Elliptic curve isogeny class with Cremona label 174240df (LMFDB label 174240.e)

• Label: 174240df
• Number of curves: $4$
• Conductor: $174240$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 174240df have rank \(1\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 174240.2.a.df

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 174240df

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
174240.e3	174240df1	\([0, 0, 0, -33033, -362032]\)	\(48228544/27225\)	\(2250253789185600\)	\([2, 2]\)	\(737280\)	\(1.6358\)	\(\Gamma_0(N)\)-optimal
174240.e2	174240df2	\([0, 0, 0, -332508, 73428608]\)	\(768575296/4455\)	\(23566294228561920\)	\([2]\)	\(1474560\)	\(1.9824\)
174240.e4	174240df3	\([0, 0, 0, 130317, -2877622]\)	\(370146232/219615\)	\(-145216377862110720\)	\([2]\)	\(1474560\)	\(1.9824\)
174240.e1	174240df4	\([0, 0, 0, -392403, -94445098]\)	\(10105715528/20625\)	\(13637901752640000\)	\([2]\)	\(1474560\)	\(1.9824\)