Elliptic curve isogeny class with Cremona label 1925a (LMFDB label 1925.f)

• Label: 1925a
• Number of curves: $3$
• Conductor: $1925$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 1925a have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1925a do not have complex multiplication.

Modular form 1925.2.a.a

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 1925a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1925.f1	1925a1	\([0, -1, 1, -2233, 41368]\)	\(-78843215872/539\)	\(-8421875\)	\([]\)	\(720\)	\(0.50972\)	\(\Gamma_0(N)\)-optimal
1925.f2	1925a2	\([0, -1, 1, -1233, 77493]\)	\(-13278380032/156590819\)	\(-2446731546875\)	\([]\)	\(2160\)	\(1.0590\)
1925.f3	1925a3	\([0, -1, 1, 11017, -1998882]\)	\(9463555063808/115539436859\)	\(-1805303700921875\)	\([]\)	\(6480\)	\(1.6083\)