Elliptic curve isogeny class with Cremona label 18496l (LMFDB label 18496.h)

• Label: 18496l
• Number of curves: $2$
• Conductor: $18496$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $0$

Elliptic curves in class 18496l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
18496.h2	18496l1	\([0, 0, 0, 4913, 0]\)	\(1728\)	\(-7589624095808\)	\([2]\)	\(34816\)	\(1.1610\)	\(\Gamma_0(N)\)-optimal	\(-4\)
18496.h1	18496l2	\([0, 0, 0, -19652, 0]\)	\(1728\)	\(485735942131712\)	\([2]\)	\(69632\)	\(1.5075\)		\(-4\)

Rank

The elliptic curves in class 18496l have rank \(0\).

Complex multiplication

Each elliptic curve in class 18496l has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 18496.2.a.l

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.