Elliptic curve isogeny class with LMFDB label 251712.eu (Cremona label 251712eu)

• Label: 251712.eu
• Number of curves: $2$
• Conductor: $251712$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 251712.eu have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(19\)	\(1 + T\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 251712.eu do not have complex multiplication.

Modular form 251712.2.a.eu

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 251712.eu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
251712.eu1	251712eu2	\([0, 0, 0, -369152076, 2729958758768]\)	\(29112011033527546515217/20192896\)	\(3858922519658496\)	\([]\)	\(23224320\)	\(3.2042\)
251712.eu2	251712eu1	\([0, 0, 0, -4567116, 3728087408]\)	\(55129288688387857/484804919296\)	\(92647662856905424896\)	\([]\)	\(7741440\)	\(2.6549\)	\(\Gamma_0(N)\)-optimal