# Properties

 Label 259920.ep Number of curves $2$ Conductor $259920$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("ep1")

sage: E.isogeny_class()

## Elliptic curves in class 259920.ep

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259920.ep1 259920ep2 $$[0, 0, 0, -525027, -146426654]$$ $$781484460931/900$$ $$18432777830400$$ $$[2]$$ $$1474560$$ $$1.8295$$
259920.ep2 259920ep1 $$[0, 0, 0, -32547, -2327006]$$ $$-186169411/6480$$ $$-132716000378880$$ $$[2]$$ $$737280$$ $$1.4829$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 259920.ep have rank $$0$$.

## Complex multiplication

The elliptic curves in class 259920.ep do not have complex multiplication.

## Modular form 259920.2.a.ep

sage: E.q_eigenform(10)

$$q + q^{5} - 2 q^{7} - 2 q^{13} + 6 q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.