# Properties

 Label 115920.ed Number of curves $4$ Conductor $115920$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("ed1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.ed

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.ed1 115920bs4 $$[0, 0, 0, -596307, 177236386]$$ $$31412749404762436/7455105$$ $$5565206062080$$ $$$$ $$688128$$ $$1.8243$$
115920.ed2 115920bs2 $$[0, 0, 0, -37407, 2747806]$$ $$31018076123344/472410225$$ $$88163085830400$$ $$[2, 2]$$ $$344064$$ $$1.4777$$
115920.ed3 115920bs1 $$[0, 0, 0, -4602, -53741]$$ $$924093773824/427810005$$ $$4989975898320$$ $$$$ $$172032$$ $$1.1312$$ $$\Gamma_0(N)$$-optimal
115920.ed4 115920bs3 $$[0, 0, 0, -3387, 7558234]$$ $$-5756278756/33056218125$$ $$-24676334605440000$$ $$$$ $$688128$$ $$1.8243$$

## Rank

sage: E.rank()

The elliptic curves in class 115920.ed have rank $$0$$.

## Complex multiplication

The elliptic curves in class 115920.ed do not have complex multiplication.

## Modular form 115920.2.a.ed

sage: E.q_eigenform(10)

$$q + q^{5} + q^{7} - 4 q^{11} + 2 q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})$$ ## 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. 