# Properties

 Label 101640.l Number of curves $4$ Conductor $101640$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 101640.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101640.l1 101640f4 $$[0, -1, 0, -3602936, -2630652660]$$ $$1425631925916578/270703125$$ $$982153418400000000$$ $$[2]$$ $$1966080$$ $$2.4535$$
101640.l2 101640f3 $$[0, -1, 0, -1579816, 740631916]$$ $$120186986927618/4332064275$$ $$15717409011882547200$$ $$[2]$$ $$1966080$$ $$2.4535$$
101640.l3 101640f2 $$[0, -1, 0, -248816, -31880484]$$ $$939083699236/300155625$$ $$544505855160960000$$ $$[2, 2]$$ $$983040$$ $$2.1069$$
101640.l4 101640f1 $$[0, -1, 0, 44004, -3418380]$$ $$20777545136/23059575$$ $$-10457969599123200$$ $$[2]$$ $$491520$$ $$1.7603$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 101640.l have rank $$1$$.

## Complex multiplication

The elliptic curves in class 101640.l do not have complex multiplication.

## Modular form 101640.2.a.l

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{7} + q^{9} + 2 q^{13} + q^{15} + 2 q^{17} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().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.

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

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.