Elliptic curve isogeny class with Cremona label 266175bb (LMFDB label 266175.bb)

• Label: 266175bb
• Number of curves: $4$
• Conductor: $266175$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 266175bb have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 266175bb do not have complex multiplication.

Modular form 266175.2.a.bb

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 266175bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
266175.bb3	266175bb1	\([1, -1, 1, -1908380, -729656378]\)	\(13980103929/3901625\)	\(214512791039244140625\)	\([2]\)	\(6193152\)	\(2.6084\)	\(\Gamma_0(N)\)-optimal
266175.bb2	266175bb2	\([1, -1, 1, -11224505, 13896659872]\)	\(2844576388809/129390625\)	\(7113944600791259765625\)	\([2, 2]\)	\(12386304\)	\(2.9550\)
266175.bb1	266175bb3	\([1, -1, 1, -177583880, 910906409872]\)	\(11264882429818809/24990875\)	\(1374007585752826171875\)	\([2]\)	\(24772608\)	\(3.3016\)
266175.bb4	266175bb4	\([1, -1, 1, 6076870, 52859356372]\)	\(451394172711/22216796875\)	\(-1221487740520477294921875\)	\([2]\)	\(24772608\)	\(3.3016\)