# Properties

 Label 87120.dt Number of curves $2$ Conductor $87120$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("dt1")

sage: E.isogeny_class()

## Elliptic curves in class 87120.dt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.dt1 87120gc1 $$[0, 0, 0, -115797, 15797639]$$ $$-68679424/3375$$ $$-8438451709446000$$ $$[]$$ $$456192$$ $$1.8175$$ $$\Gamma_0(N)$$-optimal
87120.dt2 87120gc2 $$[0, 0, 0, 602943, 37934831]$$ $$9695350016/5859375$$ $$-14650089773343750000$$ $$[]$$ $$1368576$$ $$2.3668$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 87120.2.a.dt

sage: E.q_eigenform(10)

$$q + q^{5} - 2q^{7} - 4q^{13} + 3q^{17} + 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 