Elliptic curve isogeny class with Cremona label 2304i (LMFDB label 2304.n)

• Label: 2304i
• Number of curves: $2$
• Conductor: $2304$
• CM: $\Q(\sqrt{-1})$
• Rank: $0$

Elliptic curves in class 2304i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
2304.n2	2304i1	$[0, 0, 0, 6, 0]$	$1728$	$-13824$	$[2]$	$128$	$-0.51602$	$\Gamma_0(N)$-optimal	$-4$
2304.n1	2304i2	$[0, 0, 0, -24, 0]$	$1728$	$884736$	$[2]$	$256$	$-0.16945$		$-4$

Rank

The elliptic curves in class 2304i have rank $0$.

Complex multiplication

Each elliptic curve in class 2304i has complex multiplication by an order in the imaginary quadratic field $\Q(\sqrt{-1})$.

Modular form 2304.2.a.i

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.

$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.