Elliptic curve isogeny class with Cremona label 18720l (LMFDB label 18720.b)

• Label: 18720l
• Number of curves: $4$
• Conductor: $18720$
• CM: no
• Rank: $1$

Elliptic curves in class 18720l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
18720.b3	18720l1	\([0, 0, 0, -146433, -12204632]\)	\(7442744143086784/2927948765625\)	\(136606377609000000\)	\([2, 2]\)	\(196608\)	\(1.9865\)	\(\Gamma_0(N)\)-optimal
18720.b1	18720l2	\([0, 0, 0, -2047683, -1127477882]\)	\(2543984126301795848/909361981125\)	\(339417540730944000\)	\([2]\)	\(393216\)	\(2.3331\)
18720.b2	18720l3	\([0, 0, 0, -1057683, 410068618]\)	\(350584567631475848/8259273550125\)	\(3082757334037056000\)	\([2]\)	\(393216\)	\(2.3331\)
18720.b4	18720l4	\([0, 0, 0, 469572, -88096448]\)	\(3834800837445824/3342041015625\)	\(-9979281000000000000\)	\([2]\)	\(393216\)	\(2.3331\)

Rank

The elliptic curves in class 18720l have rank \(1\).

Complex multiplication

The elliptic curves in class 18720l do not have complex multiplication.

Modular form 18720.2.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.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.