# Properties

 Label 87120ew Number of curves 4 Conductor 87120 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("87120.f1")

sage: E.isogeny_class()

## Elliptic curves in class 87120ew

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
87120.f4 87120ew1 [0, 0, 0, -49368, -4135417]  414720 $$\Gamma_0(N)$$-optimal
87120.f3 87120ew2 [0, 0, 0, -109263, 7855562]  829440
87120.f2 87120ew3 [0, 0, 0, -484968, 128352323]  1244160
87120.f1 87120ew4 [0, 0, 0, -7732263, 8275761362]  2488320

## Rank

sage: E.rank()

The elliptic curves in class 87120ew have rank $$0$$.

## Modular form 87120.2.a.f

sage: E.q_eigenform(10)

$$q - q^{5} - 4q^{7} + 4q^{13} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 