Elliptic curve isogeny class with Cremona label 38514l (LMFDB label 38514.l)

• Label: 38514l
• Number of curves: $4$
• Conductor: $38514$
• CM: no
• Rank: $1$

Elliptic curves in class 38514l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
38514.l4	38514l1	\([1, 0, 1, -1447, -3286]\)	\(2845178713/1609728\)	\(189382889472\)	\([2]\)	\(55296\)	\(0.85390\)	\(\Gamma_0(N)\)-optimal
38514.l2	38514l2	\([1, 0, 1, -17127, -862550]\)	\(4722184089433/9884736\)	\(1162929305664\)	\([2, 2]\)	\(110592\)	\(1.2005\)
38514.l3	38514l3	\([1, 0, 1, -11247, -1462310]\)	\(-1337180541913/7067998104\)	\(-831542908937496\)	\([2]\)	\(221184\)	\(1.5470\)
38514.l1	38514l4	\([1, 0, 1, -273887, -55192966]\)	\(19312898130234073/84888\)	\(9986988312\)	\([2]\)	\(221184\)	\(1.5470\)

Rank

The elliptic curves in class 38514l have rank \(1\).

Complex multiplication

The elliptic curves in class 38514l do not have complex multiplication.

Modular form 38514.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.