301806\)	\(5256336082883059566\)	\([2]\)	\(6488064\)	\(2.5957\)
155526.dd2	155526v4	\([1, 0, 0, -2774087, -1720584153]\)	\(135559106353/5037138\)	\(87728177119942641618\)	\([2]\)	\(6488064\)	\(2.5957\)
155526.dd3	155526v2	\([1, 0, 0, -441197, 76207725]\)	\(545338513/171396\)	\(2985079750773095556\)	\([2, 2]\)	\(3244032\)	\(2.2491\)
155526.dd4	155526v1	\([1, 0, 0, 77223, 8087337]\)	\(2924207/3312\)	\(-57682700498030832\)	\([2]\)	\(1622016\)	\(1.9026\)	\(\Gamma_0(N)\)-optimal