# Properties

 Label 87120.dd Number of curves $2$ Conductor $87120$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("dd1")

sage: E.isogeny_class()

## Elliptic curves in class 87120.dd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.dd1 87120fi2 $$[0, 0, 0, -475167, -100817926]$$ $$26962544/5625$$ $$2475279168104160000$$ $$$$ $$1622016$$ $$2.2444$$
87120.dd2 87120fi1 $$[0, 0, 0, 63888, -9502009]$$ $$1048576/2025$$ $$-55693781282343600$$ $$$$ $$811008$$ $$1.8978$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 87120.2.a.dd

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 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. 