Elliptic curve isogeny class with Cremona label 174240cr (LMFDB label 174240.dk)

• Label: 174240cr
• Number of curves: $4$
• Conductor: $174240$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 174240cr have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 - 3 T + 19 T^{2}\)	1.19.ad
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 174240cr do not have complex multiplication.

Modular form 174240.2.a.cr

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 174240cr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
174240.dk3	174240cr1	\([0, 0, 0, -6897, -74536]\)	\(438976/225\)	\(18597138753600\)	\([2, 2]\)	\(327680\)	\(1.2384\)	\(\Gamma_0(N)\)-optimal
174240.dk2	174240cr2	\([0, 0, 0, -61347, 5795174]\)	\(38614472/405\)	\(267798798051840\)	\([2]\)	\(655360\)	\(1.5850\)
174240.dk4	174240cr3	\([0, 0, 0, 25773, -577654]\)	\(2863288/1875\)	\(-1239809250240000\)	\([2]\)	\(655360\)	\(1.5850\)
174240.dk1	174240cr4	\([0, 0, 0, -88572, -10136896]\)	\(14526784/15\)	\(79347792015360\)	\([2]\)	\(655360\)	\(1.5850\)