# Properties

 Label 87120.cv Number of curves $4$ Conductor $87120$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("cv1")

sage: E.isogeny_class()

## Elliptic curves in class 87120.cv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.cv1 87120bj4 $$[0, 0, 0, -8218683, 466677882]$$ $$46424454082884/26794860125$$ $$35435216471319384192000$$ $$[2]$$ $$8847360$$ $$3.0164$$
87120.cv2 87120bj2 $$[0, 0, 0, -5496183, -4941840618]$$ $$55537159171536/228765625$$ $$75633530136516000000$$ $$[2, 2]$$ $$4423680$$ $$2.6698$$
87120.cv3 87120bj1 $$[0, 0, 0, -5490738, -4952154537]$$ $$885956203616256/15125$$ $$312535248498000$$ $$[2]$$ $$2211840$$ $$2.3232$$ $$\Gamma_0(N)$$-optimal
87120.cv4 87120bj3 $$[0, 0, 0, -2860803, -9690268302]$$ $$-1957960715364/29541015625$$ $$-39066906062250000000000$$ $$[2]$$ $$8847360$$ $$3.0164$$

## Rank

sage: E.rank()

The elliptic curves in class 87120.cv have rank $$1$$.

## Complex multiplication

The elliptic curves in class 87120.cv do not have complex multiplication.

## Modular form 87120.2.a.cv

sage: E.q_eigenform(10)

$$q - q^{5} + 4q^{7} - 6q^{13} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 LMFDB 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

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

The vertices are labelled with LMFDB labels.