Elliptic curve isogeny class with LMFDB label 9025.f (Cremona label 9025a)

• Label: 9025.f
• Number of curves: $2$
• Conductor: $9025$
• CM: $\Q(\sqrt{-19})$
• Rank: $1$

Elliptic curves in class 9025.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
9025.f1	9025a2	$[0, 0, 1, -342950, -77378094]$	$-884736$	$-5041995277796875$	$[]$	$53200$	$1.9268$		$-19$
9025.f2	9025a1	$[0, 0, 1, -950, 11281]$	$-884736$	$-107171875$	$[]$	$2800$	$0.45457$	$\Gamma_0(N)$-optimal	$-19$

Rank

The elliptic curves in class 9025.f have rank $1$.

Complex multiplication

Each elliptic curve in class 9025.f has complex multiplication by an order in the imaginary quadratic field $\Q(\sqrt{-19})$.

Modular form 9025.2.a.f

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.

$\left(\begin{array}{rr} 1 & 19 \\ 19 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.